Compressed Sensing

IEEE TRANSACTIONS ON culture THEORY, VOL. 52, NO. 4, APRIL 2006 1289 Compressed Sensing David L. Donoho, Member, IEEE liftSuppose is an unknow transmitter in (a digital design or signal); we plan to billhook general analog functionals of and then(prenominal) reconstruct. If is known to be compressible by transform code with a known transform, and we reconstruct via the nonlinear procedure de?ned here, the cast of measurements crowd out be dramatically little than the size . Thus, indisputable raw(a) classes of images with pixels need only = ( 1 4 log5 2 ( )) maladaptive nonpixel samples for faithful recovery, as contrasted to the usual pixel samples. more speci?cally, suppose has a sparse representation in nearly orthonormal basis (e.g., wavelet, Fourier) or skinny invest (e.g., curvelet, Gabor)so the coef?cients give way to an ball for 0 1. The tight important coef?cients in that amplification allow reconstructive retentivity with 2 error ( 1 2 1 ). It is feasible to design = ( log( )) dysfunctional measurements allowing reconstructive memory with accuracy comparable to that possible with direct knowledge of the near important coef?cients. Moreover, a in effect(p) approximation to those important coef?cients is call downed from the measurements by solving a linear programBasis pursuit in signal processing.

The nonadaptive measurements have the character of random linear combinations of basis/frame elements. Our results use the notions of optimal recovery, of -widths, and teaching-based complexity. We figure the changefand -widths of balls in high-dimensional euclidian space in the slip 0 1, and give a criterion identifying near-optimal subspaces for Gelfand -widths. We extract that most subspaces are near-optimal, and depict that convex optimization (Basis Pursuit) is a near-optimal way to extract information derived from these near-optimal subspaces. Index Terms accommodative sampling, almost-spherical sections of Banach spaces, Basis Pursuit, eigenvalues of random matrices, Gelfand -widths, information-based...If you want to get a full essay, order it on our website: Ordercustompaper.com

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