Adaptive Block Sparse Regularization Under Arbitrary Linear Transform

We propose a convex signal recovery method for block sparsity under arbitrary linear transform with unknown block structure. The proposed method is a generalization of an adaptive block sparse regularization named LOP-l2/l1 and enables us to apply LOP-l2/l1 into different domain under non-invertible linear transform. 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 the proposed method and provide conditions for its convergence to the optimal solution. Numerical experiments demonstrate the effectiveness of the proposed method for signal and image recovery.