Compressive Source Separation: Theory and Methods for Hyperspectral Imaging

With the development of numbers of high resolution data acquisition systems and the global requirement to lower the energy consumption, the development of efficient sensing techniques becomes critical. Recently, Compressed Sampling (CS) techniques, which exploit the sparsity of signals, have allowed to reconstruct signal and images with less measurements than the traditional Nyquist sensing approach. However, multichannel signals like Hyperspectral images (HSI) have additional structures, like inter-channel correlations, that are not taken into account in the classical CS scheme. In this paper we exploit the linear mixture of sources model, that is the assumption that the multichannel signal is composed of a linear combination of sources, each of them having its own spectral signature, and propose new sampling schemes exploiting this model to considerably decrease the number of measurements needed for the acquisition and source separation. Moreover, we give theoretical lower bounds on the number of measurements required to perform reconstruction of both the multichannel signal and its sources. We also proposed optimization algorithms and extensive experimentation on our target application which is HSI, and show that our approach recovers HSI with far less measurements and computational effort than traditional CS approaches.Comment: 32 page

Structured Sparsity Models for Multiparty Speech Recovery from Reverberant Recordings

We tackle the multi-party speech recovery problem through modeling the acoustic of the reverberant chambers. Our approach exploits structured sparsity models to perform room modeling and speech recovery. We propose a scheme for characterizing the room acoustic from the unknown competing speech sources relying on localization of the early images of the speakers by sparse approximation of the spatial spectra of the virtual sources in a free-space model. The images are then clustered exploiting the low-rank structure of the spectro-temporal components belonging to each source. This enables us to identify the early support of the room impulse response function and its unique map to the room geometry. To further tackle the ambiguity of the reflection ratios, we propose a novel formulation of the reverberation model and estimate the absorption coefficients through a convex optimization exploiting joint sparsity model formulated upon spatio-spectral sparsity of concurrent speech representation. The acoustic parameters are then incorporated for separating individual speech signals through either structured sparse recovery or inverse filtering the acoustic channels. The experiments conducted on real data recordings demonstrate the effectiveness of the proposed approach for multi-party speech recovery and recognition.Comment: 31 page

Inexact Gradient Projection and Fast Data Driven Compressed Sensing

We study convergence of the iterative projected gradient (IPG) algorithm for arbitrary (possibly nonconvex) sets and when both the gradient and projection oracles are computed approximately. We consider different notions of approximation of which we show that the Progressive Fixed Precision (PFP) and the $(1+\epsilon)$-optimal oracles can achieve the same accuracy as for the exact IPG algorithm. We show that the former scheme is also able to maintain the (linear) rate of convergence of the exact algorithm, under the same embedding assumption. In contrast, the $(1+\epsilon)$-approximate oracle requires a stronger embedding condition, moderate compression ratios and it typically slows down the convergence. We apply our results to accelerate solving a class of data driven compressed sensing problems, where we replace iterative exhaustive searches over large datasets by fast approximate nearest neighbour search strategies based on the cover tree data structure. For datasets with low intrinsic dimensions our proposed algorithm achieves a complexity logarithmic in terms of the dataset population as opposed to the linear complexity of a brute force search. By running several numerical experiments we conclude similar observations as predicted by our theoretical analysis

A temporal multiscale approach for MR Fingerprinting

Quantitative MRI (qMRI) is becoming increasingly important for research and clinical applications, however, state-of-the-art reconstruction methods for qMRI are computationally prohibitive. We propose a temporal multiscale approach to reduce computation times in qMRI. Instead of computing exact gradients of the qMRI likelihood, we propose a novel approximation relying on the temporal smoothness of the data. These gradients are then used in a coarse-to-fine (C2F) approach, for example using coordinate descent. The C2F approach was also found to improve the accuracy of solutions, compared to similar methods where no multiscaling was used.Comment: 4 pages, 3 figures. Title revise