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

PaFiMoCS: Particle Filtered Modified-CS and Applications in Visual Tracking across Illumination Change