Adaptive Weighted High Frequency Iterative Algorithm for Fractional-Order Total Variation with Nonlocal Regularization for Image Reconstruction

Abstract

<jats:p>We propose an adaptive weighted high frequency iterative algorithm for a fractional-order total variation (FrTV) approach with nonlocal regularization to alleviate image deterioration and to eliminate staircase artifacts, which result from the total variation (TV) method. The high frequency gradients are reweighted in iterations adaptively when we decompose the image into high and low frequency components using the pre-processing technique. The nonlocal regularization is introduced into our method based on nonlocal means (NLM) filtering, which contains prior image structural information to suppress staircase artifacts. An alternating direction multiplier method (ADMM) is used to solve the problem combining reweighted FrTV and nonlocal regularization. Experimental results show that both the peak signal-to-noise ratios (PSNR) and structural similarity index (SSIM) of reconstructed images are higher than those achieved by the other four methods at various sampling ratios less than 25%. At 5% sampling ratios, the gains of PSNR and SSIM are up to 1.63 dB and 0.0114 from ten images compared with reweighted total variation with nuclear norm regularization (RTV-NNR). The improved approach preserves more texture details and has better visual effects, especially at low sampling ratios, at the cost of taking more time.</jats:p>

Hybrid High-Order and Fractional-Order Total Variation with Nonlocal Regularization for Compressive Sensing Image Reconstruction

“…In this experiment, we compared the proposed method with several state-of-the-art algorithms: TVNLR [18], BCS-TV [21], TVAL3 [28], and two non-TV based algorithms: BCS-SPL [30] and MH-BCS [31]. In order to reduce the computational complexity and memory requirements.…”

“…Recently, a class of fractional-order TV regularization models has received considerable interest and it is widely used in image denoising [19,20]. Adaptive weighted high-frequency iterative fractional-order TV is proposed, the high frequency gradient of an image is reweighted in iterations adaptively when using fractional-order TV [21]. Another conventional way to suppress the staircase artifact is to use a high-order TV regularization [22,23], there exists a high-order total variation minimization model that removes undesired artifacts for restoring blurry and noisy images [24].…”

Nonlocal Low-Rank Regularization Combined with Bilateral Total Variation for Compressive Sensing Image Reconstruction

“…However, some problems such as staircase effect still exist in the total variation algorithm. Many variants are proposed and applied to CS reconstruction gradually, such as fractional-order total variation [19], reweighted total variation [20] and bilateral total variation [21], etc. These reconstruction algorithms using the image sparse prior have achieved good image reconstruction performance.…”

“…At present, reconstruction algorithms utilize the non-local self-similarity of image by adopting a block matching strategy to get similar image blocks. Since there are some duplicate structures in the image and the disturb of noise, the optimization model based on low-rank instead of sparsity constraint will inevitably remove these duplicate structures, and result in the problems of over-smoothing and edge information degradation of the reconstructed image [19]. In this paper, we add the bilateral total variation constraint as a global information prior to the reconstruction model based on nonlocal low-rank to propose an optimized scheme.…”