Bayesian inference for spatio-temporal spike-and-slab priors
This work addresses sparsity in inverse problems for domains like signal processing or imaging, but it is incremental as it builds on existing spike-and-slab methods.
The authors tackled the problem of solving underdetermined linear inverse problems with sparsity constraints by generalizing spike-and-slab priors to encode spatio-temporal correlations, and they developed an expectation propagation algorithm with approximations for efficiency, demonstrating results through numerical experiments on synthetic and real data.
In this work, we address the problem of solving a series of underdetermined linear inverse problems subject to a sparsity constraint. We generalize the spike-and-slab prior distribution to encode a priori correlation of the support of the solution in both space and time by imposing a transformed Gaussian process on the spike-and-slab probabilities. An expectation propagation (EP) algorithm for posterior inference under the proposed model is derived. For large scale problems, the standard EP algorithm can be prohibitively slow. We therefore introduce three different approximation schemes to reduce the computational complexity. Finally, we demonstrate the proposed model using numerical experiments based on both synthetic and real data sets.