Kalman filtered Compressed Sensing

By Namrata Vaswani. 2008 15th IEEE International Conference on Image Processing, 2008

318 citations recorded by the source corpus.

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 error (whenever it is "large").

Subfields: Biomedical Engineering, Computational Mechanics, Radiology, Nuclear Medicine and Imaging

View Paper: https://www.semanticscholar.org/paper/193cdbb4613c7fd4c74229ea950b79589635d27f

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In Biomedical Engineering

In Computational Mechanics

In Radiology, Nuclear Medicine and Imaging

Citations in the corpus

Online Adaptive Estimation of Sparse Signals: Where RLS Meets the $\ell_1$ -Norm (2010, methodology): “Sparsity-aware “RLS-like” algorithms are reported in [2], while an effort to combine Kalman filtering and compressed sensing can be found in [26].”
Modified-CS: Modifying compressive sensing for problems with partially known support (2009, background): “CS-diff and LS-CS also have significantly nonzero error since the exact sparsity size of both the signal difference and the signal residual is equal to/larger than the signal’s sparsity size.”
Compressed Sensing for Wireless Communications: Useful Tips and Tricks (2015, background): “Further improvement in the recovery performance can be achieved by exploiting the statistical correlations between the signal amplitudes [101], [102], [108].”
Sparse Signal Recovery With Temporally Correlated Source Vectors Using Sparse Bayesian Learning (2011, background): “For example, one can classify sources into several groups, say G groups, and the sources in a group are all assigned by a common matrix B i ( i = 1 , · · · , G, G ≪ M ) as the covariance matrix (up to a scalar).”
Sparse Recovery of Streaming Signals Using $\ell_1$-Homotopy (2013, methodology): “Unlike previous approaches, we do not impose any restriction on the warm-start vector to be a solution of an `1 problem; as we can accommodate an arbitrary vector to initialize the homotopy update.”