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Abstract: We study the problem of sparse reconstruction from noisy undersampledmeasurements when the following two things are available. 1 We are givenpartial, and partly erroneous, knowledge of the signal-s support, denoted by$T$. 2 We are also given an erroneous estimate of the signal values on $T$,denoted by $\hat{\mu} T$. In practice, both these may be available fromavailable prior knowledge. Alternatively, in recursive reconstructionapplications, like real-time dynamic MRI, one can use the support estimate andthe signal value estimate from the previous time instant as $T$ and$\hat{\mu} T$. In this work, we introduce regularized modified-BPDNreg-mod-BPDN and obtain computable bounds on its reconstruction error.Reg-mod-BPDN tries to find the signal that is sparsest outside the set $T$,while being -close enough- to $\hat{\mu} T$ on $T$ and while satisfying thedata constraint. Corresponding results for modified-BPDN and BPDN follow asdirect corollaries. A second key contribution is an approach to obtaincomputable error bounds that hold without any sufficient conditions. This makesit easy to compare the bounds for the various approaches. Empiricalreconstruction error comparisons with many existing approaches are alsoprovided.



Autor: Wei Lu, Namrata Vaswani

Fuente: https://arxiv.org/







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