Deblurring Images by Huber Lasso
Mustafa Çelebi Pınar, Emre Can Yayla · 2025
We propose a proximal-gradient deblurring method that replaces the least-squares data term in FISTA with the Huber loss and augments it with momentum acceleration. The resulting algorithms, called HISTA and FHISTA, combine robust Huber fidelity with an absolute value sparsity penalty and Nesterov-style extrapolation. Experiments on twelve benchmark images blurred by a Gaussian kernel and contaminated with Gaussian noise show that FHISTA improves PSNR by roughly five decibels over classical ISTA. The method is easy to implement, uses a modest number of hyper-parameters, and demonstrates strong resilience to outliers.