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Compressed sensing (CS) has recently emerged as a powerful signal acquisition paradigm. In essence, CS enables the recovery of high-dimensional sparse signals from relatively few linear observations in the form of projections onto a collection of test vectors. Existing results show that if the entries of the test vectors are independent realizations of certain zero-mean random variables, then with...
Subsampled (or partial) Fourier matrices were originally introduced in the compressive sensing literature by Candes et al. Later, in papers by Candes and Tao and Rudelson and Vershynin, it was shown that (random) subsampling of the rows of many other classes of unitary matrices also yield effective sensing matrices. The key requirement is that the rows of U, the unitary matrix, must be highly incoherent...
A multi-step adaptive resampling procedure is proposed, and shown to be an effective approach when detecting high-dimensional sparse signals in noise. Each step of the proposed procedure refines an estimate of the true signal subspace, allowing sensing energy to be focused more directly into the subspace of interest and significantly improving the performance of the final detection test. Large-sample...
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