  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.
