Oscillating Patterns in Image Processing and Nonlinear Evolution Equations: The Fifteenth Dean Jacqueline B. Lewis Memorial Lectures
Reproducible Research in Computational Harmonic Analysis
Computing in Science and Engineering
The discrete shearlet transform: a new directional transform and compactly supported shearlet frames
IEEE Transactions on Image Processing
Sparse and Redundant Representations: From Theory to Applications in Signal and Image Processing
Sparse and Redundant Representations: From Theory to Applications in Signal and Image Processing
Full length article: Compactly supported shearlets are optimally sparse
Journal of Approximation Theory
Image decomposition via the combination of sparse representations and a variational approach
IEEE Transactions on Image Processing
The contourlet transform: an efficient directional multiresolution image representation
IEEE Transactions on Image Processing
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In this paper, we present an image separation method for separating images into point- and curvelike parts by employing a combined dictionary consisting of wavelets and compactly supported shearlets utilizing the fact that they sparsely represent point and curvilinear singularities, respectively. Our methodology is based on the very recently introduced mathematical theory of geometric separation, which shows that highly precise separation of the morphologically distinct features of points and curves can be achieved by ℓ1 minimization. Finally, we present some experimental results showing the effectiveness of our algorithm, in particular, the ability to accurately separate points from curves even if the curvature is relatively large due to the excellent localization property of compactly supported shearlets.