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The authors introduce a joint decoding method for compressive sensing that can simultaneously exploit sparsity of individual components of a composite signal. Their method can significantly reduce the total number of variables decoded jointly by separating variables of large magnitudes in one domain and using only these variables to represent the domain. Furthermore, they enhance the separation accuracy by using joint decoding across multiple domains iteratively. This separation-based approach improves the decoding time and quality of the recovered signal. They demonstrate these benefits analytically and by presenting empirical results.
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