Compressed sensing Export

@article{donoho2006CS, abstract = {Suppose x is an unknown vector in R m (depending on context, a digital image or signal); we plan to acquire data and then reconstruct. Nominally this 'should ' require m samples. But suppose we know a priori that x is compressible by transform coding with a known transform, and we are allowed to acquire data about x by measuring n general linear functionals – rather than the usual pixels. If the collection of linear functionals is well-chosen, and we allow for a degree of reconstruction error, the size of n can be dramatically smaller than the size m usually considered necessary. Thus, certain natural classes of images with m pixels need only n = O(m 1/4 log 5/2 (m)) nonadaptive nonpixel samples for faithful recovery, as opposed to the usual m pixel samples. Our approach is abstract and general. We suppose that the object has a sparse representation in some orthonormal basis (eg. wavelet, Fourier) or tight frame (eg curvelet, Gabor), meaning that the coefficients belong to an ℓ p ball for 0 \< p ≤ 1. This implies that the N most important coefficients in the expansion allow a reconstruction with ℓ 2 error O(N 1/2−1/p). It is possible to design n = O(N log(m)) nonadaptive measurements which}, author = {Donoho, David L.}, citeulike-article-id = {6017903}, citeulike-linkout-0 = {http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.95.3320}, journal = {IEEE Trans. Inform. Theory}, keywords = {2006, cs}, pages = {1289--1306}, posted-at = {2009-10-28 10:10:25}, priority = {2}, title = {Compressed sensing}, url = {http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.95.3320}, volume = {52}, year = {2006} }

TY - JOUR ID - donoho2006CS L3 - citeulike-article-id:6017903 N2 - Suppose x is an unknown vector in R m (depending on context, a digital image or signal); we plan to acquire data and then reconstruct. Nominally this ‘should ’ require m samples. But suppose we know a priori that x is compressible by transform coding with a known transform, and we are allowed to acquire data about x by measuring n general linear functionals – rather than the usual pixels. If the collection of linear functionals is well-chosen, and we allow for a degree of reconstruction error, the size of n can be dramatically smaller than the size m usually considered necessary. Thus, certain natural classes of images with m pixels need only n = O(m 1/4 log 5/2 (m)) nonadaptive nonpixel samples for faithful recovery, as opposed to the usual m pixel samples. Our approach is abstract and general. We suppose that the object has a sparse representation in some orthonormal basis (eg. wavelet, Fourier) or tight frame (eg curvelet, Gabor), meaning that the coefficients belong to an ℓ p ball for 0 < p ≤ 1. This implies that the N most important coefficients in the expansion allow a reconstruction with ℓ 2 error O(N 1/2−1/p). It is possible to design n = O(N log(m)) nonadaptive measurements which JF - IEEE Trans. Inform. Theory EP - 1306 TI - Compressed sensing VL - 52 SP - 1289 KW - 2006 KW - cs AU - Donoho, David PY - 2006/// UR - http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.95.3320 ER -