2013/03/05 by Chenlu Qiu, Qiu, Chenlu, Namrata Vaswani +1
Computer Science · Engineering · Mathematics · Physics and Astronomy · #FOS: Computer and information sciences #Information Theory (cs.IT) #Microwave Imaging and Scattering Analysis #Random lasers and scattering media #Sparse and Compressive Sensing Techniques #cs.IT #math.IT
paper · pdf · doi:10.48550/arxiv.1303.1144
arxiv created 2013/03/05 · openalex publication_date 2013/03/05 · arxiv updated 2013/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the problem of recursively recovering a time sequence of sparse vectors, St, from measurements Mt := St + Lt that are corrupted by structured noise Lt which is dense and can have large magnitude. The structure that we require is that Lt should lie in a low dimensional subspace that is either fixed or changes "slowly enough"; and the eigenvalues of its covariance matrix are "clustered". We do not assume any model on the sequence of sparse vectors. Their support sets and their nonzero element values may be either independent or correlated over time (usually in many applications they are correlated). The only thing required is that there be some support change every so often. We introduce a novel solution approach called Recursive Projected Compressive Sensing with cluster-PCA (ReProCS-cPCA) that addresses some of the limitations of earlier work. Under mild assumptions, we show that, with high probability, ReProCS-cPCA can exactly recover the support set of St at all times; and the reconstruction errors of both St and Lt are upper bounded by a time-invariant and small value.