Measurements design and phenomena discrimination

The construction of measurements suitable for discriminating signal components produced by phenomena of different types is considered. The required measurements should be capable of cancelling out those signal components which are to be ignored when focusing on a phenomenon of interest. Under the hypothesis that the subspaces hosting the signal components produced by each phenomenon are complementary, their discrimination is accomplished by measurements giving rise to the appropriate oblique projector operator. The subspace onto which the operator should project is selected by nonlinear techniques in line with adaptive pursuit strategies

A Greedy Sparse Method Suitable for Spectral-Line Estimation

Rapport interne de GIPSA-labThis letter presents a variant of Matching Pursuit (MP) method for compressive sensing and sparse signal reconstruction. As an extension of MP, the proposed algorithm incorporates a new backward technique to maintain or replace the previous selected atoms in the case of coherent dictionaries. Computer simulations using Fourier dictionaries are conducted to show the effectiveness of the proposed method compared to some other sparse approximation methods

Sparse Representation of Astronomical Images

Sparse representation of astronomical images is discussed. It is shown that a significant gain in sparsity is achieved when particular mixed dictionaries are used for approximating these types of images with greedy selection strategies. Experiments are conducted to confirm: i)Effectiveness at producing sparse representations. ii)Competitiveness, with respect to the time required to process large images.The latter is a consequence of the suitability of the proposed dictionaries for approximating images in partitions of small blocks.This feature makes it possible to apply the effective greedy selection technique Orthogonal Matching Pursuit, up to some block size. For blocks exceeding that size a refinement of the original Matching Pursuit approach is considered. The resulting method is termed Self Projected Matching Pursuit, because is shown to be effective for implementing, via Matching Pursuit itself, the optional back-projection intermediate steps in that approach.Comment: Software to implement the approach is available on http://www.nonlinear-approx.info/examples/node1.htm

Sparse Representations & Compressed Sensing with application to the problem of Direction-of-Arrival estimation.

PhDThe significance of sparse representations has been highlighted in numerous signal processing applications ranging from denoising to source separation and the emerging field of compressed sensing has provided new theoretical insights into the problem of inverse systems with sparsity constraints. In this thesis, these advances are exploited in order to tackle the problem of direction-of-arrival (DOA) estimation in sensor arrays. Assuming spatial sparsity e.g. few sources impinging on the array, the problem of DOA estimation is formulated as a sparse representation problem in an overcomplete basis. The resulting inverse problem can be solved using typical sparse recovery methods based on convex optimization i.e. `1 minimization. However, in this work a suite of novel sparse recovery algorithms is initially developed, which reduce the computational cost and yield approximate solutions. Moreover, the proposed algorithms of Polytope Faces Pursuits (PFP) allow for the induction of structured sparsity models on the signal of interest, which can be quite beneficial when dealing with multi-channel data acquired by sensor arrays, as it further reduces the complexity and provides performance gain under certain conditions. Regarding the DOA estimation problem, experimental results demonstrate that the proposed methods outperform popular subspace based methods such as the multiple signal classification (MUSIC) algorithm in the case of rank-deficient data (e.g. presence of highly correlated sources or limited amount of data) for both narrowband and wideband sources. In the wideband scenario, they can also suppress the undesirable effects of spatial aliasing. However, DOA estimation with sparsity constraints has its limitations. The compressed sensing requirement of incoherent dictionaries for robust recovery sets limits to the resolution capabilities of the proposed method. On the other hand, the unknown parameters are continuous and therefore if the true DOAs do not belong to the predefined discrete set of potential locations the algorithms' performance will degrade due to errors caused by mismatches. To overcome this limitation, an iterative alternating descent algorithm for the problem of off-grid DOA estimation is proposed that alternates between sparse recovery and dictionary update estimates. Simulations clearly illustrate the performance gain of the algorithm over the conventional sparsity approach and other existing off-grid DOA estimation algorithms.EPSRC Leadership Fellowship EP/G007144/1; EU FET-Open Project FP7-ICT-225913