Second-order Total Variation Regularization Research Articles

Robust principal component analysis via weighted nuclear norm with modified second-order total variation regularization

Robust principal component analysis via weighted nuclear norm with modified second-order total variation regularization

Surface Estimation via Analysis Method: A Constrained Inverse Problem Approach.

Ultrasonic imaging is a common technique in nondestructive evaluation, as it presents advantages such as low cost and safety of operation. In many industries, the interior inspection of objects with complex geometry has become a necessity. This kind of inspection requires the transducer to be coupled to the object with the use of some technique, such as immersing the object in water. When doing so, the geometry of the object surface must be known a priori or estimated. Recent methods for surface estimation start with an image of the interface between water and the specimen. Then, the surface is estimated by processing the image using different strategies. In this article, the strategy to extract the surface profile is based on an analysis-based inverse problem, hence named surface estimation via analysis method (SEAM). The problem formulation aims to reduce the noise in the estimate and also, by including priors, reach more accurate estimates. By using a second-order total variation regularization, which favors piecewise linear functions, the proposed method can describe a great range of surface profiles. Experiments were performed to evaluate the proposed method on surface profile estimation and results show good agreement with references and lower errors than methods in the literature. In addition, the estimated profiles enhance the imaging of the interior of objects, allowing better visualization of internal defects.

Combined higher order non-convex total variation with overlapping group sparsity for impulse noise removal

A typical approach to eliminate impulse noise is to use the l1-norm for both the data fidelity term and the regularization terms. However, the l1-norm tends to over penalize signal entries which is one of its underpinnings. Hence, we propose a variational model that uses the non-convex lp-norm, 0 < p < 1 for both the data fidelity and a second-order total variation regularization term combined with an overlapping group sparse regularizer. Specifically, to robustly eliminate impulse noise, the proposed method uses a non-convex data fidelity term. The hybrid combination of a second-order non-convex total variation and an overlapping group sparse regularization term is used to eliminate the remaining staircase artifacts while maintaining a sharp restored image. A mathematical formulation is derived and to implement it, the iterative re-weighted l1 (IRL1) based alternating direction method of multipliers (ADMM) is used to solve the constraints and the subproblems. Experimental results for image denoising and deblurring on several widely used standard images demonstrate that the proposed method performed better when compared to the l1-norm total variation (TV), total generalized variation (TGV) model, and the non-convex lp-norm TV-based data fidelity model in terms of peak signal-to-noise ratio (PSNR) and structure similarity index measure (SSIM).

Compressed Imaging to Reduce Storage in Adjoint-State Calculations

To generate seismic images of the subsurface with adjoint-state methods such as reverse-time migration (RTM) and full-waveform inversion (FWI), the gradient of a misfit function is computed efficiently by applying what is referred to as an imaging condition to the forward propagated source wavefield and the backward propagated adjoint wavefield. In order to reduce the storage in adjoint-state calculations, we evaluate the imaging condition only at a randomly selected subset of spatial grid points (compressed imaging) and then efficiently reconstruct the full image from the imaged points via compressed sensing theory, which combines the compressibility characteristics of seismic images and convex optimization tools for the reconstruction. We use the second-order total variation regularization for the reconstruction and, using different numerical tests from RTM and FWI, we show that the new method allows a significant reduction in wavefield storage, while still recovering the full image accurately. Furthermore, regularization, applied on the gradient during the reconstruction stage improves the convergence of the FWI algorithm.

Hybrid variational model based on alternating direction method for image restoration

The total variation model is widely used in image deblurring and denoising process with the features of protecting the image edge. However, this model usually causes some staircase effects. To overcome the shortcoming, combining the second-order total variation regularization and the total variation regularization, we propose a hybrid total variation model. The new improved model not only eliminates the staircase effect, but also well protects the edges of the image. The alternating direction method of multipliers (ADMM) is employed to solve the proposed model. Numerical results show that our proposed model can get more details and higher image visual quality than some current state-of-the-art methods.

A Unidirectional Total Variation and Second-Order Total Variation Model for Destriping of Remote Sensing Images

Remote sensing images often suffer from stripe noise, which greatly degrades the image quality. Destriping of remote sensing images is to recover a good image from the image containing stripe noise. Since the stripes in remote sensing images have a directional characteristic (horizontal or vertical), the unidirectional total variation has been used to consider the directional information and preserve the edges. The remote sensing image contaminated by heavy stripe noise always has large width stripes and the pixels in the stripes have low correlations with the true pixels. On this occasion, the destriping process can be viewed as inpainting the wide stripe domains. In many works, high-order total variation has been proved to be a powerful tool to inpainting wide domains. Therefore, in this paper, we propose a variational destriping model that combines unidirectional total variation and second-order total variation regularization to employ the directional information and handle the wide stripes. In particular, the split Bregman iteration method is employed to solve the proposed model. Experimental results demonstrate the effectiveness of the proposed method.

A Novel Mechanical Fault Diagnosis Scheme Based on the Convex 1-D Second-Order Total Variation Denoising Algorithm

Convex 1-D first-order total variation (TV) denoising is an effective method for eliminating signal noise, which can be defined as convex optimization consisting of a quadratic data fidelity term and a non-convex regularization term. It not only ensures strict convex for optimization problems, but also improves the sparseness of the total variation term by introducing the non-convex penalty function. The convex 1-D first-order total variation denoising method has greater superiority in recovering signals with flat regions. However, it often produces undesirable staircase artifacts. Moreover, actual denoising efficacy largely depends on the selection of the regularization parameter, which is utilized to adjust the weights between the fidelity term and total variation term. Using this, algorithms based on second-order total variation regularization and regularization parameter optimization selection are proposed in this paper. The parameter selection index is determined by the permutation entropy and cross-correlation coefficient to avoid the interference by human experience. This yields the convex 1-D second-order total variation denoising method based on the non-convex framework. Comparing with traditional wavelet denoising and first-order total variation denoising, the validity of the proposed method is verified by analyzing the numerical simulation signal and the vibration signal of fault bearing in practice.