Learning the weight matrix for sparsity averaging in compressive imaging

We propose to map the fast iterative soft thresholding algorithm to a deep neural network (DNN), with a sparsity prior in a concatenation of wavelet bases, in the context of compressive imaging. We exploit the DNN architecture to learn the optimal weight matrix of the corresponding reweighted ℓ
₁
-minimization problem. We later use the learned weight matrix for the image reconstruction process, which is recast as a simple ℓ
₁
-minimization problem. The approach, denoted as learned extended FISTA, shows promising results in terms of image quality, compared to state-of-the art algorithms, and significantly reduces the reconstruction time required to solve the reweighted ℓ
₁
-minimization problem.