Browsing by Author "Lou, Yifei"
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Item A General Framework of Non-convex Models for Sparse Recovery With Applications(December 2021) Hu, Mengqi; Gassensmith, Jeremiah; Lou, Yifei; Cao, Yan; Rachinskiy, Dmitry; Pereira, Felipe; Ramakrishna, ViswanathThanks to latest developments of science and technology, large data sets are becoming increasingly popular that lead to an emerging field, called compressive sensing (CS), which is about acquiring and processing sparse signals. In this thesis, we first propose a general framework to estimate sparse coefficients of generalized polynomial chaos (gPC) used in uncertainty quantification (UQ). In particular, we aim to identify a rotation matrix such that the gPC expansion of a set of random variables after the rotation has a sparser representation. However, this rotational approach alters the underlying linear system to be solved, which makes finding the sparse coefficients more difficult than the case without rotation. To resolve this issue, we examine several popular non-convex regularizations in CS that empirically perform better than the classic `1 approach. All these regularizations can be minimized by the alternating direction method of multipliers (ADMM). Numerical examples show superior performance of the proposed combination of rotation and non-convex sparsity promoting regularizations over the ones without rotation and with rotation but using the `1 norm. We observe through the UQ study that the `1 − `2 regularization often performs satisfactorily among the others. We then apply it to synthetic aperture radar (SAR) imaging based on a mathematical model of how electromagnetic waves are scattered in the space using Maxwell’s equations. Specifically we deduce an efficient sensing matrix for SAR and examine the efficiency of the `1 − `2 regularization to promote sparsity of scattered signals. Experimental results demonstrate that `1 − `2 can enhance the resolution of reconstructed image over the classic `1 approach. Motivated by conjugate gradient and adaptive momentum in the optimization literature, we propose a novel algorithmic improvement. The proposed algorithm works for general minimization problems, though numerical experiments are limited to `1 and `1 − `2 with a least-squares data fidelity term, showcasing faster convergence of the proposed algorithm over the traditional methods. We also establish the convergence of our algorithm for a quadratic problem.Item Bi-tensor Free Water Model With Positive Definite Diffusion Tensor and Fast Optimization(2021-08-01T05:00:00.000Z) Wang, Siyuan; Cao, Yan; Stefan, Mihaela C.; Lou, Yifei; Dabkowski, Mieczyslaw K.; Minkoff, Susan E.Diffusion tensor imaging is a widely used imaging methodology to infer the microstructure of brain tissues. When an image voxel contains partial volume of brain tissue with free water, the traditional one tensor model is not appropriate. A bi-tensor free water elimination model has been proposed to correct for the mixing effects. Moreover, recent studies have shown that the free water volume derived from this model could be a biomarker for brain aging and numerous brain disorders such as Parkinson’s and Alzheimer’s disease. However, the problem of fitting this model is ill-posed without additional assumptions. Models by adding spatial constraints or using data from multi-shell acquisition are proposed to stabilize the fitting, but none of them restricts the diffusion tensor D to be positive definite, which is a necessary condition. In this work, we formulate the bi-tensor model fitting as an optimization problem over the space of symmetric positive definite matrices and show that the objective function is a ratio of two geodesically convex functions. We also demonstrate by simulation that the estimation may be highly biased with single-shell data in the presence of noise, so multi-shell data are needed for the fitting of the bi-tensor free water elimination model. Inspired by the Cholesky decomposition, we treat the diffusion tensor D as the product LLT where L is a lower triangular matrix. The optimization is performed on L which guarantees the positive definiteness of D. Our model are evaluated with both simulations and real human brain data. Simulation results show that the model is computationally efficient and the two-shell acquisition gives the best estimation.Item Cell Nuclei Segmentation Using Deep Learning Techniques(2021-08-01T05:00:00.000Z) K. C. Khatri, Rajendra; Cao, Yan; Lv, Bing; Dabkowski, Mieczyslaw K.; Ramakrishna, Viswanath; Lou, YifeiPathological examination usually involves manual inspection of hematoxylin and eosin (H&E)- stained images, which is labor-intensive, prone to significant variations, and lacking reproducibility. One of the fundamental tasks to automate this process is to find all the cell nuclei in the H&E-stained images for further analysis. We attempt this problem using deep learning techniques. First, we introduce a semantic pixel-wise segmentation technique using dilated convolutions. We show that dilated convolutions are superior in extracting information from textured images. H&E-stained images are highly textured, which makes dilated convolutions an ideal technique to apply. Our dilated convolutional network (DCN) is constructed based on SegNet, a deep convolutional encoder-decoder architecture. Dilated convolution layers with increased dilation factors are used in the encoder to preserve image resolution. Dilated convolution layers with decreased dilation factors are used in the decoder to reduce gridding artifacts. Our DCN network was tested on synthetic data sets and a publicly available data set of H&E-stained images. We achieve better segmentation results than state-of-the-art. To further separate the instance of each cell nuclei, we adapt our DCN with a single shot multibox detector (SSD) and achieve promising results. Our methods are computationally efficient and can be run on a personal laptop computer. This work is the first step to wards using mathematical models to generate diagnostic inferences and providing clinically actionable knowledge to physicians and patients.Item Computation and stability analysis of periodically stationary pulses in a short pulse laser(2022-05-01T05:00:00.000Z) Shinglot, Vrushaly; Slinker, Jason D.; Zweck, John; Minkoff, Susan E.; Rachinskiy, Dmitry; Lou, YifeiShort pulse lasers generate a regular train of ultrashort pulses by balancing gain and loss, dispersion and nonlinearity. The spectrum of such a train of pulses is called a frequency comb, which has a wide range of applications in time and frequency metrology. Modern short pulse lasers generate periodically stationary pulses that change shape as they propagate around the laser, returning to the same shape each round trip. Soliton lasers generate stationary pulses which can be studied with averaged models. How- ever, with each subsequent generation of short pulse laser, there has been a dramatic increase in the amount by which the pulse varies over each round trip. Therefore, lumped models are required to accurately compute the periodically stationary solutions generated by these lasers. A lumped model consists of various components modeled either as input-output de- vices or using partial differential equations, each having a different effect on the pulse. The key issue in the modeling of short pulse lasers is to determine those regions in parameter space in which the laser operates stably. In this thesis, we first describe an evolutionary approach to informally assess the stability of periodically stationary pulses in an experimental stretched pulse laser. We then develop a two-stage dynamical approach to more rigorously determine the stability of periodically stationary pulses in lumped laser models. In the first stage of the dynamical approach, we numerically compute periodically stationary pulses by minimizing a Poincar ́e map functional using a gradient based optimization method. We derive a formula for the gradient of the Poincar ́e map functional that is used in the numerical optimization method. In the second stage of the dynamical approach, we study the linear stability of these periodically stationary pulses. To do so, we present a method based on Floquet theory, in which the stability of periodically stationary pulses is characterized by the spectrum of the monodromy operator, which is obtained by linearizing the laser system about the periodic solution. We establish an existence, uniqueness, and regularity theorem for the monodromy operator under reasonable regularity and decay hypotheses on the periodically stationary pulse. We derive a formula for the essential spectrum of the monodromy operator, which quantifies the growth rate of continuous waves far from the pulse. We provide a rigorous proof of this formula using spectral theory and the theory of evolution semigroups. We implement the dynamical approach using a lumped model of the stretched pulse laser and compare its results with the evolutionary approach. We present results showing excellent agreement between the essential spectrum obtained using a matrix discretization of the monodromy operator and the formula. We use the dynamical approach to study bifurcations from stable to unstable periodically stationary pulses by varying the parameters in the laser. In particular, we demonstrate how the effects of fast saturable loss and slow saturable gain can be combined to generate a stable periodically stationary pulse. Our work represents the first spectral stability analysis of periodically stationary pulses in a realistic lumped model of an experimental short pulse laser.Item Existence and Spatio-temporal Patterns of Periodic Solutions to Non-autonomous Second Order Equivariant Delayed Systems(2022-05-01T05:00:00.000Z) Ye, Xiaoli; Malko, Anton V.; Krawcewicz, Wieslaw; Lou, Yifei; Ohsawa, Tomoki; Balanov, Zalman I.In this dissertation, we study the existence and spatio-temporal symmetric patterns of peri- odic solutions to second order reversible equivariant non-autonomous periodic systems with multiple delays under the Hartman-Nagumo growth conditions. Our method is based on the usage of the Brouwer D1 × Z2 × Γ-equivariant degree theory, where D1 is related to the reversing symmetry, Z2 is related to the oddness of the right-hand-side and Γ reflects the symmetric character of the coupling in the corresponding network. Abstract results are supported by a concrete example with Γ = Dn – the dihedral group of order 2n.Item Fractional-Order Total Variation Based Image Denoising, Deconvolution, and CT Reconstruction Under Poisson Statistics(2020-08) Chowdhury, Md Mujibur Rahman; Lou, YifeiImage processing and analysis have gained increasing popularity nowadays for its applications in medical imaging, astronomy, astrophysics, surveillance, image compression, and transmission. In this dissertation, we work on three types of image restoration: image denoising, deconvolution, and computer tomography (CT) reconstruction. In many photonlimited imaging systems, acquired data is usually corrupted by Poisson noise and blurring artifacts. Different from Gaussian noise that is commonly used in the scientific community, Poisson noise depends on the image intensity, which makes image restoration very challenging. Moreover, the underlying images often contain complex geometries, and hence it is desirable to impose a regularization to preserve piecewise smoothness. For this purpose, we propose to use the fractional-order total variation (FOTV) regularization. Specifically, for image denoising, we can establish the existence and uniqueness of a solution to our proposed model. To solve the problem efficiently, we adopt three numerical algorithms based on the Chambolle-Pock primal-dual method, a forward-backward splitting scheme, and the alternating direction method of multipliers (ADMM), each with guaranteed convergence. Various experimental results demonstrate the effectiveness and efficiency of our proposed methods over the state-of-the-art in Poisson denoising. Blurring is always inevitable, as the data recorded by a digital device is an average over neighboring pixels, leading to a blurred image. The blurring process can be modeled as a convolution of an underlying image with a point spread function (PSF). We consider both non-blind and blind image deblurring models, in which blind refers to the case of an unknown PSF. In the pursuit of the high-order smoothness of a restored image, we use the FOTV regularization to remove the blur and Poisson noise simultaneously. We develop an ADMM-based algorithm for non-blind deblurring and an expectation-maximization (EM) algorithm in the blind case. A variety of numerical experiments demonstrate that the proposed algorithms can efficiently reconstruct piecewise-smooth images degraded by Poisson noise and various types of blurring, including Gaussian and motion blurs. Specifically for blind image deblurring, we obtain significant improvements over the state-of-the-art. Lastly, we consider a CT reconstruction problem, where the noise is traditionally modeled by Gaussian distribution. We propose using the FOTV regularization and a data fidelity term for Poisson noise to reconstruct the CT image. We show in experiments that the Gaussian noise is indeed suitable when the highest intensity value (or called peak value) is large. But the Poisson distribution is a more appropriate distribution for relatively lower peak values. Furthermore, we demonstrate that FOTV-based regularization outperforms the classic methods in the CT reconstruction, especially when the data has a small peak value, or the signal-to-noise ratio is low.Item Geometric Integrators for Non-separable Hamiltonian Systems(2022-08-01T05:00:00.000Z) Jayawardana, Buddhika Chathuranga Bandara; Ohsawa, Tomoki; Winkler , Duane; Rachinskiy, Dmitry; Zweck, John; Lou, YifeiIn this thesis, we consider non-separable Hamiltonian systems, and we develop an integrator that combines Pihajoki’s expanded approach to phase space with the symmetric projection technique. Through this, we construct a semiexplicit numerical integrator, meaning that the primary time evolution step is explicit but the symmetric projection step is implicit. The symmetric projection fixes the major disadvantage of the extended phase space technique by binding possibly divergent copies of solutions. In addition, our semiexplicit approach gives the first extended phase space integrator that is symplectic in the original phase space. This is in contrast to those explicit extended phase space integrators of Pihajoki and Tao, which are symplectic only in the extended phase space. Our integrator tends to preserve invariants better than Tao’s. Moreover, for some higher-order implementations and higher-dimensional problems, ours is faster than Tao’s explicit method despite being partially implicit.Item Multienergy Cone-Beam Computed Tomography Reconstruction with a Spatial Spectral Nonlocal Means Algorithm(Society for Industrial and Applied Mathematics Publications) Li, B.; Shen, C.; Chi, Y.; Yang, M.; Lou, Yifei; Zhou, L.; Jia, X.; 0000-0003-1973-5704 (Lou, Y); Lou, YifeiMultienergy computed tomography (CT) is an emerging medical image modality with a number of potential applications in diagnosis and therapy. However, high system cost and technical barriers obstruct its step into routine clinical practice. In this study, we propose a framework to realize multienergy cone beam CT (ME-CBCT) on the CBCT system that is widely available and has been routinely used for radiotherapy image guidance. In our method, a kVp switching technique is realized, which acquires x-ray projections with kVp levels cycling through a number of values. For this kVp-switching based ME-CBCT acquisition, x-ray projections of each energy channel are only a subset of all the acquired projections. This leads to an undersampling issue, posing challenges to the reconstruction problem. We propose a spatial spectral nonlocal means (NLM) method to reconstruct ME-CBCT, which employs image correlations along both spatial and spectral directions to suppress noisy and streak artifacts. To address the intensity scale difference at different energy channels, a histogram matching method is incorporated. Our method is different from conventionally used NLM methods in that spectral dimension is included, which helps to effectively remove streak artifacts appearing at different directions in images with different energy channels. Convergence analysis of our algorithm is provided. A comprehensive set of simulation and real experimental studies demonstrate feasibility of our ME-CBCT scheme and the capability of achieving superior image quality compared to conventional filtered backprojection-type and NLM reconstruction methods. © 2018 Society for Industrial and Applied Mathematics.Item Multienergy Element-Resolved Cone Beam CT (MEER-CBCT) Realized on a Conventional CBCT Platform(John Wiley and Sons Ltd.) Shen, C.; Li, B.; Lou, Yifei; Yang, M.; Zhou, L.; Jia, X.; 0000-0003-1973-5704 (Lou, Y); Lou, YifeiPurpose: Cone beam CT (CBCT) has been widely used in radiation therapy. However, its main application is still to acquire anatomical information for patient positioning. This study proposes a multienergy element-resolved (MEER) CBCT framework that employs energy-resolved data acquisition on a conventional CBCT platform and then simultaneously reconstructs images of x-ray attenuation coefficients, electron density relative to water (rED), and elemental composition (EC) to support advanced applications. Methods: The MEER-CBCT framework is realized on a Varian TrueBeam CBCT platform using a kVp-switching scanning scheme. A simultaneous image reconstruction and elemental decomposition model is formulated as an optimization problem. The objective function uses a least square term to enforce fidelity between x-ray attenuation coefficients and projection measurements. Spatial regularization is introduced via sparsity under a tight wavelet-frame transform. Consistency is imposed among rED, EC, and attenuation coefficients and inherently serves as a regularization term along the energy direction. The EC is further constrained by a sparse combination of ECs in a dictionary containing tissues commonly existing in humans. The optimization problem is solved by a novel alternating-direction minimization scheme. The MEER-CBCT framework was tested in a simulation study using an NCAT phantom and an experimental study using a Gammex phantom. Results: MEER-CBCT framework was successfully realized on a clinical Varian TrueBeam onboard CBCT platform with three energy channels of 80, 100, and 120 kVp. In the simulation study, the attenuation coefficient image achieved a structural similarity index of 0.98, compared to 0.61 for the image reconstructed by the conventional conjugate gradient least square (CGLS) algorithm, primarily because of reduction in artifacts. In the experimental study, the attenuation image obtained a contrast-to-noise ratio ≥60, much higher than that of CGLS results (~16) because of noise reduction. The median errors in rED and EC were 0.5% and 1.4% in the simulation study and 1.4% and 2.3% in the experimental study. Conclusion: We proposed a novel MEER-CBCT framework realized on a clinical CBCT platform. Simulation and experimental studies demonstrated its capability to simultaneously reconstruct x-ray attenuation coefficient, rED, and EC images accurately. ©2018 American Association of Physicists in MedicineItem Optimal Control of Human Balance Models With Reflex Delay(August 2023) Rajapaksha, Lashika Nishamani 1990-; Anderson, Phillip C.; Turi, Janos; Lou, Yifei; Cao, Yan; Pereira, FelipeFalls are the leading cause of injury-related deaths among the elderly, and scientists are increasingly interested in understanding the mechanism of human balance control. A single inverted pendulum is used to model the musculoskeletal dynamics of the human body with an ankle torque. There is a brief period of time between detecting a problem in proper positioning and applying torque to correct it. We present a mathematical optimal control model with delay for identifying human balance postural dynamics considering humans as a single inverted pendulum with an ankle torque. The equation of motion is a second-order delay differential equation, and it is solved numerically. Optimal feedback gains obtained from the optimal control problem with linear quadratic regulator function vary in time for a short period of time before becoming constant. These optimal feed- back gains are time and delay-dependent to compensate for the effect of the delay. We provide numerical simulations for different parameter values and scenarios to investigate human postural dynamics’ stability and demonstrate the model’s capabilities. Finally, we extend our study by investigating the dynamics of ankle and hip movement in response to perturbations using a double-inverted pendulum.Item Phase Retrieval by Alternating Direction Method of Multipliers(2021-07-20) Akhavan, Mehdi; Lou, YifeiThis dissertation aims at reconstructing a signal from the magnitude of its Fourier transform, known as phase retrieval. The problem arises in variety of areas such as crystallography, astronomy, optics, voice recognition, and coherent diffraction imaging (CDI). In particular, we focus on two types of phaseless measurements: short-time Fourier transform (STFT) and frequency-resolved optical gating (FROG). STFT takes the Fourier transform when passing a short-time window over a signal. When the window function is given, the problem is referred to as non-blind STFT, while blind STFT means to simultaneously estimate both the signal and the window from the magnitude measurements. FROG is closely related to STFT in such a way that the window function in FROG is just the signal itself. We apply alternating direction method of multipliers (ADMM) to solve all the aforementioned problems: non-blind STFT, blind STFT, and FROG. Specifically for the blind STFT, we discuss three approaches to address the scaling ambiguity. We also consider a special type of signals that has only a few non-zero elements by minimizing the L1 norm to promote sparsity in the objective function. Numerical experiments are provided to demonstrate the proposed algorithms outperform the state-of-the-art in non-blind STFT and FROG. As the blind STFT is one of the first kind, we compare the performance of the three proposed approaches.Item Role of FimK in Mediating Host Urinary Bladder Epithelial Cell Association of Uropathogenic Klebsiella Pneumoniae and Quasipneumoniae(December 2021) Venkitapathi, Sundharamani; De Nisco, Nicole; Lou, Yifei; Palmer, Kelli; Delk, Nikki; Spiro, StephenKlebsiella spp. commonly cause both uncomplicated urinary tract infection (UTI) and recurrent UTI (rUTI). K. quasipneumoniae, a relatively newly defined species of Klebsiella, has been shown to be metabolically distinct from K. pneumoniae, but its urovirulence mechanisms have not been defined. Type 1 and type 3 fimbriae, encoded by fim and mrk operons respectively, mediate attachment of Klebsiella spp. to host epithelial cells. fimK is a regulatory gene unique to the Klebsiella fim operon that encodes an N-terminal DNA binding domain and a C-terminal phosphodiesterase domain that has been hypothesized to cross-regulate type 3 fimbriae via modulation of cellular levels of cyclic di-GMP. Comparative genomic analysis between K. pneumoniae and K. quasipneumoniae revealed a conserved premature stop codon in K. quasipneumoniae fimK that results in loss of the C-terminal phosphodiesterase domain (PDE). We hypothesized that this truncation would ablate cross-regulation of type 3 fimbriae in K. quasipneumoniae. Here, we report that K. quasipneumoniae KqPF9 bladder epithelial cell association and invasion is dependent on type 3 but not type 1 fimbriae. Further, we show that basal expression of both type 1 and type 3 fimbrial operons as well as bladder epithelial cell association are higher in KqPF9 than in K. pneumoniae TOP52. Interestingly, complementation of KqPF9∆fimK with the TOP52 fimK allele markedly reduced type 3 fimbrial expression and bladder epithelial cell attachment, a phenotype that was rescued by mutation of the C-terminal PDE active site. Taken together these data suggest that C-terminal PDE of FimK modulates type 3 fimbrial expression in K. pneumoniae and its absence in K. quasipneumoniae leads to a loss of type 3 fimbrial cross-regulation.Item Seismic Data Reconstruction With Low-rank Tensor Optimization(2022-05-01T05:00:00.000Z) Popa, Jonathan; Minkoff, Susan E.; Lou, Yifei; Meloni, Gabriele; Zweck, John; Zhu, HejunSeismic data recorded in the field often has gaps due to missing or failed receivers or aperture restrictions and may be contaminated by external noise. Reconstruction is the process of completing missing data and removing noise. Multi-dimensional seismic data, for example in 3, 4, or 5D, can be efficiently stored in a tensor or multi-dimensional array. Low-rank tensor optimization is a model used to reconstruct tensor data under the assumption that the underlying data has low rank. Data has low rank when it has redundant rows or columns, causing the singular values to decay at a rapid rate. Because minimizing rank is NP-hard, a relaxation of rank can be used such as the tensor nuclear norm (TNN), derived from the tensor singular value decomposition (tSVD). The alternating direction method of multipliers (ADMM) effectively solves the TNN model in which the sum of singular values is minimized. ADMM splits the minimization problem into smaller subproblems. The combination of the ADMM method and TNN model is referred to as TNN-ADMM and is useful for reconstruc- tion of missing data. Exploiting the conjugate symmetry of the multi-dimensional Fourier transform (the most expensive part of the tSVD algorithm) reduces the runtime of the tSVD algorithm for real- valued order-p tensors by approximately 50%. The relation between the tSVD of a tensor and the SVD of a corresponding block-diagonal matrix reveals how the singular values of the tensor and matrix change as the orientation of the tensor changes and provides evidence for the success of the most-square orientation when used for low rank data reconstruction. For seismic data, the most-square orientation has frontal faces formed over the spatial dimen- sions, so the tensor contains more redundancies than pairing a spatial dimension with time. On real data reconstruction examples, TNN-ADMM outperforms two other data completion methods, projection onto convex sets and multi-channel singular spectrum analysis (MSSA), with less error and 10-1000× faster runtime. In exploration seismology, an initial baseline survey informs decisions to produce a region, and monitor surveys conducted during production provide updated subsurface information. The time-lapse difference between the baseline and monitor surveys reveals changes in the Earth due to production. Non-repeatability issues, such as inconsistent receiver locations, negatively impact one’s ability to accurately identify time-lapse changes. If receiver locations are regularized onto a common grid, then the baseline and monitor surveys can be compared. The resulting tensors are incomplete due to the potential for grid blocks to not contain receivers, so we apply TNN-ADMM to each data tensor to successfully fill in missing data, and a time-lapse difference can be computed between the reconstructed tensors. The unconstrained formulation of TNN-ADMM simultaneously completes and denoises data. The convergence analysis of this method proves that the iterative solution converges to a local minimum, provided that the step size parameter is greater than one. The convergence proof requires new properties of the Frobenius norm for tensors, as well as Hadamard (entry- wise) product properties. On a synthetic problem unconstrained TNN-ADMM outperforms MSSA with 18%-27% less error and 10× faster runtime.Item Symmetries of Einstein’s Equations in Vacuum and Their Geodesics(2021-12-01T06:00:00.000Z) Kasmaie, Behshid; Akbar, Mohammad; Biewer, Michael; Dragovic, Vladimir; King, Lindsay; Lou, YifeiThis thesis explores symmetries of vacuum Einstein equations that are static and at least axially symmetric, i.e., Ricci-flat Lorentzian geometries that admit a timelike Killing vector field and a closed spacelike Killing vector field among their isometries. We study symmetries of the geodesics in these spacetimes as well as symmetries of the system of Einstein equations describing such spacetimes. Geodesics in three dimensions have symmetries and associated conserved quantities absent in four and higher dimensions. We employ the socalled direct method for computing the conserved quantities. For the static axisymmetric system in vacuum, we found all symmetries of the system which enabled us to explain why one cannot obtain algebraic prescriptions for generating new solutions from old ones beyond those already known. Symmetries of the geodesics in spherical symmetry show that there is no general connection between cosmological constant and projective equivalence and that one can find an appropriate coordinate system where the effect of cosmological constant disappears from the bending angle, unlike in the static coordinates.Item A Weighted Difference of Anisotropic and Isotropic Total Variation Model for Image Processing(Society for Industrial and Applied Mathematics Publications, 2015-09-10) Lou, Yifei; Zeng, T.; Osher, S.; Xin, J.; 0000-0003-1973-5704 (Lou, Y)We propose a weighted difference of anisotropic and isotropic total variation (TV) as a regularization for image processing tasks, based on the well-known TV model and natural image statistics. Due to the form of our model, it is natural to compute via a difference of convex algorithm (DCA). We draw its connection to the Bregman iteration for convex problems and prove that the iteration generated from our algorithm converges to a stationary point with the objective function values decreasing monotonically. A stopping strategy based on the stable oscillatory pattern of the iteration error from the ground truth is introduced. In numerical experiments on image denoising, image deblurring, and magnetic resonance imaging (MRI) reconstruction, our method improves on the classical TV model consistently and is on par with representative state-of-the-art methods.