Embedding prior knowledge within compressed sensing by neural networks.
ABSTRACT In the compressed sensing framework, different algorithms have been proposed for sparse signal recovery from an incomplete set of linear measurements. The most known can be classified into two categories: l(1) norm minimization-based algorithms and l(0) pseudo-norm minimization with greedy matching pursuit algorithms. In this paper, we propose a modified matching pursuit algorithm based on the orthogonal matching pursuit (OMP). The idea is to replace the correlation step of the OMP, with a neural network. Simulation results show that in the case of random sparse signal reconstruction, the proposed method performs as well as the OMP. Complexity overhead, for training and then integrating the network in the sparse signal recovery is thus not justified in this case. However, if the signal has an added structure, it is learned and incorporated in the proposed new OMP. We consider three structures: first, the sparse signal is positive, second the positions of the non zero coefficients of the sparse signal follow a certain spatial probability density function, the third case is a combination of both. Simulation results show that, for these signals of interest, the probability of exact recovery with our modified OMP increases significantly. Comparisons with l(1) based reconstructions are also performed. We thus present a framework to reconstruct sparse signals with added structure by embedding, through neural network training, additional knowledge to the decoding process in order to have better performance in the recovery of sparse signals of interest.
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ABSTRACT: A novel model is presented to learn bimodally informative structures from audio-visual signals. The signal is represented as a sparse sum of audio-visual kernels. Each kernel is a bimodal function consisting of synchronous snippets of an audio waveform and a spatio-temporal visual basis function. To represent an audio-visual signal, the kernels can be positioned independently and arbitrarily in space and time. The proposed algorithm uses unsupervised learning to form dictionaries of bimodal kernels from audio-visual material. The basis functions that emerge during learning capture salient audio-visual data structures. In addition, it is demonstrated that the learned dictionary can be used to locate sources of sound in the movie frame. Specifically, in sequences containing two speakers, the algorithm can robustly localize a speaker even in the presence of severe acoustic and visual distracters.IEEE Transactions on Neural Networks 12/2009; 20(12):1898-910. · 2.95 Impact Factor
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ABSTRACT: It is now well understood that (1) it is possible to reconstruct sparse signals exactly from what appear to be highly incomplete sets of linear measurements and (2)that this can be done by constrained ℓ 1 minimization. In this paper, we study a novel method for sparse signal recovery that in many situations outperforms ℓ 1 minimization in the sense that substantially fewer measurements are needed for exact recovery. The algorithm consists of solving a sequence of weighted ℓ 1-minimization problems where the weights used for the next iteration are computed from the value of the current solution. We present a series of experiments demonstrating the remarkable performance and broad applicability of this algorithm in the areas of sparse signal recovery, statistical estimation, error correction and image processing. Interestingly, superior gains are also achieved when our method is applied to recover signals with assumed near-sparsity in overcomplete representations—not by reweighting the ℓ 1 norm of the coefficient sequence as is common, but by reweighting the ℓ 1 norm of the transformed object. An immediate consequence is the possibility of highly efficient data acquisition protocols by improving on a technique known as Compressive Sensing.Journal of Fourier Analysis and Applications 04/2012; 14(5):877-905. · 1.08 Impact Factor
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ABSTRACT: In this article, the authors present a new approach to building simpler, smaller, and cheaper digital cameras that can operate efficiently across a broader spectral range than conventional silicon-based cameras. The approach fuses a new camera architecture based on a digital micromirror device with the new mathematical theory and algorithms of compressive sampling.IEEE Signal Processing Magazine 04/2008; · 3.37 Impact Factor