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We present an anisotropic mesh denoising algorithm that is effective, simple and fast. This is accomplished by filtering vertices of the mesh in the normal direction using local neighborhoods. Motivated by the impressive results of bilateral filtering for image denoising, we adopt it to denoise 3D meshes; addressing the specific issues required in the(More)
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)
Finding the sparsest solution to underdetermined systems of linear equations <i>y</i> = &#x03A6;<sub>x</sub> is NP-hard in general. We show here that for systems with &#x201C;typical&#x201D;/&#x201C;random&#x201D; &#x03A6;, a good approximation to the sparsest solution is obtained by applying a fixed number of standard operations from linear algebra. Our(More)
We describe multiscale representations for data observed on equispaced grids and taking values in manifolds such as the sphere S2, the special orthogonal group SO(3), the positive definite matrices SPD(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)
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)
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)
Recently, the notions of Compressed Sensing and Compressive Sampling have attracted attention as an innovative concept in signal processing. Compressed sensing proposes that, when dealing with signals which are highly compressible in a known basis, for example in a wavelet basis, one can dispense with traditional sampling and instead take a small number of(More)
Object segmentation in image sequences is one of the fundamental problems in computer vision and graphics. This problem is usually addressed either by discrete representations which are currently manifested by graph partitioning techniques, or by continuous methods typically referred to as active contours. In this work we take a unified approach by fitting(More)
Many applications in signal processing lead to the optimization problems min parxpar<sub>1</sub> subject to y = Ax, and min parxpar<sub>1</sub> subject to pary - Axpar les epsi, where A is a given d times n matrix, d &lt; n, and y is a given n times 1 vector. In this work we consider l<sub>1</sub> minimization by using LARS, Lasso, and homotopy methods(More)