Framework for Segmented threshold ℓ₀ gradient approximation based network for sparse signal recovery

Signal reconstruction from compressed sensed data need iterative methods since the sparse measurement matrix is analytically non invertible. The iterative thresholding and ℓ₀ function minimization are of special interest as these two operations provide sparse solution. However these methods need an inverse operation corresponding to the measurement matrix for estimating the reconstruction error. The pseudo-inverse of the measurement matrix is used in general for this purpose. Here a sparse signal recovery framework using an approximate inverse matrix Q and iterative segment thresholding of ℓ₀ and ℓ₁ norm with residue addition is presented. Two recovery algorithms are developed using this framework. The ℓ₀ based method is later developed to a basis function dictionary based network for sparse signal recovery. The proposed framework enables the users experiment with different inverse matrix to achieve better efficiency in sparse signal recovery and implement the algorithm in computationally efficient way.