Kaiqun Hu, Xin Feng, Journal of Information Processing Systems Vol. 16, No. 1, pp. 30-41, Feb. 2020  

https://doi.org/10.3745/JIPS.01.0048
Keywords: Curvelets, Spilt Bergman Iteration, sparse representation, Wave Atoms
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Abstract

Lines and textures are natural properties of the surface of natural objects, and their images can be sparsely represented in suitable frames such as wavelets, curvelets and wave atoms. Based on characteristics that the curvelets framework is good at expressing the line feature and wavesat is good at representing texture features, we propose a model for the weighted sparsity constraints of the two frames. Furtherly, a multi-step iterative fast algorithm for solving the model is also proposed based on the split Bergman method. By introducing auxiliary variables and the Bergman distance, the original problem is transformed into an iterative solution of two simple sub-problems, which greatly reduces the computational complexity. Experiments using standard images show that the split-based Bergman iterative algorithm in hybrid domain defeats the traditional Wavelets framework or curvelets framework both in terms of timeliness and recovery accuracy, which demonstrates the validity of the model and algorithm in this paper.

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