Fractional-order Total Variation Regularization Research Articles

A Fractional-Order Total Variation Regularization-Based Method for Recovering Geiger-Mode Avalanche Photodiode Light Detection and Ranging Depth Images

High-quality image restoration is typically challenging due to low signal–to–background ratios (SBRs) and limited statistics frames. To address these challenges, this paper devised a method based on fractional-order total variation (FOTV) regularization for recovering Geiger-mode avalanche photodiode (GM-APD) light detection and ranging (lidar) depth images. First, the spatial differential peak-picking method was used to extract the target depth image from low SBR and limited frames. FOTV regularization was introduced based on the total variation regularization recovery model, which incorporates the fractional-order differential operator, in order to realize FOTV-regularization-based depth image recovery. These frameworks were used to establish an algorithm for GM-APD depth image recovery based on FOTV. The simulation and experimental results demonstrate that the devised FOTV-recovery algorithm improved the target reduction degree, peak signal–to–noise ratio, and structural similarity index measurement by 76.6%, 3.5%, and 6.9% more than the TV, respectively, in the same SBR and statistic frame conditions. Thus, the devised approach is able to effectively recover GM-APD lidar depth images in low SBR and limited statistic frame conditions.

Non-convex fractional-order TV model for impulse noise removal

For the pursuit of high-quality restoration effects, we introduce a novel non-convex extended scheme to reconstruct blurred images under impulse noise in this paper. Because of the remarkable advantages of the combination of non-convex ℓp-norm and fractional-order total variation regularization, our developed strategy possesses a brilliant ability to overcome the staircase-like aspects and preserve neat contours. To obtain the minimizer of the optimization problem, we adopt the alternating direction method of multipliers closely integrating with the iteratively reweighted ℓ1 algorithm. Theoretically, a convergence proof is provided for the developed algorithm. By considering salt-and-pepper noise and random-valued impulse noise, comprehensive simulation comparisons with some popular methods are carried out for image restoration. And the experimental results illustrate that our proposed model behaves better with respect to visual comparison and quantitative measurement.

Truncated Fractional-Order Total Variation for Image Denoising under Cauchy Noise

In recent years, the fractional-order derivative has achieved great success in removing Gaussian noise, impulsive noise, multiplicative noise and so on, but few works have been conducted to remove Cauchy noise. In this paper, we propose a novel nonconvex variational model for removing Cauchy noise based on the truncated fractional-order total variation. The new model can effectively reduce the staircase effect and keep small details or textures while removing Cauchy noise. In order to solve the nonconvex truncated fractional-order total variation regularization model, we propose an efficient alternating minimization method under the framework of the alternating direction multiplier method. Experimental results illustrate the effectiveness of the proposed model, compared to some previous models.

A fractional-order decomposition model of image registration and its numerical algorithm

To overcome the weakness of TV based image registration models, we propose a fractional-order decomposition model for image registration. In this model, deformation is decomposed into two components: discontinuous component and smooth component. The fractional-order total variation regularization and higher order regularization are added on these two components, respectively. Furthermore, a numerical algorithm is proposed to solve this model. Numerical tests are also performed to show the efficiency of the proposed model.

Wavelet inpainting by fractional order total variation

Image inpainting in the wavelet domain refers to the recovery of an image from incomplete wavelet coefficients. In this paper, we propose a wavelet inpainting model by using fractional order total variation regularization approach. Moreover, we use a simple but very efficient primal–dual algorithm to calculate the optimal solution. In the light of saddle-point theory, the convergence of new algorithm is guaranteed. Experimental results are presented to show performance of the proposed algorithm.

Fractional order total variation regularization for image super-resolution

In this paper, we present a fractional order total variation (TV) regularization functional for image super-resolution, the role of which is to better handle the texture details of image. This regularization functional is then incorporated into a variational formulation with an image fidelity term and the usual TV regularization that can efficiently preserve the discontinuities and image structures. The resulting evolution equation is the gradient descent flow that minimizes the overall functional. The proposed model has been applied to eight real images with promising results; unlike the existing TV-based image super-resolution models, the proposed model does not suffer from block artifacts, staircase edges and false edge near the edges.