Compressed Sensing

IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 52, NO. 4, APRIL 2006 1289 Compressed perception David L. Donoho, Member, IEEE robSuppose is an unknown vector in (a digital contrive or signal); we plan to measure general one-dimensional functionals of and then(prenominal) reconstruct. If is known to be compressible by transform figure with a known transform, and we reconstruct via the nonlinear procedure de?ned here, the lay of measurements can be dramatically smaller than the size . Thus, sure natural classes of images with pels need only = ( 1 4 log5 2 ( )) nonadaptive nonpixel samples for faithful recovery, as opposed to the usual pixel samples. More speci?cally, suppose has a sparse representation in some orthonormal basis (e.g., wavelet, Fourier) or tight frame (e.g., curvelet, Gabor)so the coef?cients belong to an ball for 0 1. The closely main(prenominal) coef?cients in that expansion allow reconstructive memory with 2 hallucination ( 1 2 1 ). It is possi ble to design = ( log( )) nonadaptive measurements allowing reconstruction with accuracy comparable to that attainable with direct familiarity of the most important coef?cients. Moreover, a good approximation to those important coef?cients is extracted from the measurements by solving a linear program root word hobbyhorse in signal processing.

The nonadaptive measurements have the slip of ergodic linear combinations of basis/frame elements. Our results use the notions of optimal recovery, of -widths, and information-based complexity. We depend the colloidal gelfand -widths of balls in high-dimensional Euclidean space in the teddy 0 1, and give a criterio! n identifying near-optimal subspaces for Gelfand -widths. We extract that most subspaces are near-optimal, and show that convex optimization (Basis Pursuit) is a near-optimal way to extract information derived from these near-optimal subspaces. Index price adaptative sampling, almost-spherical sections of Banach spaces, Basis Pursuit, eigenvalues of random matrices, Gelfand -widths, information-based...If you want to sign on a full essay, order it on our website: BestEssayCheap.com

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