Adaptive Block Sparse Regularization under Arbitrary Linear Transform
This work addresses a domain-specific problem in signal processing by broadening the scope of block sparse regularization for more versatile applications, though it appears incremental as it generalizes an existing method.
The paper tackles the problem of signal reconstruction for block sparsity under arbitrary linear transforms with unknown block structure, proposing a convex and fast method that generalizes existing approaches and works with non-invertible transforms, with numerical experiments demonstrating its effectiveness.
We propose a convex and fast signal reconstruction method for block sparsity under arbitrary linear transform with unknown block structure. The proposed method is a generalization of the similar existing method and can reconstruct signals with block sparsity under non-invertible transforms, unlike the existing method. Our work broadens the scope of block sparse regularization, enabling more versatile and powerful applications across various signal processing domains. We derive an iterative algorithm for solving proposed method and provide conditions for its convergence to the optimal solution. Numerical experiments demonstrate the effectiveness of the proposed method.