Nonlocal Total Variation Method Research Articles

Nonlocal Total Variation Using the First and Second Order Derivatives and Its Application to CT Image Reconstruction.

We propose a new class of nonlocal Total Variation (TV), in which the first derivative and the second derivative are mixed. Since most existing TV considers only the first-order derivative, it suffers from problems such as staircase artifacts and loss in smooth intensity changes for textures and low-contrast objects, which is a major limitation in improving image quality. The proposed nonlocal TV combines the first and second order derivatives to preserve smooth intensity changes well. Furthermore, to accelerate the iterative algorithm to minimize the cost function using the proposed nonlocal TV, we propose a proximal splitting based on Passty’s framework. We demonstrate that the proposed nonlocal TV method achieves adequate image quality both in sparse-view CT and low-dose CT, through simulation studies using a brain CT image with a very narrow contrast range for which it is rather difficult to preserve smooth intensity changes.

A Review on CT and X-Ray Images Denoising Methods

In medical imaging systems, denoising is one of the important image processing tasks. Automatic noise removal will improve the quality of diagnosis and requires careful treatment of obtained imagery. Com-puted tomography (CT) and X-Ray imaging systems use the X radiation to capture images and they are usually corrupted by noise following a Poisson distribution. Due to the importance of Poisson noise re-moval in medical imaging, there are many state-of-the-art methods that have been studied in the image processing literature. These include methods that are based on total variation (TV) regularization, wave-lets, principal component analysis, machine learning etc. In this work, we will provide a review of the following important Poisson removal methods: the method based on the modified TV model, the adaptive TV method, the adaptive non-local total variation method, the method based on the higher-order natural image prior model, the Poisson reducing bilateral filter, the PURE-LET method, and the variance stabi-lizing transform-based methods. Our task focuses on methodology overview, accuracy, execution time and their advantage/disadvantage assessments. The goal of this paper is to provide an apt choice of denoising method that suits to CT and X-ray images. The integration of several high-quality denoising methods in image processing software for medical imaging systems will be always excellent option and help further image analysis for computer-aided diagnosis.

Weighted nonlocal total variation in image processing

In this paper, a novel weighted nonlocal total variation (WNTV) method is proposed. Compared to the classical nonlocal total variation methods, our method modifies the energy functional to introduce a weight to balance between the labeled sets and unlabeled sets. With extensive numerical examples in semi-supervised clustering, image inpainting and image colorization, we demonstrate that WNTV provides an effective and efficient method in many image processing and machine learning problems.

Unsupervised Classification in Hyperspectral Imagery With Nonlocal Total Variation and Primal-Dual Hybrid Gradient Algorithm

In this paper, a graph-based nonlocal total variation method (NLTV) is proposed for unsupervised classification of hyperspectral images (HSI). The variational problem is solved by the primal-dual hybrid gradient (PDHG) algorithm. By squaring the labeling function and using a stable simplex clustering routine, an unsupervised clustering method with random initialization can be implemented. The effectiveness of this proposed algorithm is illustrated on both synthetic and real-world HSI, and numerical results show that the proposed algorithm outperforms other standard unsupervised clustering methods such as spherical K-means, nonnegative matrix factorization (NMF), and the graph-based Merriman-Bence-Osher (MBO) scheme.

A Block Nonlocal TV Method for Image Restoration

In this paper, we propose a block nonlocal total variation (TV) regularization method for image restoration. We extend the existing nonlocal TV method in two aspects: first, some block nonlocal operators are introduced to extend the point-based nonlocal diffusion as a block-based nonlocal diffusion process; second, the weighting function in the nonlocal method can be adaptively determined by the cost functional itself. The proposed method is derived from a block-based maximum a posteriori estimation. By the assumption of the self-similarity of small patches, we formulate a regularization term as a log-likelihood functional of a mixture model. To optimize this regularization term efficiently, we employ the idea of the expectation maximum algorithm and give a variational framework to propose a block-based nonlocal TV regularization. The weighting function occurring in our model can be regarded as a probability of the similarity for image patches, and it can be updated adaptively according to the newest estimation. In addition, we mathematically prove the existence of a minimizer for one of the proposed models. Compared with the nonlocal TV method, numerical results show that our method can greatly improve the quality of the restored images, especially under heavy noise.

A novel Bayesian-based nonlocal reconstruction method for freehand 3D ultrasound imaging

Freehand three-dimensional (3D) ultrasound imaging is an important medical imaging modality in computer-assisted clinical diagnosis and image-guided intervention. In this paper, we present a novel Bayesian-based nonlocal method for the accurate volume reconstruction of freehand 3D ultrasound imaging with irregularly spaced B-scans. In the algorithm, each pixel is represented as the Gamma distribution which corresponds to the speckle noise generated by the interaction of the acoustic wave with the tissues. The variational reconstruction functional is associated with a nonlocal denoising term and a nonlocal inpainting term. To suppress speckle noise in the ultrasound image, the observed data is filtered via nonlocal total variation method firstly. The nonlocal denoising model is adapted to the speckle noise by substituting the Pearson distance-based weight function for the Gaussian weight function. To interpolate the missing data, a new inpainting scheme derived from the nonlocal means filter and its implementation based on fast marching method are introduced to fill the empty regions. This makes interpolation of missing data more accurate and effective. The Pearson distance function derived from the Bayesian estimator is not only used for speckle reduction, but also serves as weight function for building nonlocal means-based inpainting algorithm. Experimental results on synthetic cube data, in-vitro ultrasound abdominal phantom and in-vivo liver of human subject and comparisons with some classical and recent algorithms are used to demonstrate its improvement in both speckle suppression and edge preservation in 3D ultrasound reconstruction.