Tuesday, September 29, 2015

Thesis: Fusion of Sparse Reconstruction Algorithms in Compressed Sensing, Sooraj K. Ambat - implementation -

Sooraj K. Ambat just sent me know of the following:

Dear Igor,

I am happy to let you know that I have successfully defended my Ph.D. Thesis entitled "Fusion of Sparse Reconstruction Algorithms in Compressed Sensing". Thank you very much for maintaining such a wonderful blog which updated me, on a daily basis, about the cutting edge research in Compressed Sensing and related areas during my Ph.D. days.

Inspired by your collection of codes for reproducible research, I have also released my codes publicly available. The details of the links of the codes are available in my Thesis (and below)
My Thesis can be downloaded from 

You may also find my publications and related codes for reproducible research downloadable at https://sites.google.com/site/soorajkambat/home/research/ph-d

with warm regards,
Thanks Sooraj, this is impressive and congratulations ! On top of the exploration of these ensemble approach, I loved reference 78 and the mention in the acknowledgments ::-) Without further ado:

Fusion of Sparse Reconstruction Algorithms in Compressed Sensing, by Sooraj K. Ambat
Compressed Sensing (CS) is a new paradigm in signal processing which exploits the sparse or compressible nature of the signal to significantly reduce the number of measurements, without compromising on the signal reconstruction quality. Recently, many algorithms have been reported in the literature for efficient sparse signal reconstruction. Nevertheless, it is well known that the performance of any sparse reconstruction algorithm depends on many parameters like number of measurements, dimension of the sparse signal, the level of sparsity, the measurement noise power, and the underlying statistical distribution of the non-zero elements of the signal. It has been observed that a satisfactory performance of the sparse reconstruction algorithm mandates certain requirement on these parameters, which is different for different algorithms. Many applications are unlikely to fulfil this requirement. For example, imaging speed is crucial in many Magnetic Resonance Imaging (MRI) applications. This restricts the number of measurements, which in turn affects the medical diagnosis using MRI. Hence, any strategy to improve the signal reconstruction in such adverse scenario is of substantial interest in CS. Interestingly, it can be observed that the performance degradation of the sparse recovery algorithms in the aforementioned cases does not always imply a complete failure. That is, even in such adverse situations, a sparse reconstruction algorithm may provide partially correct information about the signal. In this thesis, we study this scenario and propose a novel fusion framework and an iterative framework which exploit the partial information available in the sparse signal estimate(s) to improve sparse signal reconstruction. The proposed fusion framework employs multiple sparse reconstruction algorithms, independently, for signal reconstruction. We first propose a fusion algorithm viz. Fusion of Algorithms for Compressed Sensing (FACS) which fuses the estimates of multiple participating algorithms in order to improve the sparse signal reconstruction. To alleviate the inherent drawbacks of FACS and further improve the sparse signal reconstruction, we propose another fusion algorithm called Committee Machine Approach for Compressed Sensing (CoMACS) and variants of CoMACS. For low latency applications, we propose a latency friendly fusion algorithm called progressive Fusion of Algorithms for Compressed Sensing (pFACS). We also extend the fusion framework to the Multiple Measurement Vector (MMV) problem and propose the extension of FACS called Multiple Measurement Vector Fusion of Algorithms for Compressed Sensing (MMV-FACS). We theoretically analyse the proposed fusion algorithms and derive guarantees for performance improvement. We also show that the proposed fusion algorithms are robust against both signal and measurement perturbations. Further, we demonstrate the efficacy of the proposed algorithms via numerical experiments: (i) using sparse signals with different statistical distributions in noise-free and noisy scenarios, and (ii) using real-world ECG signals. The extensive numerical experiments show that, for a judicious choice of the participating algorithms, the proposed fusion algorithms result in a sparse signal estimate which is often better than the sparse signal estimate of the best participating algorithm. The proposed fusion framework requires to employ multiple sparse reconstruction algorithms for sparse signal reconstruction. We also propose an iterative framework and algorithm called Iterative Framework for Sparse Reconstruction Algorithms (IFSRA) to improve the performance of a given arbitrary sparse reconstruction algorithm. We theoretically analyse IFSRA and derive convergence guarantees under signal and measurement perturbations. Numerical experiments on synthetic and real-world data confirm the efficacy of IFSRA. The proposed fusion algorithms and IFSRA are general in nature and does not require any modification in the participating algorithm(s).

Credits: NASA/JPL/University of Arizona
 These dark, narrow, 100 meter-long streaks called recurring slope lineae flowing downhill on Mars are inferred to have been formed by contemporary flowing water. Recently, planetary scientists detected hydrated salts on these slopes at Hale crater, corroborating their original hypothesis that the streaks are indeed formed by liquid water. The blue color seen upslope of the dark streaks are thought not to be related to their formation, but instead are from the presence of the mineral pyroxene. The image is produced by draping an orthorectified (Infrared-Red-Blue/Green(IRB)) false color image (ESP_030570_1440) on a Digital Terrain Model (DTM) of the same site produced by High Resolution Imaging Science Experiment (University of Arizona). Vertical exaggeration is 1.5.
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