Projected Improved Fista And Application To Image Deblurring

Abstract

The analysis-sparse model has been shown to be efficient as compared to the synthesis-sparse model when the sparsifying transform is redundant particularly for image restoration applications. We pose the image deblurring problem as an optimization problem based on the analysis-sparse model considering the sparsifying basis to be a tight frame, more specifically, the shift-invariant discrete wavelet transform (SIDWT). We propose two algorithms, namely, projected improved fast iterative soft-thresholding algorithm (piFISTA) and projected improved fast iterative soft-thresholding algorithm beyond Nesterov’s momentum (piFISTA-BN). The proposed algorithms are the analysis counterparts of the improved fast iterative soft-thresholding algorithm (iFISTA) and improved fast iterative soft-thresholding algorithm beyond Nesterov’s momentum (iFISTA-BN), respectively, both of which consider the synthesis-sparse model. We demonstrate that piFISTA and piFISTA-BN significantly outperform FISTA, pFISTA, iFISTA, and iFISTA-BN considering standard objective metrics such as peak signal-to-noise ratio (PSNR) and structural similarity index metric (SSIM). Further, we demonstrate empirically that the proposed algorithms converge faster than the state-of-the-art techniques.