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arXiv · 2111.09801

Theoretical Linear Convergence of Deep Unfolding Network for Block-Sparse Signal Recovery

Rong Fu·Vincent Monardo·Tianyao Huang·Yimin Liu
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Abstract

In this paper, we consider the recovery of the high-dimensional block-sparse signal from a compressed set of measurements, where the non-zero coefficients of the recovered signal occur in a small number of blocks. Adopting the idea of deep unfolding, we explore the block-sparse structure and put forward a block-sparse reconstruction network named Ada-BlockLISTA, which performs gradient descent on every single block followed by a block-wise shrinkage. Furthermore, we prove the linear convergence rate of our proposed network, which also theoretically guarantees exact recovery for a potentially higher sparsity level based on underlyingblock structure. Numerical results indicate that Ada-BlockLISTA yields better signal recovery performance compared with existing algorithms, which ignore the additional block structure in the signal model.

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Rong Fu, Vincent Monardo, Tianyao Huang, Yimin Liu. 2021-11-18. Theoretical Linear Convergence of Deep Unfolding Network for Block-Sparse Signal Recovery. https://arxiv.org/abs/2111.09801

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