Sparsity and persistence: mixed norms provide simple signal models with dependent coefficients

nombre de pages : 14International audienceSparse regression often uses $\ell_p$ norm priors (with p<2). This paper demonstrates that the introduction of mixed-norms in such contexts allows one to go one step beyond in signal models, and promote some different, structured, forms of sparsity. It is shown that the particular case of $\ell_{1,2}$ and $\ell_{2,1}$ norms lead to new group shrinkage operators. Mixed norm priors are shown to be particularly efficient in a generalized basis pursuit denoising approach, and are also used in a context of morphological component analysis. A suitable version of the Block Coordinate Relaxation algorithm is derived for the latter. The group-shrinkage operators are then modified to overcome some limitations of the mixed-norms. The proposed group shrinkage operators are tested on simulated signals in specific situations, to illustrate their different behaviors. Results on real data are also used to illustrate the relevance of the approach

Time-frequency analysis based on split spectrum applied to audio and ultrasonic signals

This thesis was submitted for the award of Doctor of Philosophy and was awarded by Brunel University LondonSignal processing is a large subject with applications integral to a number of technological fields such as communication, audio, Voice over IP (VoIP), pattern recognition, sonar, radar, ultrasound and medical imaging. Techniques exist for the analysis, modelling, extraction, recognition and synthesis of signals of interest. The focus of this thesis is signal processing for acoustics (both sonic and ultrasonic). In the applications examined, signals of interest are usually incomplete, distorted and/or noisy. Therefore, reconstructing the signal, noise reduction and removal of any distortion/interference are the main goals of the signal processing techniques presented. The primary aim is to study and develop an advanced time-frequency signal processing technique for acoustic applications to enhance the quality of the signals. In the first part of the thesis, a technique is presented that models and maintains the correlation between temporal and spectral parameters of audio signals. A novel Packet Loss Concealment (PLC) method is developed with applications to VoIP, audio broadcasting, and streaming. The problem of modelling the time-varying frequency spectrum in the context of PLC is addressed, and a novel solution is proposed for tracking and using the temporal motion of spectral flow to reconstruct the signal. The proposed method utilises a Time-Frequency Motion (TFM) matrix representation of the audio signal, where each frequency is tagged with a motion vector estimate that is assessed by cross-correlation of the movement of spectral energy within sub-bands across time frames. The missing packets are estimated using extrapolation or interpolation algorithms using a TFM matrix and then inverse transformed to the time-domain for reconstruction of the signal. The proposed method is compared with conventional approaches using objective Performance Evaluation of Speech Quality (PESQ), and subjective Mean Opinion Scores (MOS) in a range of packet loss from 5% to 20%. The evaluation results demonstrate that the proposed algorithm substantially improves performance by an average of 2.85% and 5.9% in terms of PESQ and MOS respectively. In the second part of the thesis, the proposed method is extended and modified to address challenges of excessive coherent noise arising from ultrasonic signals gathered during Guided Wave Testing (GWT). It is an advanced Non-destructive testing technique which is used over several branches of industry to inspect large structures for defects where the structural integrity is of concern. In such systems, signal interpretation can often be challenging due to the multi-modal and dispersive propagation of Ultrasonic Guided Waves (UGWs). The multi-modal and dispersive nature of the received signals hampers the ability to detect defects in a given structure. The Split-Spectrum Processing (SSP) method with application for such signal has been studied and reviewed quantitatively to measure the enhancement in terms of Signal-to-Noise Ratio (SNR) and spatial resolution. In this thesis, the influence of SSP filter bank parameters on these signals is studied and optimised to improve SNR and spatial resolution considerably. The proposed method is compared analytically and experimentally with conventional approaches. The proposed SSP algorithm substantially improves SNR by an average of 30dB. The conclusions reached in this thesis will contribute to the progression of the GWT technique through considerable improvement in defect detection capability.Centre for Electronic Systems Research (CESR) of Brunel University London, The National Structural Integrity Research Centre (NSIRC) and TWI Ltd

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