  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.
