Welcome back to Beyond the Patterns. So today I have the great pleasure to announce Dr.

Emil Siedke, professor at the University of Chicago. So he is an expert in CT reconstruction,

has been working for a very long time in the fields of inverse problems and iterative CT

reconstruction. Lately he started also looking into deep learning based reconstruction techniques

and this is also one of the many reasons you would invite him in order to give a presentation

here with our group. So Dr. Siedke is a research professor in the Department of Radiology of

the University of Chicago. He received his bachelor's degree in 1988 in physics, astronomy,

physics and mathematics from the University of Wisconsin-Madison. He went on to obtain

a master's degree in 1991 and a PhD in 1993 in physics from the University of Chicago.

Dr. Siedke worked as a postdoctoral research assistant in atomic physics at the University

of Copenhagen from 1993 to 1996 and the University of Bielefeld in 1996 and Kansas State University

from 1996 to 2001. In 2001 Dr. Siedke switched to medical imaging and joined the lab of Dr.

Xiaoshan Pan. Most recently he was promoted to research professor in 2018. Dr. Siedke

has published approximately a hundred papers and about 70 of them are in medical imaging.

His theoretical work has mainly focused on x-ray tomography with sparse or limited angle

sampling. He also applied advanced techniques for non-smooth or non-convex large optimization

applied to imaging. His application work has centered on tomographic breast imaging, CT

and tomosynthesis and developing image reconstruction algorithms and calibration techniques for

spectral CT scanners based on photon counting detectors. So today I am glad to announce

that we will be giving a talk entitled inverse problems in imaging and evidence for solution

by convolutional neural networks. Emil, it's a great pleasure to have you here as a guest

at least virtually and the stage is yours.

Well, thank you very much for the introduction and for inviting me for giving and giving

me this opportunity to speak to your group. So what I want to talk about today is work

that we did together with two researchers from actually I have University of Illinois.

It's actually Illinois Institute of Technology. Sorry, Oban and Iris. But anyway, Iris is

the PhD student and that we worked with and Yovon is another researcher in medical imaging

who's very knowledgeable on neural networks. And then you can also see Xiaochuan that's

my boss. All right. Anyway, this work was motivated by recent efforts and that we've

seen in the literature where you have claims that deep learning with the CNN based neural

networks can solve ill-posed inverse problems. So here you can see the first line in the

abstract of this paper from transactions image processing. In this paper we propose a novel

deep convolutional neural network based algorithm for solving ill-posed inverse problems. So

yeah, we've seen lots of these papers, but when we look inside we don't really see the

evidence that this is actually happening. I mean, we see a lot of nice images, but the

evidence for actually solving the inverse problem seems to be lacking. So this prompted

us to do our own investigation and we just finished a paper last year which is called

Do CNNs Solve the CT Inverse Problem? All right. And so this is pretty much what I'm

going to explain today in this talk is like what's the motivation in introducing this

work and showing our effort here and trying to see if CNNs do solve the CT inverse problem.

So here's the outline for the talk. First I'm going to give some background on inverse

problems. Then I'm going to talk about sparse view CT inverse problem and compressive sensing.

And the reason why I'm going to talk about that is because that's what this paper here

was using as their test subject in sparse view CT. Then I'll show some numerical results

that illustrate how we can show using compressive sensing that we can solve the sparse view

CT inverse problem. And then we're going to move on to some CNN numerical results and

discuss finally the evidence that CNN, for CNN solution of the sparse view CT inverse

problem. So let's start from the beginning and let's talk about the background on inverse

problems. So all the material that I'm talking about here, you can pretty much find in more

detail on these notes by Guillaume Ball. It's class notes entitled Introduction to Inverse