Confirmnet: Convolutional Firmnet and Application to Image Denoising and Inpainting
Praveen Kumar Pokala, Prakash Kumar Uttam, Chandra Sekhar Seelamantula
Abstract
We address the problem of efficient convolutional sparse coding (CSC) and develop a non-convex-penalty-regularized CSC formulation, namely, minimax-concave CSC (MC <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> SC). MC <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> SC leads to an optimal sparse representation than the standard ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -penalty based approach. In addition, suitable convergence guarantees can also be provided for MC <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> SC. 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).
BibTeX
@inproceedings{icassp2020_confirmnetconvol,
title = {Confirmnet: Convolutional Firmnet and Application to Image Denoising and Inpainting},
author = {Praveen Kumar Pokala and Prakash Kumar Uttam and Chandra Sekhar Seelamantula},
booktitle = {ICASSP 2020},
year = {2020}
}