CS: CS IR and Video, One mans's noise, Derivative CS, Aperture Synthesis Imaging

Jong Chul Ye just sent me the following:

Hi Igor,

I would like you to point out our invited paper http://bisp.kaist.ac.kr/papers/Jung10_IJIST.pdf, which appeared on IJIST this month. The paper is more detailed description of our previous contribution: compressive sensing dynamic MRI called kt FOCUSS (http://bisp.kaist.ac.kr/papers/Jung09_MRM.pdf), especially on how motion estimation and compensation can be implemented.

I believe that this concept can be used not only for dynamic MRI applications but also for compressive sensing video coding applications.

I would be happy to hear any feedback on our work.

Best regards,

-Jong

Thanks Jong.

The paper is: Motion Estimated and Compensated Compressed Sensing Dynamic Magnetic Resonance Imaging: What We Can Learn From Video Compression Techniques by Hong Jung, Jong Chul Ye. The abstract reads:

Compressed sensing has become an extensive research area in MR community because of the opportunity for unprecedented high spatio-temporal resolution reconstruction. Because dynamic magnetic resonance imaging (MRI) usually has huge redundancy along temporal direction, compressed sensing theory can be effectively used for this application. Historically, exploiting the temporal redundancy has been the main research topics in video compression technique. This article compares the similarity and differences of compressed sensing dynamic MRI and video compression and discusses what MR can learn from the history of video compression research. In particular, we demonstrate that the motion estimation and compensation in video compression technique can be also a powerful tool to reduce the sampling requirement in dynamic MRI. Theoretical derivation and experimental results are presented to support our view

As some of you know I am interested in compressive EEG as shown in the discussion with Esther Rodriguez-Villegas a while back on the subject (CS: Q&A with Esther Rodriguez-Villegas on a Compressive Sensing EEG). But I have a hard time getting references on what is really the type of inverse problem that is being solved. This week, the arxiv blog, points to a new description of what EEGs and ECGs signals actually measure in a paper entitled: Electrophysiology of living organs from first principles by Gunter Scharf, Lam Dang and Christoph Scharf. The abstract of the paper reads:

Based on the derivation of the macroscopic Maxwell’s equations by spatial averaging of the microscopic equations, we discuss the electrophysiology of living organs. Other methods of averaging (or homogenization) like the bidomain model are not compatible with Maxwell’s theory. We also point out that modelling the active cells by source currents is not a suitable description of the situation from first principles. Instead, it turns out that the main source of the measured electrical potentials is the polarization charge density which exists at the membranes of active cells and adds up to a macroscopic polarization. The latter is the source term in the Laplace equation, the solution of which gives the measured far-field potential. As a consequence it is the polarization or dipole density which is best suited for localization of cardiac arrhythmia.

So the question becomes "is the dipole density sparse in some basis ?"

Recall the Heard Island Feasibility Test entry ? where one man's noise is another's signal.




Here is a new twist: The folks at Goddard found out that the the noise background in the coded aperture X-ray cameras on-board current spacecraft like XMM or Herschel can be used to detect Space Weather events (check Astrophysics Noise: A Space Weather Signal )

Finally, here is a small list of documents found on the interwebs:

Chien-Chia Chen has a report on Compressed Sensing Framework on TinyOS. In it one learns about a set of compressed sensing tools on both sensor side using TinyOS and host PC side using Matlab.

Derivative Compressive Sampling with Application to Phase Unwrapping by Mahdi S. Hosseini and Oleg V. Michailovich. The abstract reads:

Reconstruction of multidimensional signals from the samples of their partial derivatives is known to be an important problem in imaging sciences, with its fields of application including optics, interferometry, computer vision, and remote sensing, just to name a few. Due to the nature of the derivative operator, the above reconstruction problem is generally regarded as ill-posed, which suggests the necessity of using some a priori constraints to render its solution unique and stable. The ill-posed nature of the problem, however, becomes much more conspicuous when the set of data derivatives occurs to be incomplete. In this case, a plausible solution to the problem seems to be provided by the theory of compressive sampling, which looks for solutions that fit the measurements on one hand, and have the sparsest possible representation in a predefined basis, on the other hand. One of the most important questions to be addressed in such a case would be of how much incomplete the data is allowed to be for the reconstruction to remain useful. With this question in mind, the present note proposes a way to augment the standard constraints of compressive sampling by additional constraints related to some natural properties of the partial derivatives. It is shown that the resulting scheme of derivative compressive sampling (DCS) is capable of reliably recovering the signals of interest from much fewer data samples as compared to the standard CS. As an example application, the problem of phase unwrapping is discussed.

Compressed Sensing For Aperture Synthesis Imaging by Stephan Wenger, Soheil Darabiy, Pradeep Sen, Karl-Heinz Glaßmeier, and Marcus Magnor. The abstract reads:

The theory of compressed sensing has a natural application in interferometric aperture synthesis. As in many real-world applications, however, the assumption of random sampling, which is elementary to many propositions of this theory, is not met. Instead, the induced sampling patterns exhibit a large degree of regularity. In this paper, we statistically quantify the effects of this kind of regularity for the problem of radio interferometry where astronomical images are sparsely sampled in the frequency domain. Based on the favorable results of our statistical evaluation, we present a practical method for interferometric image reconstruction that is evaluated on observational data from the Very Large Array (VLA) telescope.