Locally Permuted Low Rank Column-wise Sensing

Ahmed Ali Abbasi; Namrata Vaswani

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arXiv · 2509.09820

Locally Permuted Low Rank Column-wise Sensing

Ahmed Ali Abbasi·Namrata Vaswani

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Abstract

We precisely formulate, and provide a solution for, the Low Rank Columnwise Sensing (LRCS) problem when some of the observed data is scrambled/permuted/unlabeled. This problem, which we refer to as permuted LRCS, lies at the intersection of two distinct topics of recent research: unlabeled sensing and low rank column-wise (matrix) sensing. We introduce a novel generalization of the recently developed Alternating Gradient Descent and Minimization (AltGDMin) algorithm to solve this problem. We also develop an alternating minimization (AltMin) solution. We show, using simulation experiments, that both converge but PermutedAltGDmin is much faster than Permuted-AltMin.

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Ahmed Ali Abbasi, Namrata Vaswani. 2025-09-11. Locally Permuted Low Rank Column-wise Sensing. https://arxiv.org/abs/2509.09820

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