Compressive Sensing Theory for Optical Systems Described by a Continuous Model

A brief survey of the author and collaborators' work in compressive sensing applications to continuous imaging models.Comment: Chapter 3 of "Optical Compressive Imaging" edited by Adrian Stern published by Taylor & Francis 201

Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)

The implicit objective of the biennial "international - Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST) is to foster collaboration between international scientific teams by disseminating ideas through both specific oral/poster presentations and free discussions. For its second edition, the iTWIST workshop took place in the medieval and picturesque town of Namur in Belgium, from Wednesday August 27th till Friday August 29th, 2014. The workshop was conveniently located in "The Arsenal" building within walking distance of both hotels and town center. iTWIST'14 has gathered about 70 international participants and has featured 9 invited talks, 10 oral presentations, and 14 posters on the following themes, all related to the theory, application and generalization of the "sparsity paradigm": Sparsity-driven data sensing and processing; Union of low dimensional subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph sensing/processing; Blind inverse problems and dictionary learning; Sparsity and computational neuroscience; Information theory, geometry and randomness; Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?; Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website: http://sites.google.com/site/itwist1

A unified approach to sparse signal processing

A unified view of the area of sparse signal processing is presented in tutorial form by bringing together various fields in which the property of sparsity has been successfully exploited. For each of these fields, various algorithms and techniques, which have been developed to leverage sparsity, are described succinctly. The common potential benefits of significant reduction in sampling rate and processing manipulations through sparse signal processing are revealed. The key application domains of sparse signal processing are sampling, coding, spectral estimation, array processing, compo-nent analysis, and multipath channel estimation. In terms of the sampling process and reconstruction algorithms, linkages are made with random sampling, compressed sensing and rate of innovation. The redundancy introduced by channel coding i

Disjoint sparsity for signal separation and applications to hybrid inverse problems in medical imaging

The main focus of this work is the reconstruction of the signals f and gi, i=1,\u2026,N, from the knowledge of their sums hi=f+gi, under the assumption that f and the gi's can be sparsely represented with respect to two different dictionaries Af and Ag. This generalizes the well-known \u201cmorphological component analysis\u201d to a multi-measurement setting. The main result of the paper states that f and the gi's can be uniquely and stably reconstructed by finding sparse representations of hi for every i with respect to the concatenated dictionary [Af,Ag], provided that enough incoherent measurements gi are available. The incoherence is measured in terms of their mutual disjoint sparsity. This method finds applications in the reconstruction procedures of several hybrid imaging inverse problems, where internal data are measured. These measurements usually consist of the main unknown multiplied by other unknown quantities, and so the disjoint sparsity approach can be directly applied. As an example, we show how to apply the method to the reconstruction in quantitative photoacoustic tomography, also in the case when the Gr\ufcneisen parameter, the optical absorption and the diffusion coefficient are all unknown

Interference Suppression in WCDMA with Adaptive Thresholding based Decision Feedback Equaliser

WCDMA is considered as one of the 3G wireless standards by 3GPP. Capacity calculation shows that WCDMA systems have more capacity compared to any other multiple access technique such as time division multiple access (TDMA) or frequency division multiple access (FDMA). So it is widely used. Rake receivers are used for the detection of transmitted data in case of WCDMA communication systems due to its resistance to multipath fading. But rake receiver treat multiuser interference (MUI) as AWGN and have limitation in overcoming the effect of multiple access interference (MAI) when the SNR is high. A de-correlating matched filter has been used in this thesis, which eliminates and improves system performance. But the given receiver works well only in the noise free environment. A DFE, compared to linear equaliser, gives better performance at severe ISI condition. The only problem in this equalisation technique is to select the number of symbols that are to be fed back. This thesis gives an idea on multiple symbol selection, based on sparity where an adaptive thresholding algorithm is used that computes the number of symbols to feedback. Simulated results show a significant performance improvement for Regularised Rake receiver along with thresholding in terms of BER compared to a rake receiver, de-correlating rake receiver and regularised rake receiver. The performance of the receiver in different channels is also analysed