Poisson noisy image restoration via overlapping group sparse and nonconvex second-order total variation priors

The restoration of the Poisson noisy images is an essential task in many imaging applications due to the uncertainty of the number of discrete particles incident on the image sensor. In this paper, we consider utilizing a hybrid regularizer for Poisson noisy image restoration. The proposed regularizer, which combines the overlapping group sparse (OGS) total variation with the high-order nonconvex total variation, can alleviate the staircase artifacts while preserving the original sharp edges. We use the framework of the alternating direction method of multipliers to design an efficient minimization algorithm for the proposed model. Since the objective function is the sum of the non-quadratic log-likelihood and nonconvex nondifferentiable regularizer, we propose to solve the intractable subproblems by the majorization-minimization (MM) method and the iteratively reweighted least squares (IRLS) algorithm, respectively. Numerical experiments show the efficiency of the proposed method for Poissonian image restoration including denoising and deblurring.

Comparative Analysis of Multiplicative and Additive Noise Based Automated Regularizations in Non-Linear Diffusion Image Reconstruction

Multiplicative and additive noises are often introduced in image signals during the image acquisition process and result into degradation of image features. The work done by Perona and Malik in 1990 and its modified versions revolutionized the way through which noises or speckles are removed. The Perona-Malik model requires tuning of the regularization parameter to control and prevent staircase artifacts in restored images. The current manual tuning is a challenging and time consuming practice when a long queue of images is registered for processing. Attempt to automate the regularization parameter appeared in Perona-Malik model with self-adjusting shape-defining constant. Although both multiplicative and additive noise based automated regularizations were presented, the paper stayed silent on matters concerning the automation method that fits with speckle reduction. This paper therefore, presents a comparative analysis of additive and multiplicative noise based automated regularizations. Simulation results and paired samples T-tests reveal that the multiplicative noise based automation outperforms the additive noise based automation for small speckle variances. However, the two automation methods do not significantly differ when large speckle variances are assumed.

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

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.

Infrared Image Deblurring via High-Order Total Variation and Lp-Pseudonorm Shrinkage

The quality of infrared images is affected by various degradation factors, such as image blurring and noise pollution. Anisotropic total variation (ATV) has been shown to be a good regularization approach for image deblurring. However, there are two main drawbacks in ATV. First, the conventional ATV regularization just considers the sparsity of the first-order image gradients, thus leading to staircase artifacts. Second, it employs the L1-norm to describe the sparsity of image gradients, while the L1-norm has a limited capacity of depicting the sparsity of sparse variables. To address these limitations of ATV, a high-order total variation is introduced in the ATV deblurring model and the Lp-pseudonorm is adopted to depict the sparsity of low- and high-order total variation. In this way, the recovered image can fit the image priors with clear edges and eliminate the staircase artifacts of the ATV model. The alternating direction method of multipliers is used to solve the proposed model. The experimental results demonstrate that the proposed method does not only remove blurs effectively but is also highly competitive against the state-of-the-art methods, both qualitatively and quantitatively.

Seismic fault attribute estimation using a local fault model

Faults in the subsurface can be an avenue of, or a barrier to, hydrocarbon flow and pressure communication. Manual interpretation of discontinuities on 3D seismic amplitude volume is the most common way to define faults within a reservoir. Unfortunately, 3D seismic fault interpretation can be a time-consuming and tedious task. Seismic attributes such as coherence help define faults, but suffer from “staircase” artifacts and nonfault-related stratigraphic discontinuities. We assume that each sample of the seismic data is located at a potential fault plane. The hypothesized fault divides the seismic data centered at the analysis sample into two subwindows. We then compute the coherence for the two subwindows and full analysis window. We repeat the process by rotating the hypothesized fault plane along a set of user-defined discrete fault dip and azimuth. We obtain almost the same coherence values for the subwindows and the full window if the analysis point is not located at a fault plane. The “best” fault plane results in maximum coherence for the subwindows and minimum coherence for the full window if the analysis point is located at a fault plane. To improve the continuity of the fault attributes, we finally smooth the fault probability attribute along the estimated fault plane. We illustrate the effectiveness of our workflow by applying it to a synthetic and two real seismic data. The results indicate that our workflow successfully produces a continuous fault attribute without staircase artifacts and stratigraphic discontinuities.

Infrared Image Super-Resolution Reconstruction Based on Quaternion Fractional Order Total Variation with Lp Quasinorm

Owing to the limitations of the imaging principle as well as the properties of imaging systems, infrared images often have some drawbacks, including low resolution, a lack of detail, and indistinct edges. Therefore, it is essential to improve infrared image quality. Considering the information of neighbors, a description of sparse edges, and by avoiding staircase artifacts, a new super-resolution reconstruction (SRR) method is proposed for infrared images, which is based on fractional order total variation (FTV) with quaternion total variation and the L p quasinorm. Our proposed method improves the sparsity exploitation of FTV, and efficiently preserves image structures. Furthermore, we adopt the plug-and-play alternating direction method of multipliers (ADMM) and the fast Fourier transform (FFT) theory for the proposed method to improve the efficiency and robustness of our algorithm; in addition, an accelerated step is adopted. Our experimental results show that the proposed method leads to excellent performances in terms of an objective evaluation and the subjective visual effect.

Semiautomated fault interpretation based on seismic attributes

Three-dimensional fault interpretation is a time-consuming and tedious task. Huge efforts have been invested in attempts to accelerate this procedure. We present a novel workflow to perform semiautomated fault illumination that uses a discontinuity attribute as input and provides labeled fault surfaces as output. The procedure is modeled after a biometric algorithm to recognize capillary vein patterns in human fingers. First, a coherence or discontinuity volume is converted to binary form indicating possible fault locations. This binary volume is then skeletonized to produce a suite of fault sticks. Finally, the fault sticks are grouped to construct fault surfaces using a classic triangulation method. The processing in the first two steps is applied time slice by time slice, thereby minimizing the influence of staircase artifacts seen in discontinuity volumes. We illustrate this technique by applying it to a seismic volume acquired over the Netherlands Sector of the North Sea Basin and find that the proposed strategy can produce highly precise fault surfaces.

Local and Nonlocal Regularization to Image Interpolation

This paper presents an image interpolation model with local and nonlocal regularization. A nonlocal bounded variation (BV) regularizer is formulated by an exponential function including gradient. It acts as the Perona-Malik equation. Thus our nonlocal BV regularizer possesses the properties of the anisotropic diffusion equation and nonlocal functional. The local total variation (TV) regularizer dissipates image energy along the orthogonal direction to the gradient to avoid blurring image edges. The derived model efficiently reconstructs the real image, leading to a natural interpolation which reduces blurring and staircase artifacts. We present experimental results that prove the potential and efficacy of the method.