Distributed Compressive Sensing: A Deep Learning Approach

TL;DR

This paper introduces a deep learning-based method using LSTM to improve the reconstruction of sparse vectors in distributed compressive sensing, especially when their dependencies are unknown, outperforming traditional methods.

Contribution

It proposes a novel LSTM-based model to estimate conditional probabilities for sparse vector recovery without assuming joint sparsity, enhancing reconstruction accuracy.

Findings

Significantly outperforms SOMP and Bayesian methods in experiments.

Does not increase encoding complexity, only at the decoder.

Effective when training data is available for learning dependencies.

Abstract

Various studies that address the compressed sensing problem with Multiple Measurement Vectors (MMVs) have been recently carried. These studies assume the vectors of the different channels to be jointly sparse. In this paper, we relax this condition. Instead we assume that these sparse vectors depend on each other but that this dependency is unknown. We capture this dependency by computing the conditional probability of each entry in each vector being non-zero, given the "residuals" of all previous vectors. To estimate these probabilities, we propose the use of the Long Short-Term Memory (LSTM)[1], a data driven model for sequence modelling that is deep in time. To calculate the model parameters, we minimize a cross entropy cost function. To reconstruct the sparse vectors at the decoder, we propose a greedy solver that uses the above model to estimate the conditional probabilities. By performing extensive experiments on two real world datasets, we show that the proposed method significantly outperforms the general MMV solver (the Simultaneous Orthogonal Matching Pursuit (SOMP)) and a number of the model-based Bayesian methods. The proposed method does not add any complexity to the general compressive sensing encoder. The trained model is used just at the decoder. As the proposed method is a data driven method, it is only applicable when training data is available. In many applications however, training data is indeed available, e.g. in recorded images and videos.