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Finding the sparsest solution to underdetermined systems of linear equations y = Φx is NP-hard in general. We show here that for systems with 'typical'/'random' Φ, a good approximation to the sparsest solution is obtained by applying a fixed number of standard operations from linear algebra. Our proposal, Stagewise Orthogonal Matching Pursuit (StOMP),(More)
We present a new method for completing missing parts caused by the removal of foreground or background elements from an image. Our goal is to synthesize a complete, visually plausible and coherent image. The visible parts of the image serve as a training set to infer the unknown parts. Our method iteratively approximates the unknown regions and composites(More)
We describe multiscale representations for data observed on equispaced grids and taking values in manifolds such as the sphere S 2 , the special orthogonal group SO(3), the positive definite matrices SP D(n), and the Grassmann manifolds G(n, k). The representations are based on the deployment of Deslauriers–Dubuc and average-interpolating pyramids " in the(More)
Many applications in signal processing lead to the optimization problems min x 1 subject to y = Ax, and min x 1 subject to y − Ax ≤ ε, where A is a given d times n matrix, d < n, and y is a given n × 1 vector. In this work we consider 1 minimization by using LARS, Lasso, and homotopy methods [1, 2, 3] (Efron et el., Tibshi-rani, Osborne et al.). While these(More)
Fast multidimensional NMR is important in chemical shift assignment and for studying structures of large proteins. We present the first method which takes advantage of the sparsity of the wavelet representation of the NMR spectra and reconstructs the spectra from partial random measurements of its free induction decay (FID) by solving the following(More)
A wide class of operations on images can be performed directly in the wavelet domain by operating on coefficients of the wavelet transforms of the images and other matrices defined by the operation. Operating in the wavelet domain enables to perform these operations progressively in a coarse-to-fine fashion, to operate on different resolutions, manipulate(More)
BACKGROUND We applied the Virtual Northern technique to human brain mRNA to systematically measure human mRNA transcript lengths on a genome-wide scale. METHODOLOGY/PRINCIPAL FINDINGS We used separation by gel electrophoresis followed by hybridization to cDNA microarrays to measure 8,774 mRNA transcript lengths representing at least 6,238 genes at high(More)