00:00 00:00 we ought to start with a little bit of your background so what did you start 我们应该从你的一些背景开始，那么你是从什么开始的 researching and then what are you researching now okay so I started out my 研究然后你现在在研究什么好吧所以我开始了我的 research in mathematics in Austria in Vienna where I actually didn't look at 奥地利维也纳的数学研究，我实际上没有看过 image processing or imaging at all I started out with so-called partial 图像处理或成像我从所谓的部分开始 differential equations which are equations of a function and its 微分方程是函数及其方程 derivatives so you like they can express change over time or space and they are 导数，所以你喜欢它们可以表达随时间或空间的变化，它们是 models for various natural phenomena and physics and biology lots of things are 各种自然现象以及物理学和生物学的模型很多东西都是 explained by these differential equations and my first paper again had 由这些微分方程解释，我的第一篇论文再次有 nothing to do with image processing it was actually on the con hillard equation 与图像处理无关，它实际上是在康希拉德方程上 which is an equation that describes phase separation and corseting and 这是一个描述相分离和紧身衣的方程 alloys in metallic alloys for instance so when you cool them down to a certain 例如金属合金中的合金，因此当你将它们冷却到一定温度时 temperature you have a you have a mixture of two and you if you cool them 你有一个你有两种的混合物，如果你冷却它们 00:01 00:01 down to a certain temperature they are starting to separate from each other and 降低到一定温度，它们开始相互分离 korsun out and build these larger areas and so there is an equation that models korsun 出来并建造这些更大的区域，因此有一个方程可以模拟 this kind of phenomenon which is to cannulate equation okay and my first 这种现象是可以插入方程的，好吧，我的第一个 paper was on the stability analysis of a certain type of solutions to disk and 论文是关于某种类型的磁盘解决方案的稳定性分析 hillard equation stability analysis meaning that if you perturb your initial 希拉德方程稳定性分析意味着如果你扰乱你的初始 condition a little bit how much is your stationary solution that is when you let 条件一点，当你让 time evolve infinitely okay how you know when a stationary state is a state of 时间无限演化好吧你怎么知道什么时候静止状态是一种状态 where the system is in no change okay how much do these stationary states 系统没有变化的情况下这些静止状态有多少 differ from each other when you just put up the initial condition a little bit 当你只设置初始条件一点点时，彼此会有所不同 and this is in the context of creating alloys or building structure alloys for 这是在制造合金或建筑结构合金的背景下 structures or what was there any particular purpose well the purpose is 结构或有什么特定目的以及目的是 allotted with these differential equations to simulate certain phenomena 分配这些微分方程来模拟某些现象 00:02 00:02 mm-hmm and so if you understand how stable these stationary states are so if 嗯嗯，如果你了解这些静止状态有多稳定，那么如果 you are at a stationary state and then you perturb the stationary state a 你处于静止状态，然后你扰乱静止状态 little bit is it going back to the same stationary state or is it going 它会回到相同的静止状态还是会继续前进 somewhere completely different so you kind of understand 完全不同的地方所以你有点理解 and how the system how these systems react to perturbations that are 以及系统如何对扰动做出反应 naturally occurring because we are in real life and things happen gosh okay 自然发生，因为我们在现实生活中，事情发生了天哪，好吧 yeah so it's more an understanding of the physical processes involved in you 是的，所以这更多的是对你所涉及的物理过程的理解 know mixture of alloys for instance or things like that and where you at a 知道例如合金的混合物或类似的东西以及你在哪里 Technical University where you would be likes focusing on alloys or this was a 您可能会喜欢专注于合金的技术大学，或者这是一所 personal interest actually you know a lot of Applied Mathematics on the 个人兴趣其实你了解很多应用数学 continent which is everything else okay basically here in Europe is applied 大陆，其他一切都很好，基本上在欧洲这里适用 mathematics very much means that you're what you're doing is inspired by 数学很大程度上意味着你正在做的事情受到了启发 applications but eventually you end up with a mathematical problem so it was 应用程序，但最终你会遇到一个数学问题，所以它是 00:03 00:03 really the driving factor was well we were interested in analyzing this 确实，驱动因素很好，我们有兴趣分析这个 equation and and there were techniques coming up that they're kind of cool yeah 方程式，而且出现了一些技术，它们有点酷，是的 so it was just a kind of intellectual interest in this equation okay it was 所以这只是对这个方程的一种智力兴趣好吧 the driving factor for this particular paper but then during writing this paper 这篇特定论文的驱动因素，但在撰写本文期间 [Music] research at UCLA researchers at UCLA in [音乐] 加州大学洛杉矶分校研究人员在加州大学洛杉矶分校的研究 particular the group of Andrea patate C used this same equation to do image 特别是 Andrea patate C 小组使用相同的方程来制作图像 restoration and image restoration meaning you have a digital image and 恢复和图像恢复意味着您拥有数字图像和 there is there are parts of this image which are damaged for some reason or 该图像的某些部分由于某种原因被损坏或 which way which which are where you have objects which are occluding some other 哪条路有物体遮挡其他物体 object of interest that you want to get rid of the occlusion or something like 您想要摆脱遮挡的感兴趣的对象或类似的东西 this so you have one part in the image that you somehow want to replace by 这样你就可以在图像中找到一个你想要替换的部分 00:04 00:04 something that is suggested by the surrounding okay area of this of this 这个的周围好的区域所建议的东西 region so is this similar to like content-aware fill in photoshop exactly 区域，这与 Photoshop 中的内容感知填充类似吗 okay but this predates the Photoshop development I assume it actually does 好吧，但这早于 Photoshop 的开发，我想它实际上是这样的 and I mean also to content-aware I feel is actually very much based on some of 我的意思是，我觉得内容意识实际上很大程度上基于一些内容 the things that have been initiated by people like Andrea bethought see so I 像安德里亚这样的人发起的事情我认为是这样的 mean the technique is different in what Photoshop is using 意味着 Photoshop 使用的技术不同 but it's still based on research in mathematics in fact yeah it's a 但它实际上仍然基于数学研究，是的，这是一个 differential equation maybe if you want if you wish that this more it's not a 微分方程也许如果你想要的话如果你希望这更多它不是一个 convenient equation of it is a different type of differential equation that is 它的方便方程是一种不同类型的微分方程，即 non-local is taking patches and images and kind of copy and pasting them into 非本地正在获取补丁和图像，并将它们复制并粘贴到 the region that you want to replace yep but anyway so she used the chameleon 你想要替换的区域是的，但无论如何，她使用了变色龙 equation to do that and that was a kind of eye-opening moment and then I moved 方程式来做到这一点，那是一种令人大开眼界的时刻，然后我移动了 00:05 00:05 into image processing still sticking to differential equations at the time and 当时仍坚持使用微分方程进行图像处理 actually looking at image restoration so 实际上是在研究图像恢复 it is Photoshop content-aware field type problem and yeah that and that was 这是 Photoshop 内容感知字段类型问题，是的，那是 basically my PhD my PhD was about image restoration okay and during my postdoc 基本上我的博士学位是关于图像恢复的，在我博士后期间 then I moved more and more into what is called inverse imaging problems where 然后我越来越多地转向所谓的逆成像问题，其中 what you are observing or what you're measuring in the first place is not an 你所观察到的或你首先测量的并不是一个 image like when you take a photo you know the digital image is an image 图像就像当你拍照时你知道数字图像是图像 so but there are certain applications like in biomedical imaging where what 所以，但是有一些应用，比如生物医学成像，其中什么 you're observing is not an image directly but is some transform of this 你观察到的不是直接的图像，而是它的某种变换 image like an image tomography for instance okay 例如，图像断层扫描等图像可以 think about CT for instance computer tomography what you are what the CT Tom 想想 CT，例如计算机断层扫描，您是什么 CT Tom 00:06 00:06 what the tomograph is measuring are projections of your 3-dimensional object 断层扫描仪测量的是 3 维物体的投影 which is whatever you have in your body and from that you want to reconstruct 这是你体内所拥有的以及你想要重建的东西 the objects all right projections meaning in the CT sends a particular CT 中的物体正确投影意味着发送特定的 sense which is that you send x-rays through the body and what you're 感觉就是你发送 X 射线穿过身体以及你是什么 measuring so you're sending them through what you're measuring at the other end 测量，以便您将它们发送到您在另一端测量的内容 is the attenuation that they feel when they travels through the body depending 是它们穿过身体时感受到的衰减，具体取决于 on which type of tissues they hit and so that's what you're measuring on the 它们击中的是哪种类型的组织，这就是您在 other and and you can model that by saying you 其他，并且你可以通过说“你”来建模 what you're measuring is a is a line in isn't it's an integral along the line 你测量的是 a 是一条线，它不是沿着这条线的积分 that the X ray takes through your body where you're integrating over the X 射线穿过您的身体，在那里您正在整合 attenuation that it feels yeah and so from that and that is a very old problem 衰减，感觉是的，所以这是一个非常老的问题 it goes back to rod on it's called the rod on transform what you're measuring 它回到了杆上它被称为杆上变换你正在测量的东西 is not an image but it's the ronald transform of your image which are line 不是图像，而是图像的罗纳德变换，它是线 00:07 00:07 integrals over the image density that you want to reconstruct right the gutter 您想要在装订线处重建的图像密度的积分 consists then where density is different 那么其中密度不同 in different parts of your body and then you can see organs in your body and 在你身体的不同部位然后你可以看到你身体的器官 stuff like that right and so they'll the 这样的事情是对的，所以他们会 likelihood of there to be some amount of it missing that you need to fill or 可能有一些缺失需要您补充或 recreate or denoise is much higher than an image yeah that's obvious that's 重建或降噪比图像高得多，是的，这是显而易见的 quite obvious because well first of all we are in a finite dimensional world so 非常明显，因为首先我们处于一个有限维度的世界中，所以 you know you don't have all possible infinitely many line integrals of your 你知道你没有所有可能的无限多个线积分 body measured yeah and then it's not even you know it's not even that would 身体测量是的，然后它甚至你都不知道它甚至不会 be still okay if you're measuring as many line integrals as your 如果您测量的线积分与您的一样多，那还是没问题的 corresponding to the resolution of the image that you then want to compute from 对应于您要计算的图像的分辨率 these line integrals but then very often it's not like that because you don't 这些线积分，但通常情况并非如此，因为你不 want to you want a very high resolution image because you want to look at all 想要你想要一个非常高分辨率的图像，因为你想看所有 00:08 00:08 the details in the body right but you don't want to measure so many line 身体的细节是对的，但你不想测量那么多线 integrals because you don't want to radiate the patient so much you don't 积分，因为您不想对患者进行过多的辐射 want to send some x-rays through through the patient so you have a lack of data 想要通过患者发送一些 X 射线，这样您就缺乏数据 you you don't have as much data as you want the you know for the high 你没有你想要的那么多数据 你知道高 resolution image to reconstruct and then there is noise because these are 要重建的分辨率图像，然后存在噪声，因为这些是 measurements right and there is always noise and measurements and so were you 测量正确，总是有噪音和测量，你也是如此 doing denoising work as well at the same time it's it's it's it's integrated in 同时进行去噪工作，它集成在 the reconstruction approach so in in in the mathematical algorithm that 重建方法在数学算法中是这样的 reconstructs an image or do you know the three-dimensional yeah inside of your 重建图像或者你知道你的三维空间中的三维空间吗？ body from these line measurements there's the denoising is integrated into 从这些线测量中的身体，去噪被集成到 into this reconstruction step coming you know from from these line integrals 进入这个重建步骤，您可以从这些线积分中了解到 reconstructing is for you gosh okay and so what I know about 重建是为了你，好吧，所以我所知道的 00:09 00:09 denoising mostly through audio like a Fourier transform and that kind of thing 主要通过音频去噪，比如傅立叶变换之类的 so how are you doing it with an image how are you denoising in the algorithm 那么你是如何处理图像的，你是如何在算法中进行去噪的 so so with images it depends of what you 所以对于图像来说，这取决于你的内容 think is important in an image that will 认为在图像中很重要 determine how you're going to dino is it okay a very successful assumption that 确定你要如何恐龙可以吗这是一个非常成功的假设 has been made for designing image denoising approaches isn't as has been 专为设计图像去噪方法而设计，但并不像以前那样 and still is that the most important information that visually guides you of 仍然是视觉上引导您的最重要的信息 what this image is showing you but also that helps you if you want later want to 这张图片向您展示了什么，而且如果您以后想要的话，它也会对您有所帮助 quantify something indium which are the edges and the image this is the most 量化某些铟，即边缘和图像，这是最 important thing where our boundaries between different objects okay yeah when 重要的是我们不同物体之间的界限好吧是的 you think about it what really what really makes an impression on you of 你想想到底是什么给你留下了深刻的印象 00:10 00:10 what this image shows are colors you know and to the end the boundary between 该图像显示的是您所知道的颜色以及最终之间的边界 these colors where are the colors changing and these are the edges in the 这些颜色在哪里变化，这些是边缘 image interesting and to preserve those and not make them blurry blur blur blur 图像有趣并保留它们而不使它们模糊模糊模糊 doubt is something that a lot of research in image denoising has gone 怀疑是图像去噪方面的大量研究已经消失 into so image denoising methods which can preserve edges in an image and so 可以保留图像边缘的图像去噪方法等等 the fourier you know fourier type techniques are good they can smooth out 你知道傅立叶类型技术很好，它们可以平滑 your noise by changing my two high frequencies yeah but they will take away 你的噪音通过改变我的两个高频是的，但它们会消失 two high frequencies everywhere right which means they will also take away two 两个高频无处不在，这意味着它们也会带走两个 high frequencies that correspond to edges where the image function is 对应于图像函数的边缘的高频 changing rapidly yeah so you're looking to the Delta 变化很快，是的，所以你正在寻找三角洲 is a very high frequency component of your image and but this is a component 是图像的高频成分，但这是一个成分 you would like to keep yeah okay so you want to differentiate between the high 你想保持“是的”，所以你想区分高 00:11 00:11 frequency components in the image which is which are just noise and two high 图像中的频率分量只是噪声和两个高频率分量 frequency components which correspond to these very characteristic features that 与这些非常典型的特征相对应的频率分量 you want to keep and so you know their various techniques but one very 你想保留，所以你知道他们的各种技术，但其中一项非常 successful one is total variation regularization for instance which is a 成功的一个是全变分正则化，例如 technique that has been used a lot by people in image denoising you know that 人们在图像去噪中广泛使用的技术你知道 models just this assumption that you have sharp discontinuities medium 模型只是假设你有尖锐的不连续性介质 filtering is a is a is a maybe simpler thing to understand or that people might 过滤可能是一个更容易理解的事情，或者人们可能会 have heard about which is not exactly total variation denoising but it's 听说过这并不完全是全变分去噪，但它是 related gotchu so median filtering instead of gaussian filtering right we 相关的问题所以中值滤波而不是高斯滤波对我们来说 work also filtering corresponds to your Fourier taking away to high frequency 工作还过滤对应于你的傅里叶带走高频 stuff okay sure you know it's so funny when I was doing Photoshop of the onion 好吧，你肯定知道，当我用 Photoshop 制作洋葱时，这很有趣 we were always actually interested in blurring edges because one of the most 我们实际上一直对模糊边缘感兴趣，因为最重要的之一 obvious things to spot a photoshop is a sharp edge and a soft edge in the same 在 Photoshop 中发现的明显的事情是同一处的锐边和软边 00:12 00:12 photo so for instance like if I were to cut you out and then put you in front of 照片，例如，如果我把你剪下来，然后把你放在前面 the white house if the photo has a slight blur so like the depth of field 白宫，如果照片有轻微模糊，就像景深一样 in the photos like say like a 1.4 aperture which creates a very very like 在照片中就像说1.4光圈创造了一个非常非常像 shallow depth of field so there's a lot of blur but if you're crispy someone can 景深较浅，所以有很多模糊，但如果你很脆，有人可以 immediately spot that you were dropped into the photo so it was all about 立即发现您被放入照片中，所以这一切都是关于 blurring the edges oh to trick someone into thinking that it was in the same 模糊边缘哦，欺骗某人认为它是在同一个地方 photo yeah so so in your context these these algorithms that will handle the 照片是的所以在你的上下文中这些算法将处理 edge sharpness are they hand coated or are using machine learning to create 边缘清晰度是手工涂层还是使用机器学习来创建 them how does that work so they are classically hand coded and this is maybe 他们是如何工作的，所以他们是经典的手工编码，这可能是 something that is now you know more and more being replaced by other things 现在你越来越了解的东西正在被其他东西取代 where image denoising nowadays I think the best image denoising approaches are 现在的图像去噪我认为最好的图像去噪方法是 actually coming from deep neural networks okay so you know these hand 实际上来自深度神经网络，所以你知道这些手 00:13 00:13 crafted methods get more and more beaten in terms of performance 精心设计的方法在性能方面越来越失败 by some of these neural network approaches they get beaten in certain 通过其中一些神经网络方法，他们在某些方面被打败了 scenarios though they get beaten on the on the type of examples they have seen 尽管他们在所见过的例子类型上被打败了 already or similar type of images that they have seen already right if you 已经或他们已经看过的类似类型的图像，如果您 present them with something completely different right if they if you only 向他们展示一些完全不同的东西，如果他们只 train them on photographs of animals or whatever right and then you present them 对他们进行动物照片或任何正确的照片训练，然后你向他们展示 with a CT image over the CT scanner will they will not be able to handle that so 如果通过 CT 扫描仪获取 CT 图像，他们将无法处理该问题，因此 that is one of the things I think we're still hand-crafted models have a certain 这是我认为我们手工制作的模型仍然具有一定的优势之一 justification of existence in a sense because there is not there still you 从某种意义上说，存在的合理性是因为你已经不存在了 know although we can do GPU programming and everything there is still not enough 知道虽然我们可以进行 GPU 编程，但现有的一切仍然不够 computational power to train a machine to know everything to learn everything 训练机器了解一切、学习一切的计算能力 00:14 00:14 about the world right and so I think a lot so while you know in certain 关于世界的正确性，所以我想了很多，而你在某些方面知道 scenarios if you know what you want to apply your image denoising approach well 如果您知道想要很好地应用图像去噪方法，请考虑以下场景 it's like the image net thing from like almost 10 years exactly yeah if you know 这就像近 10 年前的图像网络事物，是的，如果你知道的话 that then it's fine and that's good but if you if you want 那就好，那很好，但是如果你愿意的话 you know think about for instance one big thing in CT let's say or in 你知道，想想 CT 中的一件大事，或者说 different types of biomedical imaging let's say MRI the aromatic resins 不同类型的生物医学成像 比如说 MRI 芳香树脂 tomography the the type of image that you get the resolution the contrast and 断层扫描 您获得的图像类型 分辨率 对比度 everything very much depends on how you do the acquisition how many let's say in 一切很大程度上取决于你如何进行收购，比如说有多少 the CT case how many x-rays you have you could have been shooting through the CT 病例 您可以通过 CT 拍摄多少张 X 光片 patient but also also and that is actually connected to what I just said 耐心而且也，这实际上与我刚才所说的有关 00:15 00:15 also the type of scanner you're using are you using G or Siemens or Toshiba or 还有您使用的扫描仪类型是使用 G 还是西门子还是东芝还是 whatever they they have different settings and they have different ways of 无论他们有不同的设置，他们有不同的方式 going from the measurements to an image and so you know if you train an 从测量到图像，这样你就知道你是否训练了 algorithm for instance and your own network on one of these 例如算法和您自己的网络之一 scanners it doesn't mean that it works on the own images of another scanner 扫描仪，这并不意味着它可以处理另一台扫描仪自己的图像 really so they're producing entirely different data I thought they were just 真的所以他们产生了完全不同的数据我认为他们只是 like basically the same tools inside with a different logo well it's so so 就像基本上相同的工具，里面有不同的标志，嗯，一般般 this is the other interesting thing is not entirely different like you might 这是另一件有趣的事情，并不像你想象的那样完全不同 not spot also visually what the difference is but this is one of the 视觉上也看不出区别是什么，但这是其中之一 things that also people start you know more and more hopeful he started you 人们开始的事情你越来越了解他开始你 know do some research and understanding this that even small perturbance s that 知道做一些研究并理解这一点，即使是很小的扰动也是如此 are but that are consistent yeah in small differences that are consistent 但那是一致的 是的，小差异是一致的 between the different scanners might contribute to your algorithm than 不同扫描仪之间的差异可能会对您的算法有所贡献 00:16 00:16 failing you know I don't know if you have seen these adversarial errors where 如果你知道我不知道你是否在哪里见过这些对抗性错误 you do a little perturbation and then all of a sudden it classifies the image 你做了一点扰动，然后突然它对图像进行了分类 into something completely different right so yeah so I think the the the 进入完全不同的东西所以是的所以我认为 really very exciting and for mathematicians in particular the 真的非常令人兴奋，特别是对于数学家来说 exciting opportunity that neural networks are now offering in contrast to 与之前相比，神经网络现在提供的令人兴奋的机会 these handcrafted models yeah are that they can go beyond just saying here I 这些手工制作的模型是的，它们不仅仅是在这里说我 want an algorithm that look that preserves edges right which is a very 想要一个看起来可以保留边缘的算法，这是一个非常好的算法 simplistic view of the world yeah but on the other hand that there are lots of 简单化的世界观是的，但另一方面，有很多 unknowns in these algorithms on the one hand that mathematicians I think should 一方面，这些算法中存在未知数，我认为数学家应该 be exploring and try to bring some of the analysis and some of the 正在探索并尝试带来一些分析和一些 00:17 00:17 methodologies that help us to understand why these handcrafted models work 帮助我们理解这些手工模型为何有效的方法 because we can prove properties about the denoising abilities of these methods 因为我们可以证明这些方法的去噪能力的属性 of how stable they are for instance to perturbations in the images we know we 例如，我们知道它们对图像中的扰动有多稳定 know how that works so we can prove things about them we have Aero estimates 知道它是如何工作的，这样我们就可以证明它们的事情，我们有 Aero 估计 and things like this and to bring those over to neural networks I think would is 诸如此类的事情并将其带入神经网络我认为是 very exciting but for that bringing some structure into these 非常令人兴奋，但为此引入了一些结构 neural networks is also important and that might on the other hand when you 神经网络也很重要，另一方面，当你 think about these new networks having these 100 millions of parameters that 想想这些具有 1 亿个参数的新网络 that are adapting that are adapting themselves to the data maybe in some 正在适应 可能在某些方面正在适应数据 case it would be better to not have a million parameters but have a 在这种情况下，最好不要有一百万个参数，但有一个 intelligent structural way of reducing the search space right and as such bring 减少搜索空间权的智能结构方式因此带来 00:18 00:18 some structure into the problem which helps you make statements about 问题的一些结构可以帮助你做出有关的陈述 stability and things like that and also statements about what the algorithm is 稳定性之类的东西以及关于算法是什么的陈述 actually doing yeah because so that is another thing right 实际上是这样做的，因为这是另一件事 because since when you look at these handcrafted models you have started with 因为当你看到这些手工制作的模型时，你就开始 a hypothesis right you have started with our policies of edges are important and 您从我们的边缘政策开始的正确假设很重要并且 image right and then you've you come up with a mathematical algorithm that is 右图然后你就想出了一个数学算法 exactly doing what you wanted to do right you know then you have to make 准确地做你想做的事，然后你就必须做 sure that it is actually doing what you want 确保它确实在做你想做的事 it doesn't code is bad then it's not the coldest bed or your model is bad maybe 它没有编码是坏的那么它不是最冷的床或者你的模型可能是坏的 you have to change your model in a certain way okay but you understand why 你必须以某种方式改变你的模型，好吧，但你明白为什么 things are happening yeah if you have millions of parameters and then you know 事情正在发生，是的，如果你有数百万个参数，然后你就知道了 you train this algorithm to do something 你训练这个算法来做某事 and then you get a parameterization then 然后你得到一个参数化 00:19 00:19 there's a 1 million different parameters 有 100 万个不同的参数 how are you ever going to interpret that there are ways you know what machine 你如何解释你有办法知道什么机器 learning people are are trying to interpret classification results for 学习者正在尝试解释分类结果 instance yeah you have these salient features that you can detect and image 例如，是的，您有这些可以检测和成像的显着特征 what was important for the classification to do this or this yeah 对于分类来说什么是重要的 是的 but it's still limited and I think yeah there are lots of very very cool 但它仍然是有限的，我认为是的，有很多非常非常酷的 opportunities and so are you guys working on hand stitching the two 机会，你们正在手工缝合这两者吗 together at this point like what's the status with the current research yeah so 目前的研究进展如何 是的，所以 they're they're different people are trying to do different things so I can I 他们是不同的人正在尝试做不同的事情所以我可以 can first tell you what I've been doing over the last 我可以先告诉你我最近在做什么 couple of years so the last couple of years what I've been doing is I've been 几年来所以过去几年我一直在做的是 trying to starting with these more handcrafted models nothing to do yet 尝试从这些更手工制作的模型开始，目前无事可做 00:20 00:20 with neural networks I started with the handcrafted models and then for certain 对于神经网络，我从手工制作的模型开始，然后对于某些 parts and these models where I wasn't quite sure about our edges really the 零件和这些模型，我不太确定我们的边缘是否真的 only thing I'm looking for for instance I've tried to parameterize them in a 我唯一正在寻找的东西例如我试图在一个中参数化它们 certain way okay but not with with a million parameters but maybe with ten 某种方式可以，但不能用一百万个参数，但可能用十个 parameters or something like this and then learn these parameters from 参数或类似的东西，然后从中学习这些参数 actual examples that I would like my handcrafted model to spit out mmm and 我希望我的手工模型能吐出嗯和的实际例子 this is what we call PI level optimization or a parameter estimation I 这就是我们所说的 PI 级优化或参数估计 I mean people have been doing this for a long time but now I think the motivation 意味着人们已经这样做很长时间了，但现在我认为动机 comes more from you know there's a certain interpretation in terms of 更多来自于你知道有一定的解释 machine learning that is kind of exciting that where people are yeah yeah 机器学习让人兴奋不已 是的 是的 even more more more more interested in so this is one way and levels of 甚至更多更多更感兴趣所以这是一种方式和水平 parameterization vary in this context but the good thing is you haven't 参数化在这种情况下会有所不同，但好处是你还没有 00:21 00:21 handcrafted model in the end that you still understand right and that you can 手工制作的模型最终你仍然理解正确并且你可以 still prove things about you still have guarantees on your solution you know you 仍然证明关于你的事情仍然对你的解决方案有保证你了解你 have guarantees that if you you you don't have these adversarial errors that 保证如果你你就不会犯这些对抗性错误 if you put have a little bit you get a completely different result this is 如果你放一点点，你会得到完全不同的结果，这是 really something you don't want right the other thing is and do this this is 确实是你不想要的东西，另一件事是，这样做，这是 more blue sky and this actually goes a little bit against what I said before 更多的蓝天，这实际上有点违背我之前所说的 which is we have been starting to use steep neural networks for problems in 也就是说，我们已经开始使用陡峭神经网络来解决以下问题 computer tomography for instance and there at the moment we cannot prove a 例如计算机断层扫描，目前我们无法证明 lot of things but we can see some ways of how to combine these more handcrafted 很多东西，但我们可以看到一些如何将这些更手工制作的东西结合起来的方法 models with neural networks and a sense of what you feed them with for instance 例如，具有神经网络的模型以及对您所提供的内容的感知 the prior information you feed them with the data maybe not just a measurement 您向他们提供的数据的先验信息可能不仅仅是测量结果 00:22 00:22 or maybe also the information that the measurements are actually line integrals 或者也可能是测量结果实际上是线积分的信息 okay of the 3d object that you want to reconstruct yep 好的，您想要重建的 3D 对象是的 and doing this in a kind of iterative fashion where you always go back to the 并以一种迭代的方式做到这一点，你总是回到 fact that I actually remember neural network these are line measurements that 事实上，我实际上记得神经网络这些是线测量 I'm feeding you with remember this and then you you you do another sweep 我喂你记住这个然后你你再扫一遍 through neural network with it but then how does that work in the context of 通过神经网络来处理它，但是它在以下情况下是如何工作的 building out a model around say like I mean I don't even know in an MRI how 围绕说建立一个模型，我的意思是我什至不知道在 MRI 中如何 many images are created or like 10 or lines are monitored but like say you 创建了许多图像，或者像 10 个图像或监控了线条，但就像你说的 have 10,000 images but you want to create a combination of a hand coding 有 10,000 张图像，但您想要创建手动编码的组合 algorithm and machine learning system mm-hmm how do you go about tagging all 算法和机器学习系统嗯嗯，你如何标记所有 that stuff what do you mean exactly how are you going to so what I understand 那些东西你到底是什么意思 你打算怎么做所以我明白 you're saying it's like yep giving it more data than just like the original 你是说，是的，给它提供了比原始数据更多的数据 source material yes and so how do you do that with a Morse like at larger scale 源材料是的，那么你如何用更大的莫尔斯电码来做到这一点 00:23 00:23 ah computationally you mean yeah okay so computationally we're doing this in a 啊，从计算上来说，你的意思是，好吧，所以从计算上来说，我们正在这样做 sequential manner okay so we're not so you can do it in different ways but in a 顺序方式好吧，所以我们不是这样你可以用不同的方式来做，但可以 sequential manner means that you're not feeding it to 10,000 images at the same 顺序方式意味着您不会同时将其输入 10,000 张图像 time but you're doing it bit by bit and you're adapting your objective towards 时间，但你正在一点一点地做，并且你正在调整你的目标 this okay another thing about computational performance is also of 这好吧，关于计算性能的另一件事也是 course that the optimization that is underlying but this is not just the 当然，这是底层的优化，但这不仅仅是 problem that we have that you know neural networks have in general is that 你知道神经网络普遍存在的问题是 you do not necessarily need to solve your optimization problem your training 您不一定需要通过训练来解决优化问题 exactly and maybe sometimes or most of the time you actually don't want it want 确切地说，也许有时或大多数时候你实际上不想要它想要 to save it exactly because you only have 保存它正是因为你只有 a finite amount of training examples and so when you think about what these 有限数量的训练示例，因此当您考虑这些内容时 neural networks are doing they're trying to minimize the loss over the training 神经网络正在尝试将训练过程中的损失最小化 00:24 00:24 examples that you have but this loss is only an approximation of many many many 你有的例子，但这个损失只是很多很多很多的近似值 many more images that you want your neural network 您的神经网络需要更多图像 to work right for and so very often you do not want to solve that exactly you 正确地工作，所以很多时候你并不想解决你想要的问题 don't want to minimize your losses actly for this training set okay and so there 不想在这个训练集上最小化你的损失，好吧，所以就这样 are different types of optimization methods that people are using but the 人们正在使用不同类型的优化方法，但 main thing in machine learning is stochastic optimization so you don't 机器学习的主要内容是随机优化，所以你不需要 minimize X you know exactly for all the variables that you have but you randomly 最小化 X 你确切地知道你拥有的所有变量，但你是随机的 pick a certain amount in every sweep through the network that you're 在您每次扫描网络时选择一定的金额 optimizing for and then you randomly change which ones you're optimizing the 优化然后你随机改变你正在优化的那些 next sweep and so on and just so I understand 下一次扫描等等，只是为了让我明白 minimizing lost why don't you want to do 尽量减少损失你为什么不想做 that so what you're minimizing if you so 那就是你要最小化的，如果你是这样的话 if you're so the loss let's say it could be the least squares error yeah between 如果你是如此的损失，可以说它可能是最小二乘误差是的 let's let's go back to denoising let's say you want you you want to train your 让我们回到去噪假设你想要你想要训练你的 00:25 00:25 neural network to optimally denoise images by saying for this training set 神经网络通过训练集来优化图像去噪 where I have both noisy and clean images 我同时拥有嘈杂和干净的图像 I want that if I sum over the difference between the denoise image so you feed 我希望如果我总结降噪图像之间的差异，这样你就可以了 your neural network with a noisy image it gives you a denoise image you want 你的神经网络带有噪声图像，它会为你提供你想要的去噪图像 that this denoise image is closest in a least square sense to the clean image 该去噪图像在最小二乘意义上最接近干净图像 that you know in this case because you have a training set you have a label you 在这种情况下你知道因为你有一个训练集你有一个标签你 have a true label for this noisy image which the label in this case is your 对于这个嘈杂的图像有一个真实的标签，在这种情况下的标签是你的 ground truth image okay and you want your denoising method which is new this 地面真实图像好吧，你想要你的去噪方法，这是新的 neural network to produce the noise images such that all of them are in the 神经网络产生噪声图像，使所有图像都在 least square sense closest to the original label to the ground label just 最小二乘感最接近原始标签到地面标签正好 00:26 00:26 a clean image okay and you want that to work over all the images on the training 干净的图像可以，并且您希望它适用于训练中的所有图像 set gotcha okay okay so but let's say you have 10,000 of these images that you 设置陷阱 好吧好吧，但是假设你有 10,000 张这样的图像 both know the clean and noisy image if you would perfectly fit to this training 如果您完全适合此培训，则两人都知道干净和嘈杂的图像 set if you would perfect minimize this loss function you could 如果你想完美地最小化这个损失函数，你可以设置 think and again you know people are not really understanding this and I and I 再想一想，你知道人们并没有真正理解这一点，而我和我 also don't really understand this but conceptually the idea is what you 也不太明白这一点，但从概念上讲，这个想法就是你的 actually want to minimize is not the lost just over training set but it's the 实际上想要最小化的不是训练集上的损失，而是 loss over an infinite amount of images which you then want to denoise right 损失无限量的图像，然后您想要对其进行正确的去噪 okay but you don't have all these infinite amount images so why would you 好吧，但是你没有那么多无限量的图像，那你为什么要这么做呢？ want to very accurately minimize the loss over this finite amount of images 想要非常准确地最小化有限数量图像的损失 maybe you don't maybe you only approximately want such that you still 也许你不知道也许你只是大约想要这样你仍然 00:27 00:27 have freedom right such that it could be optimal also for more images that you 拥有自由权，这样它也可以为您提供的更多图像提供最佳选择 don't have is so if you in other words you get you could train it on the wrong 没有，所以如果你换句话说你得到了，你可能会以错误的方式训练它 thing and it could only work for you know like denoising photos of apple 它只能对你知道的东西起作用，比如苹果的去噪照片 trees exactly yeah and then you're in the same place that you were in yeah 树完全是的，然后你就在原来的地方是的 exactly okay so the idea is if you only do it approximately you might be able to 完全没问题，所以我们的想法是，如果你只做大约，你也许能够 generalize it more but all of this really I mean there are some attempts to 更概括地说，但所有这些实际上我的意思是有一些尝试 understand this but all of this is not really is I'm hand waving here because I 明白这一点，但这一切并不是真的，我在这里挥手是因为我 can't really say anything mathematically about that but I have you pushed your 确实不能从数学上说任何东西，但我让你推了你的 research into practical practical applications at this point like are you 在这一点上研究实际应用，就像你一样 working with you know companies or student groups or anyone else so mine 与您认识的公司、学生团体或其他任何人一起工作，所以我的 collaborations are actually with people in academia but from other disciplines 合作实际上是与学术界但来自其他学科的人进行的 so we have been collaborating a lot in recent years with people in the hospital 所以近年来我们与医院的人们进行了很多合作 and the University Hospital in Cambridge so with clinicians and medical 和剑桥大学医院以及临床医生和医疗人员 00:28 00:28 physicists different types of applications you know one of the things 物理学家不同类型的应用你知道的事情之一 I I said before is that I got more and more interested in these problems where 我之前说过我对这些问题越来越感兴趣了 you don't measure an image directly but only indirectly via these x-rays for 您不直接测量图像，而是通过这些 X 射线间接测量图像 instance so yeah developing algorithms which which can 例如，是的，开发算法可以 get the most out of very limited amount of data the most out of in terms of very 充分利用非常有限的数据 high resolution images is something we have been collaborating a lot with 高分辨率图像是我们一直合作的领域 people in magnetic resonance tomography in particular in 从事磁共振断层扫描的人，特别是 the N Brookes Hospital which is the local Cambridge Hospital here but also N Brookes 医院是当地的剑桥医院，也是 with people in chemical engineering where one of the driving factors for 与化学工程领域的人们一起，其中的驱动因素之一 people in chemical engineering is for instance there is a there is a group 例如，化学工程领域的人有一个小组 here which is the magnetic resonance Research Centre where they look in 这是他们查看的磁共振研究中心 particular at processes through processes which are dynamic so they they 特别是通过动态过程的过程，因此它们 have these tubes filled with water and then they pump certain things through 让这些管子充满水，然后将某些东西泵入其中 and they want to understand what the dynamics of this process are so now if 他们想了解这个过程的动态是什么，所以现在如果 00:29 00:29 you think about not just having a static 3d object but having something that 你不仅考虑拥有一个静态 3D 对象，还考虑拥有一些 changes over time as well and now thinking back about how many x-rays not 随着时间的推移也会发生变化，现在回想一下有多少 X 射线没有变化 in magnetic resonance tomography DS arnott x-rays but just going back so not 在磁共振断层扫描 DS 阿诺特 X 射线但只是回去所以不是 sending through as so many x-rays means you don't have a lot of data to 发送如此多的 X 射线意味着您没有太多数据可供使用 reconstruct break which now if you want to track something dynamically also 如果您还想动态跟踪某些内容，请重建中断 means you're not measuring a lot per time step if you want to have a very 意味着如果你想有一个非常好的结果，你就不会在每个时间步测量很多 high resolution over time it means per timestamp you can't acquire 随着时间的推移，高分辨率意味着您无法获取每个时间戳 as much data as if you would have you know if you just have one second for 如果您只有一秒钟的时间，您就会知道尽可能多的数据 reconstructing your organ inside the body uh-huh at this particular time 在这个特定的时间重建你体内的器官嗯嗯 stamp and then you then the organ is moving again and you need to go to the 戳一下，然后风琴又开始移动，你需要去 next time stamp and so on you have less data for reconstructing 下一个时间戳等，您需要重建的数据较少 00:30 00:30 each time stamp as if you would have a static object and you would have 10 每个时间戳就好像您有一个静态对象并且您将有 10 seconds to acquire this instead of one second you can measure much more right 秒来获得这个而不是一秒你可以测量更多正确的 right and then you reconstruct just one image but now we have maybe you want to 对，然后你只重建一张图像，但现在我们也许你想要 reconstruct not just one image in 10 seconds but 10 images because we want to 10 秒内重建的不仅仅是一张图像，而是 10 张图像，因为我们想要 see something evolving over time right so here also the challenges are along 看到一些东西随着时间的推移而演变，所以挑战也随之而来 these lines of getting high resolution out of limited data not a thing which is 这些从有限的数据中获得高分辨率的方法并不是什么 not connected to indirect measurements so much then 与间接测量没有太大关系 than these applications in magnetic resonance MOG Rafi is that we have 与磁共振 MOG Rafi 中的这些应用相比，我们有 collaborations with people in Plant Sciences for instance so they are 例如与植物科学领域的人们合作，所以他们 interested in monitoring forest health or forest constituencies let's say from 对监测森林健康或森林选区感兴趣，让我们说 from airborne imaging data so they fly mostly in my collaboration they fly so 来自机载成像数据，所以它们主要在我的合作中飞行，所以它们飞行 00:31 00:31 not so much satellite but more flying they fly over forest regions and then 卫星数量不多，但飞行次数较多，它们飞过森林地区，然后 they require different types of imaging data they acquire just photographs okay 他们需要不同类型的成像数据 他们只获取照片 好吧 aerial photographs hyperspectral imaging 航空照片高光谱成像 data or multispectral imaging data which means you do not only have RGB but you 数据或多光谱成像数据，这意味着您不仅拥有 RGB，还拥有 have a broader range you cover a broader range okay over the light spectrum so 范围更广 你覆盖的光谱范围更广，所以 also the invisible light so you don't have just three channels sure you have 还有不可见光，因此您不仅仅只有三个通道 200 channels yeah and hyperspectral imaging is interesting sort of spectral 200 个通道是的，高光谱成像是一种有趣的光谱 component that you get from these measurements gives you an idea of what 从这些测量中获得的分量可以让您了解什么 the material properties are of these trees so it it it tells you something 这些树的材料属性所以它告诉你一些东西 about what really yeah so this is so so so the spectral component tells you 关于什么是真的所以这就是如此所以光谱成分告诉你 something about the material that you that you are looking at so in other 关于你正在看的材料的一些东西，所以在其他方面 words like the light spectrum of how they reflects light back they have a 像光谱这样的词，它们如何反射光回来，它们有 00:32 00:32 different signature in the light spectrum okay and so the intent would be 光谱中的不同签名好吧，所以意图是 to figure out you know say for instance like an invasive tree that was taking 弄清楚你知道，例如，就像一棵入侵的树正在采取 over an area they could figure that out by just by flying right over it 在一个区域上空，他们只需飞过该区域就可以弄清楚 gotcha okay and then the other thing so this is one and then or two aerial 好的，然后是另一件事，所以这是一个然后两个天线 photographs and hyperspectral imaging and then the third thing that they often 照片和高光谱成像，然后是他们经常做的第三件事 acquiring are lidar measurements yeah where you do not just get kind of a 获取激光雷达测量是的，您不只是获得某种 planar picture of the trees but you actually get a 3d model of the trees 树木的平面图片，但您实际上得到了树木的 3D 模型 yeah I was just watching a documentary about that about searching for my in 是的，我刚刚在看一部关于寻找我的纪录片 rooms with lidar flying I really like flying over the Yucatan Peninsula or 带有激光雷达的房间 飞行 我真的很喜欢飞越尤卡坦半岛或 something essentially like saying like a week 本质上就像说一周 take 20 years for an archaeologist to like dig around in the dirt or where you 考古学家需要20年的时间才能喜欢在泥土中或你所在的地方挖掘 just fly over and look for the hard stuff and let's see what happens yeah 飞过去寻找困难的东西，让我们看看会发生什么是的 yeah very interesting and and our people also looking to this in the context of 是的，非常有趣，我们的人也在考虑这一点 00:33 00:33 you know for instance like denoising a camera footage from anything you know 你知道，例如，从你知道的任何东西中对摄像机镜头进行去噪 like security on one hand yeah I haven't done so much working that myself but 一方面是安全，是的，我自己并没有做那么多工作，但是 there are of course you know the I mean CCTV cameras are everywhere yeah I mean 你当然知道我的意思是闭路电视摄像机无处不在是的我的意思是 it's like it's kind of a terrifying output of figuring out this research 这就像搞清楚这项研究的可怕结果 right like being tracked everywhere like in the UK in particular like I imagine 就像在英国一样被跟踪，特别是像我想象的那样 people are looking to do this right you know it's quite funny because when you 人们希望正确地做到这一点，你知道这很有趣，因为当你 think about these crime TV shows CSI whatever Miami or whatever they're 想想这些犯罪电视节目《犯罪现场调查》，无论是迈阿密还是其他什么 always these so you told you have very pixelated image and you press a magic 总是这些，所以你告诉你有非常像素化的图像，然后你按下一个魔法 button man and you can zoom in you can see everything so when you think it's oh 按钮人，你可以放大你可以看到一切，所以当你认为它是哦 this is ridiculous of course you can't do that but you 这很荒谬，你当然不能这样做，但是你 can't do it now maybe you know if you have all these machine learning methods 现在做不到也许你知道你是否拥有所有这些机器学习方法 00:34 00:34 which have learned to look at just pixels and then know what what is the 它们学会了只看像素，然后知道什么是什么 motive what is a very probable match in terms of high resolution maybe at some 动机 就高分辨率而言，可能在某些情况下很可能匹配 point you can do it but then you don't know haha if you're right or wrong right 点你可以做到，但你不知道哈哈，如果你是对还是错，对吧 just just by chance I was reading a New Yorker article from I think 2010 about 只是偶然，我读到了《纽约客》的一篇文章，内容是《我认为 2010 年》 this guy in Montreal allegedly finding five hundred year old 据称蒙特利尔的这个人发现了五百岁的老人 fingerprints using different kinds of like spectral photography so I don't 使用光谱摄影等不同类型的指纹，所以我不 want to give away the whole thing about and then there was an ensuing lawsuit 想要放弃一切，然后发生了一场诉讼 actually from him to The New Yorker saying they like it was libel but the 事实上，他向《纽约客》表示，他们喜欢这是诽谤，但 basically what happens was like he was accused of faking these fingerprints 基本上发生的事情就像他被指控伪造这些指纹 that may or may not oh yeah and like copying them from a 这可能会也可能不会哦，是的，就像从一个地方复制它们一样 00:35 00:35 real one duplicating them onto the back using like proprietary methods to find 真正的使用类似专有方法将它们复制到背面以找到 them out but you are interested in doing it whether whether or not it's legit 他们出去了，但你有兴趣这样做，无论它是否合法 like you want to do it you want to work I work so I mean I'm going to tell 就像你想做的那样你想工作我工作所以我的意思是我要告诉 people that it's fake yeah is it like yeah what direction are you going with 人们说这是假的 是的 是的 是的 你打算朝哪个方向走 with art so it kind of in Cambridge it's not well okay let me say bit more so 艺术，所以在剑桥有点不太好，让我多说一点吧 when I again during my PhD in Vienna there was a collaboration that we had 当我再次在维也纳攻读博士学位时，我们进行了一次合作 with physically conservator with conservatives who are we're looking at 与身体保护者 与保守派 我们正在关注谁 at particular wall frescoes at frescoes in an old apartment in the city centre 在市中心一间旧公寓的壁画中的特定壁画 of Vienna which are called the night Hut frescoes I'm not going to more into 维也纳的被称为夜间小屋壁画我不打算更多 detail but they were in the process of restoration this Friendly's yes these 细节，但他们正在恢复这个友好的，是的这些 00:36 00:36 frescoes and so that was my first hand experience there and there the idea was 壁画，所以这是我在那里的第一手经验，那里的想法是 that you know takes them a long time to physically restore these wall paintings 你知道他们需要很长时间才能修复这些壁画 and once you have restored it there is no way back right you need to decide 一旦你恢复了它，就没有回头路了，你需要做出决定 what to do yeah because then it's it sticks and so what our idea was to help 该怎么办是的，因为这样它就粘在一起了，所以我们的想法是帮助 them by creating a virtual template of how the restoration could look if they 通过创建一个虚拟模板来展示修复体的外观，如果它们 do this or it isn't right yeah so because the important part is a fresco 这样做，否则不对，是的，因为重要的部分是壁画 is actually part of the wall chemically it's not paint exactly yeah exactly but 实际上是化学墙壁的一部分，它不完全是油漆，是的，但是 even with paintings you know if you do something if you do if you manually 即使是绘画，你也知道如果你手动做了某事 really you know physically restore them yeah you've done it I mean you can still 你真的知道物理上恢复它们是的你已经做到了我的意思是你仍然可以 maybe you know try to do I mean you're you are your your your treat your your 也许你知道尝试去做我的意思是你是你你是你你对待你你 00:37 00:37 your just well you're changing a historical piece right of the world 你很好，你正在改变世界的历史部分 price I mean this is yeah yeah anyway so so coming here to Cambridge 价格我的意思是这是是的，无论如何，所以来到剑桥 I got to know people in the Fitzwilliam Museum which is the which is a Museum 我在菲茨威廉博物馆认识了人们，这是一个博物馆 here in Cambridge and there they're interested in illuminated manuscripts so 在剑桥这里，那里他们对彩绘手稿感兴趣，所以 I met a very good colleague of mine who's - who is the keeper of manuscripts 我遇到了一位非常好的同事，他是手稿的保管人 in the Fitzwilliam Museum got interested in this idea of virtual restoration 在菲茨威廉博物馆对虚拟修复的想法感兴趣 because illuminated manuscripts are so fragile that you that the culture is you 因为彩绘手稿是如此脆弱，文化就是你 never physically restored them you never 从来没有从物理上恢复过它们，你从来没有 physically restored and they you know if they get damaged or altered over time 物理修复，您知道它们是否随着时间的推移而损坏或改变 you leave it Wow okay you leave them like this and so there the idea was 你就这样留下吧 哇，好吧，你就这样留下它们，所以就有了这个想法 couldn't we create a virtual restoration and you know kind of exhibit the 我们不能创建一个虚拟修复体吗？你知道可以展示一下吗？ 00:38 00:38 original manuscript and the virtual restoration next to each other and so 原稿和虚拟修复体彼此相邻，等等 last year there was an exhibition in the Fitzwilliam Museum which is which was 去年菲茨威廉博物馆举办了一场展览 called color and in this exhibition we had one piece which was in a page of an 叫做颜色，在这次展览中我们有一件作品，它在一张纸上 illuminated manuscript which had been altered over time actually manually over 随着时间的推移而改变的插图手稿实际上是手动完成的 painted okay and what we did was that we exhibited 画得不错，我们所做的是展示 the manuscript and next to it the virtual restoration where we took off 手稿和旁边是我们起飞的虚拟修复体 the over paint and yeah and that has led to add to other things but I mean this 过度油漆，是的，这导致了添加其他东西，但我的意思是这个 is so this is kind of the idea that you don't physically change something but 所以这是一种想法，你不会物理上改变一些东西，但是 you you virtually do it which is you know nothing damaged you just yeah 你几乎做到了，你知道没有任何东西损害你只是是的 virtually create a digital copy of this manuscript and you play around with it 以虚拟方式创建该手稿的数字副本，然后您可以使用它 so you're not only going like back in time to see maybe like restoring it to 所以你不仅要回到过去看看也许要把它恢复到 its original you know vitality like its original color but you're actually like 它原来的你知道活力就像它原来的颜色但你实际上就像 00:39 00:39 going deeper into the layers like this is an agent over yeah yeah go further in 深入到各个层，就像这样是一个代理，是的，是的，进一步深入 yeah with imaging and then you kind of apply everything you might already yeah 是的，通过成像，然后你可以应用你可能已经拥有的一切是的 Wow so if someone's really excited about this kind of research if they want to 哇，如果有人真的对这种研究感到兴奋，如果他们愿意的话 get into it what would you point them to where should they get started 进入其中，你会向他们指出什么，他们应该从哪里开始 depends what their background is okay yeah say they have like you know they 取决于他们的背景，好吧，是的，说他们有你知道的样子 have a CS degree they're interested in imaging so they're like technical but 拥有计算机科学学位，他们对成像感兴趣，所以他们喜欢技术，但 they haven't done anything in particular like in this field okay so so what I 他们没有在这个领域做过任何特别的事情，所以我 would advise is to look so I think in particular when you think about the US I 我的建议是看看，特别是当你想到美国时，我认为 think some of the cool things that came out of image in image processing in the 想想图像处理中图像中出现的一些很酷的东西 last couple of years were from UCLA so if you look at some of the idea applied 过去几年来自加州大学洛杉矶分校，所以如果你看看其中应用的一些想法 math faculty there and some of the online lecture material or you know 那里的数学教师和一些在线讲座材料或者你知道 00:40 00:40 youtube videos of some of their talks I think that would be a good source to 他们的一些演讲的 YouTube 视频我认为这将是一个很好的来源 look at so I mean very classically names are Stan oh sure Andreea patottie I 看看，我的意思是非常经典的名字是斯坦哦当然安德烈亚·帕蒂蒂我 mentioned Malik Pomona Stephano SWAT oh there are lots of people there is not a 提到 Malik Pomona Stephano SWAT 哦，有很多人，没有一个 name is Casey I can tell you beer yeah a few more things afterwards but I think 我的名字是凯西，我可以告诉你啤酒，是的，之后还有一些事情，但我想 just to look for mathematical approaches to image processing I think it would be 只是为了寻找图像处理的数学方法，我认为这将是 the first thing I would do there are very good introductory books to look at 我要做的第一件事就是看一些非常好的入门书籍 that explain a bit of the basics great but yeah I would first start reading a 这解释了一些基础知识，很好，但是是的，我首先要开始阅读 little bit in these more general foundational books and then I think just 这些更一般的基础书籍中的一些内容然后我想 citing from that you immediately come go 引用你立即来去 00:41 00:41 to the you know more modern recent years research I think that would be a that 就你所知，近年来更现代的研究，我认为这将是 would be a good way just not you can catch up to you maybe or apply here 这将是一个好方法，只是你可能找不到你或在这里申请 awesome well thank you so much thanks for making time yeah thanks you 太棒了，非常感谢您抽出时间，是的，谢谢您