Particle Filtered Modified Compressive Sensing (PaFiMoCS) for tracking signal sequences

In this paper, we propose a novel algorithm for recursive reconstruction of a time sequence of sparse signals from highly under-sampled random linear measurements. In our method, the idea of recently proposed regularized modified compressive sensing (reg-mod-CS) is merged with sequential Monte Carlo techniques like particle filtering. Reg-mod-CS facilitates sequential reconstruction by utilizing a partial knowledge of the support and previous signal estimates. Under the assumption of a dynamical model on the support, the sequential Monte Carlo step renders various possibilities of the current support and choose the most likely support given the current observation. The algorithm is similar in sprit to particle filter with mode tracker (PF-MT), where, the support could be considered to be the effective basis whereas the signal values on the current support could be considered to be the residual space; the difference being the fact that in our algorithm, the mode tracking step is replaced by the reg-mod-CS for each particle and the support is re-estimated from the residual part. We compare our algorithm with other techniques like traditional particle filtering, particle filter with mode tracker (PFMT), static compressive sensing, modified compressive sensing, regularized modified compressive sensing and weighted ℓ₁. We demonstrate that our algorithm outperforms all the other methods in terms of reconstruction accuracy for a simulated sequence of sparse signals.