In conjunction with the entry of the extraordinary Reinterpretable Imager of Amit Agrawal, Ashok Veeraraghavan and Ramesh Raskar. I caught up a discussion between Zachary Harmany and Eric Trammel on twitter that started with:
More specifically, I was interested in hearing Zachary tell me more about coded aperture especially in the context of compressive sensing providing new tools to this old problem. As one can see from Gerry Skinner's interview there is/was some distrust of nonlinear reconstruction methods because, it seems to me, they are/were not grounded in a good framework. Compressive Sensing changes all that really and I am very kin on hearing how these new nonlinear techniques can go in a direction people did not dare going before because it was not grounded theoretically. More specifically, when coded aperture started about 50 years ago, we did not have harmonic functions like wavelets, so can the whole dictionary business help us ? The most sophisticated older methods used some type of greedy schemes: It looks like we have better schemes even some that are looking at solving the l_0 problem instead of just the l_1. We also have some approaches to quantization and structured sparsity: how can we use those in new schemes that would make coded aperture a full fledged imaging system ? Finally, as one can see from yesterday's entry, we are now looking at 3-D data and compression in time and while sometimes SNR is of paramount importance, other times one is only interested not in the best picture possible but rather in a good-enough quality. How do CS reconstruction methods highlighted above could provide so-so results whereas linear methods like MURA could not ? As it happens, Zachary pointed out to the paper they had recently presented in Europe. Yes the one that got them stuck a little longer due to the cloud. So with no further due, here it is:
Compressive Coded Apertures for High-Resolution Imaging by Roummel Marcia, Zachary Harmany, and Rebecca Willett. The abstract reads:
@fujikanaeda @igorcarron Much of CS requires very high SNRs to work well. We learned this when working on compressive coded aperture imagingTo what I replied about the excellent response from Gerry Skinner on the subject as featured in this entry: A Short Discussion with Gerry Skinner, a Specialist in Coded Aperture Imaging of specific interest is this illuminating paper.
More specifically, I was interested in hearing Zachary tell me more about coded aperture especially in the context of compressive sensing providing new tools to this old problem. As one can see from Gerry Skinner's interview there is/was some distrust of nonlinear reconstruction methods because, it seems to me, they are/were not grounded in a good framework. Compressive Sensing changes all that really and I am very kin on hearing how these new nonlinear techniques can go in a direction people did not dare going before because it was not grounded theoretically. More specifically, when coded aperture started about 50 years ago, we did not have harmonic functions like wavelets, so can the whole dictionary business help us ? The most sophisticated older methods used some type of greedy schemes: It looks like we have better schemes even some that are looking at solving the l_0 problem instead of just the l_1. We also have some approaches to quantization and structured sparsity: how can we use those in new schemes that would make coded aperture a full fledged imaging system ? Finally, as one can see from yesterday's entry, we are now looking at 3-D data and compression in time and while sometimes SNR is of paramount importance, other times one is only interested not in the best picture possible but rather in a good-enough quality. How do CS reconstruction methods highlighted above could provide so-so results whereas linear methods like MURA could not ? As it happens, Zachary pointed out to the paper they had recently presented in Europe. Yes the one that got them stuck a little longer due to the cloud. So with no further due, here it is:
Compressive Coded Apertures for High-Resolution Imaging by Roummel Marcia, Zachary Harmany, and Rebecca Willett. The abstract reads:
Traditionally, optical sensors have been designed to collect the most directly interpretable and intuitive measurements possible. However, recent advances in the fields of image reconstruction, inverse problems, and compressed sensing indicate that substantial performance gains may be possible in many contexts via computational methods. In particular, by designing optical sensors to deliberately collect “incoherent” measurements of a scene, we can use sophisticated computational methods to infer more information about critical scene structure and content. In this paper, we explore the potential of physically realizable systems for acquiring such measurements. Specifically, we describe how given a fixed size focal plane array, compressive measurements using coded apertures combined with sophisticated optimization algorithms can significantly increase image quality and resolution.
The website for the Compressive Coded Aperture project at Duke is here.
I am glad that Roummel, Zachary, and Rebecca are on the right side of the force. To understand what the video shows, you need to go the CCA site.
Thanks Zachary and Eric for the discussion.
Nicolas Cusseau just mentioned to me that Mathworks, the maker of Matlab, is having a contest that features producing a reconstruction solver for a series of compressive sensing problems. The encoding uses elements from the {0,1} set. The rules are here:
Spring 2010 MATLAB Programming Contest, April 28-May 5 2010, Compressive Sensing is the 21st MATLAB Online Programming Contest.The prize is a matlab licence. Hurry up it'll be over next week on May 5th.
Thanks Nicolas
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