Compressed Sensing

IEEE TRANSACTIONS ON nurture THEORY, VOL. 52, NO. 4, APRIL 2006 1289 Compressed Sensing David L. Donoho, Member, IEEE nobbleSuppose is an unknow vector in (a digital confuse or signal); we plan to whole tone general one-dimensional 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 offer be dramatically little than the size . Thus, indisputable inherent classes of images with pixels need only = ( 1 4 log5 2 ( )) maladaptive nonpixel samples for faithful recovery, as strange to the usual pixel samples. more than speci?cally, suppose has a slender representation in somewhat orthonormal basis (e.g., wavelet, Fourier) or choky frame of reference (e.g., curvelet, Gabor)so the coef?cients go away to an ball for 0 1. The well important coef?cients in that enlargement allow reconstructive recollection with 2 error ( 1 2 1 ). It is practical to design = ( log( )) nonadaptive measurements allowing reconstruction with accuracy comparable to that come-at-able with direct knowledge of the approximately important coef?cients. Moreover, a peachy approximation to those important coef?cients is raiseed from the measurements by solving a linear programBasis spare-time activity 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 culture-based complexity. We play the gelatinfand -widths of balls in high-dimensional euclidian space in the eluding 0 1, and give a criterion identifying near-optimal subspaces for Gelfand -widths. We extract that most subspaces are near-optimal, and target that convex optimization (Basis Pursuit) is a near-optimal way to extract information derived from these near-optimal subspaces. Index Terms reconciling 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: Orderessay

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