Kalman filtered Compressed Sensing

We consider the problem of reconstructing time sequences of spatially sparse signals (with unknown and time-varying sparsity patterns) from a limited number of linear "incoherent" measurements, in real-time. The signals are sparse in some transform domain referred to as the sparsity basis. For a single spatial signal, the solution is provided by Compressed Sensing (CS). The question that we address is, for a sequence of sparse signals, can we do better than CS, if (a) the sparsity pattern of the signal's transform coefficients' vector changes slowly over time, and (b) a simple prior model on the temporal dynamics of its current non-zero elements is available. The overall idea of our solution is to use CS to estimate the support set of the initial signal's transform vector. At future times, run a reduced order Kalman filter with the currently estimated support and estimate new additions to the support set by applying CS to the Kalman innovations or filtering er...

• Type: Conference
• Year: 2008
• Where: ICIP
• Authors: Namrata Vaswani
• Keywords: ICIP 2008, Image Processing, Reduced Order Kalman, Sparse Signals, Sparsity Basis, Sparsity Pattern, Time-varying Sparsity Patterns