Stable Signal Reconstruction via $\ell^1$ -Minimization in Redundant, Non-Tight Frames
作者： Markus Haltmeier
关键词: Signal reconstruction 、 Minification 、 Mathematics 、 Orthonormal basis 、 Artificial intelligence 、 Compressed sensing 、 A priori and a posteriori 、 Signal transfer function 、 Image processing 、 Computer vision 、 System of linear equations
摘要: In many signal and image processing applications, a desired clean is distorted from blur noise. Reconstructing the usually yields to high dimensional ill-conditioned system of equations, where direct solution would severely amplify Stable reconstruction requires use regularization techniques, which incorporate priori knowledge about signal. A particular successful property for that purpose sparsity analysis coefficients in suitable frame or dictionary, can be implemented via l1 -minimization. Most existing stable recovery results l1-analysis minimization require an orthonormal basis. This contrasts practical redundant frames often perform better than bases. this paper we address issue derive redundant, possibly non-tight frames.
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