  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.
