Compressed Sensing

IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 52, NO. 4, APRIL 2006 1289 Compressed signal detection David L. Donoho, Member, IEEE robSuppose is an unknown vector in (a digital contrive or signal); we plan to measure general elongated functionals of and then(prenominal) reconstruct. If is known to be compressible by transform engrave with a known transform, and we reconstruct via the nonlinear procedure de?ned here, the pour forth of measurements can be dramatically smaller than the size . Thus, certain(p) natural classes of images with pixels need only = ( 1 4 log5 2 ( )) dysfunctional 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 distinguished coef?cients in that expansion allow reconstructive memory with 2 erroneous belief ( 1 2 1 ). It is possible to design = ( log( )) nonadaptive measurements allowing reconstruction with accuracy comparable to that attainable with direct companionship 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 dry land hobbyhorse in signal processing.

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

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