Combined Total Variation Research Articles

Noniterative least-squares reverse time migration based on an efficient asymptotic Hessian/point-spread function estimation

Although reverse time migration (RTM) is a powerful imaging method, it uses only the adjoint of the wave-propagation operator and produces only a blurred image. Through linearized inversion, least-squares RTM (LSRTM) reduces migration artifacts, balances the amplitudes, and improves the resolution of the imaging results. Compared to data-domain LSRTM, image-domain LSRTM (ID-LSRTM) is a more practical choice because it typically requires one round of RTM and subsequently solves the deblurring problem of the conventional RTM image involving the Hessian matrix. The Hessian matrix can be effectively replaced by a set of point-spread functions (PSFs). PSFs are traditionally obtained through one round of demigration-migration; hence, the traditional PSF estimation has a computational cost that is twice that of the RTM. We have deduced an analytic expression of the Hessian/PSF by using an asymptotic Green’s function and derived an efficient estimation strategy for the Hessian/PSF. The proposed method significantly reduces the computational cost and allows more flexible spatial sampling of PSFs without interference. Based on the explicitly calculated PSFs, ID-LSRTM can be achieved by solving an optimization problem with combined total-variation and curvelet-domain [Formula: see text] regularizations. The total computational cost of the proposed LSRTM is approximately the same as that of the conventional RTM. Numerical examples of synthetic and field data find that the proposed LSRTM significantly improves image quality while being highly efficient.

A multi-frame super-resolution based on new variational data fidelity term

The main idea of multi-frame super-resolution (SR) algorithm is to recover a single high-resolution (HR) image from a sequence of low resolution ones of the same scene. Since the restoration step of super-resolution algorithms is always an ill-posed problem, the choice of the fidelity term and the regularization are always crucial. In this paper, we propose a new variational SR framework based on an automatic selection of the weighting parameter that control the balance between the L1 and L2 fidelity terms, which handle different type of noise distributions. Concerning the regularization, we use the combined total variation (TV) and the total variation of the first derivatives (TV2) model with a new implementation of the Primal-dual algorithm to solve the corresponding discretized problem. The obtained results are compared with some competitive algorithms and confirm that the proposed method has much benefices over the others in avoiding some undesirable artifacts.

Single Image Superresolution via Directional Group Sparsity and Directional Features.

Single image superresolution (SR) aims to construct a high-resolution version from a single low-resolution (LR) image. The SR reconstruction is challenging because of the missing details in the given LR image. Thus, it is critical to explore and exploit effective prior knowledge for boosting the reconstruction performance. In this paper, we propose a novel SR method by exploiting both the directional group sparsity of the image gradients and the directional features in similarity weight estimation. The proposed SR approach is based on two observations: 1) most of the sharp edges are oriented in a limited number of directions and 2) an image pixel can be estimated by the weighted averaging of its neighbors. In consideration of these observations, we apply the curvelet transform to extract directional features which are then used for region selection and weight estimation. A combined total variation regularizer is presented which assumes that the gradients in natural images have a straightforward group sparsity structure. In addition, a directional nonlocal means regularization term takes pixel values and directional information into account to suppress unwanted artifacts. By assembling the designed regularization terms, we solve the SR problem of an energy function with minimal reconstruction error by applying a framework of templates for first-order conic solvers. The thorough quantitative and qualitative results in terms of peak signal-to-noise ratio, structural similarity, information fidelity criterion, and preference matrix demonstrate that the proposed approach achieves higher quality SR reconstruction than the state-of-the-art algorithms.

A combined total variation and bilateral filter approach for image robust super resolution

In this paper, we consider the image super-resolution (SR) reconstitution problem. The main goal consists of obtaining a high-resolution (HR) image from a set of low-resolution (LR) ones. For that, we propose a novel approach based on a regularized criterion. The criterion is composed of the classical generalized total variation (TV) but adding a bilateral filter (BTV) regularizer. The main goal of our approach consists of the derivation and the use of an efficient combined deblurring and denoising stage that is applied on the high-resolution image. We demonstrate the existence of minimizers of the combined variational problem in the bounded variation space, and we propose a minimization algorithm. The numerical results obtained by our approach are compared with the classical robust super-resolution (RSR) algorithm and the SR with TV regularization. They confirm that the proposed combined approach allows to overcome efficiently the blurring effect while removing the noise.

GAUSSIAN NOISE REDUCTION ON IMAGES AUTOMATICALLY

The various images can be taken by camera, due to some artifacts image become noisy and blur .As a result the image may be containing the noise and unwanted details. This noise will be degrading the image information. The proposed method also used removes the noise in images. These methods are using combined total variation and wavelet thresholding to removing the noise from images. The image quality can be measured using the MSE (Mean Square Error),PSNR (Peak Signal to Noise Ratio),Entropy, Correlation Coefficient.

Single image super-resolution using combined total variation regularization by split Bregman Iteration

This paper addresses the problem of generating a high-resolution (HR) image from a single degraded low-resolution (LR) input image without any external training set. Due to the ill-posed nature of this problem, it is necessary to find an effective prior knowledge to make it well-posed. For this purpose, we propose a novel super-resolution (SR) method based on combined total variation regularization. In the first place, we propose a new regularization term called steering kernel regression total variation (SKRTV), which exploits the local structural regularity properties in natural images. In the second place, another regularization term called non-local total variation (NLTV) is employed as a complementary term in our method, which makes the most of the redundancy of similar patches in natural images. By combining the two complementary regularization terms, we propose a maximum a posteriori probability framework of SR reconstruction. Furthermore, split Bregman iteration is applied to implement the proposed model. Extensive experiments demonstrate the effectiveness of the proposed method.

An Alternating Direction Method for Mixed Gaussian Plus Impulse Noise Removal

A combined total variation and high-order total variation model is proposed to restore blurred images corrupted by impulse noise or mixed Gaussian plus impulse noise. We attack the proposed scheme with an alternating direction method of multipliers (ADMM). Numerical experiments demonstrate the efficiency of the proposed method and the performance of the proposed method is competitive with the existing state-of-the-art methods.