CS: Bob's questions, MPTK, flat-panel-detector cone-beam CT, A data-driven sparse GLM for fMRI analysis, Off-axis compressed holographic microscopy, LDPC Codes for Compressed Sensing

Let give Bob some props for putting near real time his investigation on the CMP algorithm and putting up his doubts..I am sure that some of you can help him out in answering these questions, don't be shy:

• So, l_1 minimization works fine, but greedy methods perform much better for certain sparse signals?
• Why Isn't BP Working?

As mentioned yesterday, The Matching Pursuit Tool Kit (MPTK) provides a fast implementation of the Matching Pursuit algorithm for the sparse decomposition of multichannel signals. It comprises a C++ library, standalone command line utilities, and some scripts for running it and plotting the results through Matlab. Some more informations can be found here : http://mptk.irisa.fr/. The downloads can be found here : https://gforge.inria.fr/frs/?group_id=36 .

Here are the two papers mentioned yesterday by Emil Sidky and Jong Chul Ye:

Evaluation of sparse-view reconstruction from flat-panel-detector cone-beam CT by Junguo Bian, Jeffrey H Siewerdsen, Xiao Han, Emil Y Sidky, Jerry L Prince, Charles A Pelizzari and Xiaochuan Pan. The attendant presentation is here. The abstract reads:

Flat-panel-detector x-ray cone-beam computed tomography (CBCT) is used in a rapidly increasing host of imaging applications, including image-guided surgery and radiotherapy. The purpose of the work is to investigate and evaluate image reconstruction from data collected at projection views significantly fewer than what is used in current CBCT imaging. Specifically, we carried out imaging experiments using a bench-top CBCT system that was designed to mimic imaging conditions in image-guided surgery and radiotherapy; we applied an image reconstruction algorithm based on constrained total-variation (TV)-minimization to data acquired with sparsely sampled view-angles and conducted extensive evaluation of algorithm performance. Results of the evaluation studies demonstrate that, depending upon scanning conditions and imaging tasks, algorithms based on constrained TV-minimization can reconstruct images of potential utility from a small fraction of the data used in typical, current CBCT applications. A practical implication of the study is that the optimization of algorithm design and implementation can be exploited for considerably reducing imaging effort and radiation dose in CBCT.

A data-driven sparse GLM for fMRI analysis using sparse dictionary learning with MDL criterion by Kangjoo Lee, Sungho Tak, Jong Chul Ye. The abstract reads:

We propose a novel statistical analysis method for functional MRI to overcome the drawbacks of conventional datadriven methods such as the independent component analysis (ICA). Although ICA has been broadly applied to functional MRI due to its capacity to separate spatially or temporally independent components, the assumption of independence has been challenged by recent studies showing that ICA does not guarantee independence of simultaneously occurring distinct activity patterns in the brain. Instead, sparsity of the signal has been shown to be more promising. This coincides with biological findings such as sparse coding in V1 simple cells, electrophysiological experiment results in the human medial temporal lobe, and etc. The main contribution of this paper is, therefore, a new data driven fMRI analysis that is derived solely based upon the sparsity of the signals. A compressed sensing based data-driven sparse generalized linear model is proposed that enables estimation of spatially adaptive design matrix as well as sparse signal components that represent synchronous, functionally organized and integrated neural hemodynamics. Furthermore, an MDL based model order selection rule is shown to be essential in selecting unknown sparsity level for sparse dictionary learning. Using simulation and real fMRI experiments, we show that the proposed method can adapt individual variation better compared to the conventional ICA methods.

I also just found the following hardware development: Off-axis compressed holographic microscopy in low light conditions by Marcio Marim, Elsa Angelini, Jean-Christophe Olivo-Marin and Michael Atlan. The abstract reads;

This article reports a demonstration of off-axis compressed holography in low light level imaging conditions. An acquisition protocol relying on a single exposure of a randomly undersampled diffraction map of theoptical field, recorded in high heterodne gain regime, is proposed. The image acquisition scheme is based on compressed sensing, a theory establishing that near-exact recovery of an unknown spare signal is possible from a small number of non-structured measurements. Image reconstruction is further enhanced by inroducing an off-axis spatial support constraint to the image estimation algorithm. We report accurate experimental recovering of holographhic images of a resolution target in low light conditions with a frame exposure of 5 microseconds, scaling down measurment to 9 % of random pixels within the array detector.

and this arxiv paper: LDPC Codes for Compressed Sensing by Alexandros G. Dimakis, Roxana Smarandache, Pascal O. Vontobel. The abstract reads:

We present a mathematical connection between channel coding and compressed sensing. In particular, we link, on the one hand, \emph{channel coding linear programming decoding (CC-LPD)}, which is a well-known relaxation of maximum-likelihood channel decoding for binary linear codes, and, on the other hand, \emph{compressed sensing linear programming decoding (CS-LPD)}, also known as basis pursuit, which is a widely used linear programming relaxation for the problem of finding the sparsest solution of an under-determined system of linear equations. More specifically, we establish a tight connection between CS-LPD based on a zero-one measurement matrix over the reals and CC-LPD of the binary linear channel code that is obtained by viewing this measurement matrix as a binary parity-check matrix. This connection allows the translation of performance guarantees from one setup to the other. The main message of this paper is that parity-check matrices of "good" channel codes can be used as provably "good" measurement matrices under basis pursuit. In particular, we show that for basis pursuit the deterministic LDPC matrices constructed by Gallager form the best known sparse measurement matrices, in the sense that they provide the largest provable recovery guarantees for sparse measurement matrices and sparse signals.

Credit: NASA/JPL/University of Arizona, Layering in Exhumed Crater at Meridiani Planum (PSP_001374_1805) on Mars.