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A regularized sparse representation method. (Chinese. English summary) Zbl 1349.94096

Summary: We propose a regularized method to sparsely represent signals using a given dictionary. Our method differs from the widely used models in the literatures in two respects. Firstly, we directly use the \(\ell_0\) norm rather than the alternative \(\ell_1\) norm to measure the sparsity in the model. Secondly, we add a regularization term to the model to select an optimal representation from all of the possible representation ways that can approximately attain the sparsity. The frame potential is used in the regularization term to measure the quality of the selected atoms. We use the twice continuously differentiable and concave functions to approximate the \(\ell_0\) norm in the proposed model and develop a minimization algorithm. Our numerical experiments demonstrate that the proposed method can represent the signals using the atoms with less mutual coherence than the widely used models.

MSC:

94A12 Signal theory (characterization, reconstruction, filtering, etc.)
42C15 General harmonic expansions, frames
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