Total Variation Regularization Algorithm Research Articles

Sub-Nyquist underwater denoising ghost imaging with a Coiflet-wavelet-order-based Hadamard matrix

Underwater ghost imaging (GI) plays an important role in the marine research, marine environment protection, and engineering applications. However, underwater GI encounters the challenges of numerous measurements and noise interference caused by the scattering lights. To solve these problems, we propose a sub-Nyquist denoising GI method to acquire high-quality images of the underwater objects. The proposed method first uses a Coiflet-wavelet decomposition method to create an index order and then utilizes the order to reorder the Hadamard pattern sequence. Then, a total variation regularization algorithm is designed to restore the object images, and a nuclear-norm-minimization algorithm is developed to remove the noises from the restored images. Finally, an experimental setup is built to simulate the complicated underwater environment that includes the turbulence and bubbles. The numerical and experimental results show that the denoising capability of the proposed method is strong, and the imaging performance of the proposed method is similar (slightly better in some cases) to the recently reported state-of-the-art GI methods in the complicated underwater environment and sub-Nyquist sampling ratio condition (e.g., 0.03). The proposed method may find applications in marine underwater imaging areas.

Application of Deep Neural Network to the Reconstruction of Two-Phase Material Imaging by Capacitively Coupled Electrical Resistance Tomography

A convolutional neural network (CNN)-based image reconstruction algorithm for two-phase material imaging is presented and verified with experimental data from a capacitively coupled electrical resistance tomography (CCERT) sensor. As a contactless version of electrical resistance tomography (ERT), CCERT has advantages such as no invasion, low cost, no radiation, and rapid response for two-phase material imaging. Besides that, CCERT avoids contact error of ERT by imaging from outside of the pipe. Forward modeling was implemented based on the practical circular array sensor, and the inverse image reconstruction was realized by a CNN-based supervised learning algorithm, as well as the well-known total variation (TV) regularization algorithm for comparison. The 2D, monochrome, 2500-pixel image was divided into 625 clusters, and each cluster was used individually to train its own CNN to solve the 16 classes classification problem. Inherent regularization for the assumption of binary materials enabled us to use a classification algorithm with CNN. The iterative TV regularization algorithm achieved a close state of the two-phase material reconstruction by its sparsity-based assumption. The supervised learning algorithm established the mathematical model that mapped the simulated resistance measurement to the pixel patterns of the clusters. The training process was carried out only using simulated measurement data, but simulated and experimental tests were both conducted to investigate the feasibility of applying a multi-layer CNN for CCERT imaging. The performance of the CNN algorithm on the simulated data is demonstrated, and the comparison between the results created by the TV-based algorithm and the proposed CNN algorithm with the real-world data is also provided.

A Novel CT-Mode Through-the-Wall Imaging Method Based on Time Delay Estimation

Through-the-wall (TTW) imaging is an important class of applications with the goal of sensing the environment inside the unknown area. In the computerized tomography (CT)-mode TTW imaging method, the layout of the area is reconstructed with the received signal strength (RSS). However, the multipath included in the RSS is difficult to mitigate, resulting in blurring, wall missing, or ghosts. In this letter, a novel imaging method is proposed. First, the received signal is processed by pulse compression. The multipath signals are separated from the directly transmitted wave (DTW), and then, the time delay of the latter one is easily estimated. Second, an improved total variation regularization algorithm is used to reconstruct the layout by assuming that there are only horizontal and vertical walls in the area. The validity of the proposed method is verified by the experimental results, where a clearer image could be obtained compared with the one generated by the traditional RSS method.

Nonconvex Wavelet Thresholding Total Variation Denoising Method for Planetary Gearbox Fault Diagnosis

The vibration-based analysis is an effective technique for planetary gearbox fault diagnosis, but a difficult task is how to accurately identify fault features from noisy vibration signals. In this paper, a nonconvex wavelet thresholding total variation (WATV) denoising method is proposed for planetary gearbox fault diagnosis, which combines wavelet-domain sparsity and total variation (TV) regularization. The TV regularization algorithm is employed to modify the retained wavelet coefficients so that the occurrence of oscillations caused by wavelet thresholding is suppressed. To overcome the underestimation shortcoming of L1-norm regularization, nonconvex penalty function regularization is used to strongly promote the sparsity of estimation while guaranteeing that the global optimal solutions are obtained even though the objective function is nonconvex. Then, the split augmented Lagrangian shrinkage (SALSA) method is developed to solve the nonconvex WATV denoising problem. Two experimental studies are performed to verify the performance and effectiveness of the proposed method. Comparisons with the soft thresholding and basis pursuit denoising (BPD) methods show that the proposed method can accurately estimate the fault features from vibration signals, which means that the proposed method is an effective and promising tool for planetary gearbox fault diagnosis.

A convex nonlocal total variation regularization algorithm for multiplicative noise removal

This study proposes a nonlocal total variation restoration method to address multiplicative noise removal problems. The strictly convex, objective, nonlocal, total variation effectively utilizes prior information about the multiplicative noise and uses the maximum a posteriori estimator (MAP). An efficient iterative multivariable minimization algorithm is then designed to optimize our proposed model. Finally, we provide a rigorous convergence analysis of the alternating multivariable minimization iteration. The experimental results demonstrate that our proposed model outperforms other currently related models both in terms of evaluation indices and image visual quality.

A fast total variation regularization algorithm for 2D piecewise constant radially symmetric functions

In this paper, we considered total variation regularization (TV regularization) for 2D radially symmetric piecewise constant (RSPC) functions. We obtained a system of equations solving the direct variational problem with the subgradient method. Using the system, we propose a Condat’s type algorithm for computation of an extremal function.

Fast Long-Range Photon Counting Depth Imaging With Sparse Single-Photon Data

Fast depth imaging of noncooperative targets at a range of up to 900 m is demonstrated based on the time-of-flight time-correlated single-photon counting technique. Experimental results shown that our image system has the ability of reconstructing depth images with data of less than one photon per pixel. Especially, utilizing a modified total variation regularization algorithm with an optimal initial value, the acquisition time necessary for each pixel could be reduced by a factor of 8 compared to the traditional median filter approach, and the image processing time is extremely improved. This depth imaging system is a low-light-level device for a variety of applications, such as target detection, space surveillance, and distance measurement.

Chemical Imaging of Self-Assembled Monolayers on Copper Using Compressive Hyperspectral Sum Frequency Generation Microscopy.

Sum frequency generation microscopy is a label-free optical imaging technique with intrinsic molecular vibrational contrast for surface studies. Recent developments of compressive sensing broad-band hyperspectral SFG microscopy have demonstrated the potential application for imaging monolayer at metal surfaces with micrometer spatial resolution. Here is presented the capability of chemical imaging of spatially patterned monolayers of 1-octadecanethiol (ODT) and 16-methoxy-1-hexadecanethiol (MeOHT) molecules assembled on a copper surface. The spatial distributions of the monolayer with vibrational-spectral contrast are well-demonstrated at different frequency regions through reconstruction of the hypercube using a 3-dimensional total variation regularization algorithm (3DTV). Spatial-chemical distributions of each component are also reconstructed directly from the compressive measurements by endmember unmixing (CEU) scheme. Compared to 3DTV algorithm, the reconstruction from CEU shows spatial distribution of each component on the surfaces, and demonstrates the ability to characterize the domains of mixed-molecules on surfaces.

Fast Weighted Total Variation Regularization Algorithm for Blur Identification and Image Restoration

Images obtained from unconstrained environments may be blurred by unknown kernels and affected due to noise. This paper presents a new total variation minimization-based method for blindly deblurring such images. Unlike the alternating optimization-based algorithms, the proposed algorithm adopts a joint estimation strategy to estimate the unknown blurring kernel and the unknown image in an iterative manner, where each iteration performs two separate image denoising subproblems that admit fast implementation. Experiments are performed on multiple synthetic, grayscale, and color images, and the results demonstrate that the proposed method is effective in blind deblurring.

A new nonlocal total variation regularization algorithm for image denoising

The staircasing effect inevitably emerges in the recovered image via the local total variation (TV) based methods. To overcome this drawback, this paper elaborates on a novel nonlocal TV scheme associated with the quadratic perturbation of the ROF model for noise removal. Computationally, we present an improved split Bregman algorithm for minimizing the proposed energy functional recursively. Experimental results clearly demonstrate that our proposed strategy outperforms the corresponding TV scheme, especially in possessing higher computation speed and preserving the textures and fine details better when image denoising.

Image reconstruction method of electrical capacitance tomography based on compressed sensing principle

To improve the image reconstruction quality of electrical capacitance tomography (ECT), a new ECT image reconstruction method based on compressed sensing principle is proposed. The capacitances’ collection of the ECT system is regarded as linear measurement of compressed sensing; the measurement matrix is designed by randomly realigning the row vectors of a new sensitivity matrix, which is reconstructed by zero vectors’ expansion of the original sensitivity matrix, and the capacitance vectors expanded in the same way are regarded as measurement signals of compressed sensing. The original signal, i.e. permittivity distribution of some object inside a pipeline, is recovered by orthogonal matching pursuit algorithm. Finally, the simulation experiments are performed. The experimental results have shown that the average image reconstruction error and correlation coefficient obtained by this method are better than the corresponding indicators obtained by linear back-projection algorithm, Landweber iterative algorithm and total variation regularization algorithm. Therefore, it is a kind of ECT image reconstruction method with high accuracy, which also provides a new method and means for ECT research.

Computation of a 3-D Model for Lung Imaging With Electrical Impedance Tomography

The electrical impedance tomography (EIT) has been developed and evolved over the past 30 years, which has the great potential for clinical diagnosis in lung imaging and detection of thorax ventilation; however, EIT possesses the difficult problems in terms of developing hardware for data acquisition and the image reconstruction. In this paper, a cylinder geometry 3-D model for human thorax has been constructed with finite element method (FEM). A nodal-based total variation regularization algorithm has been evaluated with phantom tests which have been implemented by our EIT system in a salt-water tank. The in vivo experiments on the subject have been carried out, and then the lung images have been reconstructed during breath with the nodal total variation regularization algorithm. The result shows that the resistivity distribution of the lung is well reconstructed with the 3-D model and gives high contrast images. It also verifies that the nodal total variation regularization algorithm has the potential capability to become a useful algorithm for lung imaging with EIT.

SU‐C‐301‐01: Methodological Improvements in Voxel‐Based Analysis of Diffusion Tensor Imaging: Applications to Study the Impact of APOE on White Matter Integrity

Purpose: We utilize the DTI indices of apparent diffusion coefficient (ADC) and fractional anisotropy (FA) to investigate 14 normal subjects with the specific genes that increase (APOE e2) and that decrease (APOE e4) the age of onset of Alzhiemerˈs Disease. Methods: DTI acquisitions were performed in clinically acceptable scan times and thus had a low signal‐to‐noise ratio. The DTI data was denoised with a total variation regularization algorithm prior to affine and nonlinear registration to generate a common reference frame for the image volumes of all subjects. Region of interest (ROI), voxel‐based analysis (VBA), and tract based spatial statistics (TBSS) were performed on the aligned ADC and FA maps to identify differences in the cohorts segregated by these alleles as well as segregated by mean age of the group. Results: VBA on the denoised tensor data identified regions of reduced FA (primarily in the genu which was confirmed by ROI analysis) in the APOE e4 cohort compared to the APOE e2 cohort. The most consistent results were obtained for VBA using the denoised tensor and anisotropic smoothing prior to statistical testing. In contrast, isotropic smoothing identified regional differences for small filter sizes alone, emphasizing that this method introduces bias in FA values for higher smoothing kernel sizes. TBSS did not identify any regional differences in the white matter tracts and this may be related to the small localized area of change (found by VBA and ROI methods) that may not be detectable when analyzing voxels averaged normal to the tract. Conclusions: The current findings are consistent with the age trajectories of the transverse relaxation rate studies of APOE ε2 and ε4 cohorts. The relaxometry study confirms the current DTI study that the late myelinating regions such as the genu are more susceptible to age‐related myelin breakdown and this was associated with APOE status.

An algorithm for total variation regularization in high-dimensional linear problems

This paper describes an iterative algorithm for high-dimensional linear inverse problems, which is regularized by a differentiable discrete approximation of the total variation (TV) penalty. The algorithm is an interlaced iterative method based on optimization transfer with a separable quadratic surrogate for the TV penalty. The surrogate cost function is optimized using the block iterative regularized algebraic reconstruction technique (RSART). A proof of convergence is given and convergence is illustrated by numerical experiments with simulated parallel-beam computerized tomography (CT) data. The proposed method provides a block-iterative and convergent, hence efficient and reliable, algorithm to investigate the effects of TV regularization in applications such as CT.