Alternating minimization algorithm with initialization analysis for r-local and k-sparse unlabeled sensing

11/14/2022

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by   Ahmed Abbasi, et al.

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The unlabeled sensing problem is to recover an unknown signal from permuted linear measurements. We propose an alternating minimization algorithm with a suitable initialization for the widely considered k-sparse permutation model. Assuming either a Gaussian measurement matrix or a sub-Gaussian signal, we upper bound the initialization error for the r-local and k-sparse permutation models in terms of the block size r and the number of shuffles k, respectively. Our algorithm is computationally scalable and, compared to baseline methods, achieves superior performance on real and synthetic datasets.