Abstract
A greedy algorithm used for the recovery of sparse signals, multiple orthogonal least squares (MOLS) have recently attracted quite a big of attention. In this paper, we consider the number of iterations required for the MOLS algorithm for recovery of a K-sparse signal x ∈ ℝn. We show that MOLS provides stable reconstruction of all K-sparse signals x from y = Ax + w in \(\left\lceil {{{6K} \over M}} \right\rceil \) iterations when the matrix A satisfies the restricted isometry property (RIP) with isometry constant δ7K ≤ 0.094. Compared with the existing results, our sufficient condition is not related to the sparsity level K.
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This work was partially supported by the National Natural Science Foundation of China (61907014, 11871248, 11701410, 61901160), Youth Science Foundation of Henan Normal University (2019QK03).
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Li, H., Zhang, J. A New Sufficient Condition for Sparse Recovery with Multiple Orthogonal Least Squares. Acta Math Sci 42, 941–956 (2022). https://doi.org/10.1007/s10473-022-0308-4
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DOI: https://doi.org/10.1007/s10473-022-0308-4
Key words
- Sparse signal recovery
- multiple orthogonal least squares (MOLS)
- sufficient condition
- restricted isometry property (RIP)