Confirmnet: Convolutional Firmnet And Application To Image Denoising And Inpainting

We address the problem of efficient convolutional sparse coding (CSC) and develop a non-convex-penalty-regularized CSC formulation, namely, minimax-concave CSC (MC2SC). MC2SC leads to an optimal sparse representation than the standard ell_1-penalty based approach. In addition, suitable convergence guarantees can also be provided for MC2SC. We propose a convolutional iterative firm-thresholding algorithm (CIFTA) building on our previously proposed IFTA, and its deep-unfolded version, namely, convolutional-FirmNet (ConFirmNet). As an application, we develop the ConFirmNet based sparse autoencoder (ConFirmNet-SAE) for learning an application-specific convolutional dictionary, the applications being image denoising and inpainting. Further, we also show that training ConFirmNet-SAE with the Huber loss imparts robustness to outliers. It also turns out that ConFirmNet-SAE is robust to mismatch between training and test noise conditions than convolutional learned iterative soft-thresholding algorithm (LISTA).