Higher Total Variation Research Articles

Weighted and Well-Balanced Nonlinear TV-Based Time-Dependent Model for Image Denoising

The partial differential equation (PDE)-based models are widely used to remove additive Gaussian white noise and preserve edges, and one of the most widely used methods is the total variation denoising algorithm. Total variation (TV) denoising algorithm-based time-dependent models have seen considerable success in the field of image-denoising and edge detection. TV denoising algorithm is based on that signals with spurious detail have a high total variation and reduction of unwanted signals to achieve noise-free images. It is a constrained optimization-type algorithm. The Lagrange multiplier and gradient descent method are used to solve the TV algorithm to reach the PDE-based time dependent model. To eliminate additive noise and preserve edges, we investigate a class of weighted time-dependent model in this study. The proposed method is investigated in a well-balanced flow form that extends the time-dependent model with an adaptive fidelity element. Adaptive function is fusing into the regularization term of the classical time-dependent model which successfully enhances the intensity of the regularizer function. We maintain the ability of the time-dependent model without any oscillation effects. Furthermore, we want to prove the viscosity solution of our weighted and well balanced time-dependent model, demonstrating its existence and uniqueness. The finite difference method is applied to discretize the nonlinear time-dependent models. The numerical results are expressed as a statistic known as the peak signal-to-noise ratio (PSNR) and structural similarity index metric (SSIM). Numerical experiments demonstrate that the proposed model yields good performance compared with the previous time-dependent model.

Adaptive-weighted high order TV algorithm for sparse-view CT reconstruction.

With the development of low-dose computed tomography (CT), incomplete data reconstruction has been widely concerned. The total variation (TV) minimization algorithm can accurately reconstruct images from sparse or noisy data. However, the traditional TV algorithm ignores the direction of structures in images, leading to the loss of edge information and block artifacts when the object is not piecewise constant. Since the anisotropic information can facilitate preserving the edge and detail information in images, we aim to improve the TV algorithm in terms of reconstruction accuracy via this approach. In this paper, we propose an adaptive-weighted high order total variation (awHOTV) algorithm. We construct the second order TV-norm using the second order gradient, adapt the anisotropic edge property between neighboring image pixels, adjust the local image-intensity gradient to keep edge information, and design the corresponding Chambolle-Pock (CP) solving algorithm. Implementing the proposed algorithm, comprehensive studies are conducted in the ideal projection data experiment where the Structural similarity (SSIM), Root Mean Square Error (RMSE), Contrast to noise ratio (CNR), and modulation transform function (MTF) curves are utilized to evaluate the quality of reconstructed images in statism, structure, spatial resolution, and contrast, respectively. In the noisy data experiment, we further use the noise power spectrum (NPS) curve to evaluate the reconstructed images and compare it with other three algorithms. We use the 2D slice in the XCAT phantom, 2D slice in TCIA Challenge data and FORBILD phantom as simulation phantoms and use real bird data for real verification. The results show that, compared with the traditional TV and FBP algorithms, the awHOTV has better performance in terms of RMSE, SSIM, and Pearson correlation coefficient (PCC) under the projected data with different sparsity. In addition, the awHOTV algorithm is robust against the noise of different intensities. The proposed awHOTV method can reconstruct the images with high accuracy under sparse or noisy data. The awHOTV solves the strip artifacts caused by sparse data in the FBP method. Compared with the TV method, the awHOTV can effectively suppress block artifacts and has good detail protectionability.

Channel rearrangement multi-branch network for image super-resolution

In image super-resolution task, the existing convolutional neural network methods proceed to increase the number of network layers and filters to achieve better performance. Nevertheless, such approaches not only lead to a dramatic increase in network parameters, but also restrict the practical application of super-resolution methods. In order to address this problem, we propose a lightweight model called Channel Rearrangement Multi-Branch Network (CRMBN) for super-resolution of single images. Specifically, we design a channel rearrangement algorithm based on the total variation of the feature maps. It is inspired by the fact that the feature maps with high total variation contain more high-frequency details, which are valuable for super-resolution reconstruction. Therefore, for the super-resolution networks, the more feature maps with high total variation, the better performance of reconstruction. The rearranged channels are divided into two groups, one with high total variation and the other with the opposite. In order to reduce the parameters while mining for more details, we send the features with low total variation to the deep network. Finally, high total variation features and deep features are fused to reconstruct high-resolution image. The experimental results show that compared with other lightweight models, the proposed method can offer a favorable improvement in terms of PSNR and SSIM.

A simple and fast ASD-POCS algorithm for image reconstruction.

The adaptive steepest descent projection onto convex set (ASD-POCS) algorithm is a promising algorithm for constrained total variation (TV) type norm minimization models in computed tomography (CT) image reconstruction using sparse and/or noisy data. However, in ASD-POCS algorithm, the existing gradient expression of the TV-type norm appears too complicated in the implementation code and reduces image reconstruction speed. To address this issue, this work aims to develop and test a simple and fast ASD-POCS algorithm. Since the original algorithm is not derived thoroughly, we first obtain a simple matrix-form expression by thorough derivation via matrix representations. Next, we derive the simple matrix expressions of the gradients of TV, adaptive weighted TV (awTV), total p-variation (TpV), high order TV (HOTV) norms by term combinations and matrix representations. The deep analysis is then performed to identify the hidden relations of these terms. The TV reconstruction experiments by use of sparse-view projections via the Shepp-Logan, FORBILD and a real CT image phantoms show that the simplified ASD-POCS (S-ASD-POCS) using the simple matrix-form expression of TV gradient achieve the same reconstruction accuracy relative to ASD-POCS, whereas it enables to speed up the whole ASD process 1.8-2.7 time fast. The derived simple matrix expressions of the gradients of these TV-type norms may simplify the implementation of the ASD-POCS algorithm and speed up the ASD process. Additionally, a general gradient expression suitable to all the sparse transform-based optimization models is demonstrated so that the ASD-POCS algorithm may be tailored to extended image reconstruction fields with accelerated computational speed.

Iterative volume of interest based 4D cone-beam CT.

4D cone-beam CT (CBCT) has potential applications in soft tissue alignment and tumor motion verification at the time of radiation treatment. However, prominent streak artifacts with conventional image reconstructions have limited its clinical use and alternative reconstructions are generally too computationally expensive for the time available. We propose an iterative volume of interest based (I4D VOI) reconstruction technique, where 4D reconstruction is only performed within a VOI, to limit streak artifacts with limited added computation time. The I4D VOI technique is compared to standard cone-beam filtered back projection (FDK), an FDK VOI technique, and unconstrained total variation (TV) minimization by comparing tumor motion quantification errors and image quality. 14 long CBCT scans (6.5 to 12 min) of patients receiving radiation treatment for lung cancer were used for the comparison. Rigid registration between phase images of FDK reconstructions using all projections were used to quantify the gold standard motion. Projections were removed to simulate 2 minute scans and these new projection sets were used for each of the test reconstructions. Excluding two patients where registration failed, the average root mean square (RMS) error for each method was as follows: 1.5 ± 0.2 mm for FDK, 1.4 ± 0.2 mm for FDK VOI, 1.3 ± 0.2 mm for I4D VOI, 1.7 ± 0.4 mm for low regularization TV minimization, and 1.1 ± 0.2 mm for high regularization TV minimization. No significant difference was observed between RMS error for I4D VOI and the other methods, except for unsmoothed FDK VOI (P = 0.02). An increase in RMS error difference between I4D VOI and smoothed FDK VOI was observed going from 2 min to 1 min scans (0.1 mm to 0.3 mm, P = 0.20 to P = 0.09). I4D VOI and FDK VOI reconstruction measured tumor trajectories with equivalent accuracy as TV minimization with improved bony anatomy image quality and computation time (I4D VOI was approximately 15 and 95 times faster than low and high regularization TV minimization, respectively). Within the VOI, streak artifact reduction compared to FDK VOI may be beneficial for tumor visualization and motion measurement, but requires further study.

Speckle Noise Reduction via Nonconvex High Total Variation Approach

We address the problem of speckle noise removal. The classical total variation is extensively used in this field to solve such problem, but this method suffers from the staircase-like artifacts and the loss of image details. In order to resolve these problems, a nonconvex total generalized variation (TGV) regularization is used to preserve both edges and details of the images. The TGV regularization which is able to remove the staircase effect has strong theoretical guarantee by means of its high order smooth feature. Our method combines the merits of both the TGV method and the nonconvex variational method and avoids their main drawbacks. Furthermore, we develop an efficient algorithm for solving the nonconvex TGV-based optimization problem. We experimentally demonstrate the excellent performance of the technique, both visually and quantitatively.