  We study the problem of tracking (causally estimating) a time sequence of
sparse spatial signals with changing sparsity patterns, as well as other
unknown states, from a sequence of nonlinear observations corrupted by
(possibly) non-Gaussian noise. In many applications, particularly those in
visual tracking, the unknown state can be split into a small dimensional part,
e.g. global motion, and a spatial signal, e.g. illumination or shape
deformation. The spatial signal is often well modeled as being sparse in some
domain. For a long sequence, its sparsity pattern can change over time,
although the changes are usually slow. To address the above problem, we propose
a novel solution approach called Particle Filtered Modified-CS (PaFiMoCS). The
key idea of PaFiMoCS is to importance sample for the small dimensional state
vector, while replacing importance sampling by slow sparsity pattern change
constrained posterior mode tracking for recovering the sparse spatial signal.
We show that the problem of tracking moving objects across spatially varying
illumination change is an example of the above problem and explain how to
design PaFiMoCS for it. Experiments on both simulated data as well as on real
videos with significant illumination changes demonstrate the superiority of the
proposed algorithm as compared with existing particle filter based tracking
algorithms.
