Compressed Sensing

IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 52, NO. 4, APRIL 2006 1289 Compressed detecting David L. Donoho, Member, IEEE robSuppose is an unknown vector in (a digital contrive or signal); we plan to measure general linear functionals of and then(prenominal) reconstruct. If is known to be compressible by transform jurisprudence with a known transform, and we reconstruct via the nonlinear procedure de?ned here, the sink of measurements can be dramatically smaller than the size . Thus, incontestable natural classes of images with picture elements 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 cardinal coef?cients in that expansion allow reconstructive memory with 2 error ( 1 2 1 ). It is poss ible to design = ( log( )) nonadaptive measurements allowing reconstruction with accuracy comparable to that attainable with direct intimacy 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 primer coat hobbyhorse in signal processing.

The nonadaptive measurements have the suit of ergodic linear combinations of basis/frame elements. Our results use the notions of optimum recovery, of -widths, and information-based complexity. We depend the jellyfand -widths of balls in high-dimensional Euclidean space in the ted dy 0 1, and give a criterion identifying nea! r-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 scathe adaptative sampling, almost-spherical sections of Banach spaces, Basis Pursuit, eigenvalues of random matrices, Gelfand -widths, information-based...If you want to enamor a full essay, order it on our website: OrderCustomPaper.com

If you want to get a full essay, visit our page: write my paper