Dictionary Identification - Sparse Matrix-Factorisation via $\ell_1$-Minimisation
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The direct sparse matrix solver is based on a domain decomposition technique to achieve data and work parallelization. Geometries that have long and thin structures are specially efficiently tractable with this solver, provided that they can be decomposed ...
Natural images are often modeled through piecewise-smooth regions. Region edges, which correspond to the contours of the objects, become, in this model, the main information of the signal. Contours have the property of being smooth functions along the dire ...
In the present paper we propose a new framework for the construction of meaningful dictionaries for sparse representation of signals. The dictionary approach to coding and compression proves very attractive since decomposing a signal over a redundant set o ...
We derive a stable and fast solver for nonsymmetric linear systems of equations with shift structured coefficient matrices (e.g., Toeplitz, quasi-Toeplitz, and product of two Toeplitz matrices). The algorithm is based on a modified fast QR factorization of ...
Society for Industrial and Applied Mathematics1998
We develop an algorithm for the solution of indefinite least-squares problems. Such problems arise in robust estimation, filtering, and control, and numerically stable solutions have been lacking. The algorithm developed herein involves the QR factorizatio ...
Society for Industrial and Applied Mathematics1998
Compression efficiency is mainly driven by redundancy of the overcomplete set of functions chosen for the signal decomposition. In Matching Pursuit algorithms for example, the redundancy of the dictionary influences the convergence of the residual energy. ...
This paper presents a new image representation method based on anisotropic refinement. It has been shown that wavelets are not optimal to code 2-D objects which need true 2-D dictionaries for efficient approximation. We propose to use rotations and anisotr ...
