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The total variation (TV) regularization method is an effective method for image deblurring in preserving edges. However, the TV based solutions usually have some staircase effects. In this paper, in order to alleviate the staircase effect,…
Total Variation (TV) is a popular regularization strategy that promotes piece-wise constant signals by constraining the $\ell_1$-norm of the first order derivative of the estimated signal. The resulting optimization problem is usually…
This paper considers the constrained total variation (TV) denoising problem for complex-valued images. We extend the definition of TV seminorms for real-valued images to dealing with complex-valued ones. In particular, we introduce two…
Image restoration is one of the most fundamental issues in imaging science. Total variation (TV) regularization is widely used in image restoration problems for its capability to preserve edges. In the literature, however, it is also well…
Total Variation (TV) and related extensions have been popular in image restoration due to their robust performance and wide applicability. While the original formulation is still relevant after two decades of extensive research, its…
Total variation (TV) regularization is a classical tool for image denoising, but its convex $\ell_1$ formulation often leads to staircase artifacts and loss of contrast. To address these issues, we introduce the Transformed $\ell_1$ (TL1)…
A class of mixed-order \emph{PDE}-constraint regularizer for image processing problem is proposed, generalizing the standard first order total variation $(TV)$. A semi-supervised (bilevel) training scheme, which provides a simultaneous…
Recently, total variation (TV) based minimization algorithms have achieved great success in compressive sensing (CS) recovery for natural images due to its virtue of preserving edges. However, the use of TV is not able to recover the fine…
The parameter selection is crucial to regularization based image restoration methods. Generally speaking, a spatially fixed parameter for regularization item in the whole image does not perform well for both edge and smooth areas. A larger…
The problem of restoration of digital images from their degraded measurements plays a central role in a multitude of practically important applications. A particularly challenging instance of this problem occurs in the case when the…
In this paper, we design an efficient, multi-stage image segmentation framework that incorporates a weighted difference of anisotropic and isotropic total variation (AITV). The segmentation framework generally consists of two stages:…
The total variation (TV) regularization has phenomenally boosted various variational models for image processing tasks. We propose to combine the backward diffusion process in the earlier literature of image enhancement with the TV…
Owing to the edge preserving ability and low computational cost of the total variation (TV), variational models with the TV regularization have been widely investigated in the field of multiplicative noise removal. The key points of the…
Total variation (TV) regularization is popular in image restoration and reconstruction due to its ability to preserve image edges. To date, most research activities on TV models concentrate on image restoration from blurry and noisy…
Image structure-texture decomposition is a long-standing and fundamental problem in both image processing and computer vision fields. In this paper, we propose a generalized semi-sparse regularization framework for image structural analysis…
In a number of tomographic applications, data cannot be fully acquired, resulting in a severely underdetermined image reconstruction. In such cases, conventional methods lead to reconstructions with significant artifacts. To overcome these…
Compressed sensing (CS) methods in magnetic resonance imaging (MRI) offer rapid acquisition and improved image quality but require iterative reconstruction schemes with regularization to enforce sparsity. Regardless of the difficulty in…
In this paper, we propose a new variational model for image reconstruction by minimizing the $L^1$ norm of the \emph{Weingarten map} of image surface $(x,y,f(x,y))$ for a given image $f:{\mathrm{\Omega}}\rightarrow \mathbb R$. We…
Solving inverse problems requires appropriate regularization techniques to ensure well-posedness and stability. In recent years, denoiser-driven methods have emerged as effective regularization strategies, achieving state-of-the-art…
Variational regularization models are one of the popular and efficient approaches for image restoration. The regularization functional in the model carries prior knowledge about the image to be restored. The prior knowledge, in particular…