Total Variation Regularization Research Articles

A rotation total variation regularization for full waveform inversion

Abstract Mathematically, full waveform inversion is a nonlinear and ill-posed inverse problem, requiring a regularization method to obtain a reasonable result. Total variation regularization is an effective regularization method which can preserve the sharp edges of the solution. It is well-known that the standard total variation regularization usually leads to stair-casing artifacts in slanted structures. Thus, the standard total variation regularization may not be effective in solving the full waveform inverse problem, due to the slanted properties of the subsurface structures. In this paper, we propose a rotational total variation regularization method based on the weighting rotational transform operator and the standard total variation regularization for the full waveform inverse problem. To further improve the resolution of the inverted results for different directional structures, a hybrid regularization method combining the rotational and standard total variation regularization is proposed. An efficient version of the conjugate gradient method, i.e., CGOPT, is used to efficiently solve the proposed methods. Numerical experiments based on Sigsbee and Marmousi2 models are carried out to demonstrate the effectiveness of our methods.

Model-based temporal unmixing towards quantitative photo-switching optoacoustic tomography

Optoacoustic (OA) imaging combined with reversibly photoswitchable proteins has emerged as a promising technology for the high-sensitivity and multiplexed imaging of cells in live tissues in preclinical research. Through carefully designed illumination schedules of ON and OFF laser pulses, the resulting OA signal is a multiplex of different reporter species and the background. We propose a model-based variational framework to computationally unmix and image different species of photo-switching reporters using optoacoustic tomography. It is based on a detailed mathematical description of the photo-switching mechanism, which models how relevant physical parameters such as the kinetic constants and light fluence impact the switching signal. We introduce an algorithm that operates on images, as opposed to traditional pixelwise approaches. It takes the form of an iterative inversion combined with tailored ℓ1 and total-variation regularization to increase the robustness to noise and to improve the unmixing quality. We show that our method can disentangle multiple spatially overlapping labels and recover continuous maps of quantities of interest on controlled phantoms and mice experiments.

Physically enhanced neural network based on projection map synthesis for chemiluminescence tomography reconstruction with limited views

In many combustion systems, data collection through optical windows is often hindered by fixed mechanical components that limit the number of available observation angles. This restriction poses a significant challenge to the accurate reconstruction of chemiluminescence tomography images with limited views. To address this limitation, we propose a novel projection interpolation approach for physically enhanced neural networks (PIPEN) to address this limitation. The PIPEN utilizes projection maps from two intersecting viewpoints and employs an interpolation network to estimate the projection maps for occluded views between these two angles. The interpolated and original projections are input into a physically enhanced neural network (PENN) to perform a volumetric tomography reconstruction. The PENN was designed to accommodate practical scenarios in which ground-truth data are unavailable. Furthermore, the loss function in PENN is enhanced with a total variation (TV) regularization term that mitigates noise and artifacts and improves the quality of the visual reconstruction. Experimental evaluations indicate that the PIPEN achieves a reconstruction performance comparable to that using a complete set of seven directions despite only utilizing projection maps from two orthogonal views. These results suggest that the PIPEN has significant potential for practical 3D flame reconstruction under constrained observation conditions.

Frequency-domain learning-driven lightweight phase recovery method for in-line holography

Retrieving phase information from a single-intensity image poses a highly ill-posed inverse problem in the field of optical imaging, particularly in applications such as in-line holography, where phase information is critical for accurate reconstruction. Traditional methods exhibit limited applicability in dynamic scenes and struggle to ensure consistent reconstruction quality. Recent advancements in deep learning and the emergence of physics-informed methods have introduced novel strategies to address this challenge. However, despite reduced reliance on extensive datasets, the complexity of network architectures remains a significant barrier. In this study, we propose a frequency-domain learning-driven lightweight phase recovery method (FNet) based on complex-valued networks. By analyzing the characteristics of the optical diffraction process in the frequency domain, we design models with fewer parameters through frequency-domain learning. This lightweight approach effectively minimizes computational resource demands, facilitating efficient phase recovery in resource-constrained environments. Simulation and experimental results on multiple in-line holography datasets demonstrate that FNet achieves performance comparable to conventional methods and real-valued networks while utilizing significantly fewer parameters and computational resources, thereby validating its efficacy. Furthermore, the incorporation of complex-valued total variation regularization markedly reduces artifacts and enhances reconstruction quality in complex datasets. We contend that this work highlights the necessity for alignment between neural networks and physical models, thereby improving operational efficiency and expanding the applicability of phase recovery technologies.

Hyperspectral image restoration via RPCA model based on spectral-spatial correlated total variation regularizer

Hyperspectral image restoration via RPCA model based on spectral-spatial correlated total variation regularizer

Artifact removal of EEG data using wavelet total variation denoising and independent component analysis

Artifact removal of EEG data using wavelet total variation denoising and independent component analysis

Total variational noise reduction method for EBAPS image based on weighted nuclear norm minimization.

The electron-bombarded active pixel sensor (EBAPS) is a highly sensitive vacuum-solid hybrid low-light imaging device capable of functioning in ultra-low illumination environments as low as 10-4 lx. However, this high sensitivity also causes problems, such as a low signal-to-noise ratio and complex noise. To enhance the quality of low-light night vision images captured by EBAPS and achieve effective imaging in ultra-low illumination, this study proposes a noise reduction algorithm based on the noise characteristics of EBAPS images. By utilizing the weighted nuclear norm minimization (WNNM) as the fundamental framework, several enhanced methods to address the multi-source noise of the EBAPS under ultra-low illumination have been proposed. These methods include outlier removal and variance-stabilizing transformation. To address the lack of edge preservation, a four-directional total variational regularization term has been incorporated into the WNNM model to maintain the image edge. Experimental results demonstrated that the improved method effectively eliminates various types of EBAPS noise while considerably returning the edges, ultimately enhancing the quality of low-light images. This study greatly facilitates subsequent applications of the low-light night vision technology.

Flyscan terahertz multi-plane lensless imaging with suppressed coherent noise.

Coherent lensless imaging usually suffers from coherent noise and twin-image artifacts. In the terahertz (THz) range, where wavelengths are 2 to 4 orders of magnitude longer than those in the visible spectrum, the coherent noise manifests primarily as parasitic interference fringes and edge diffraction, rather than speckle noise. In this work, to suppress the Fabry-Pérot (F-P) interference fringes, we propose a novel method, which involves the averaging over multiple diffraction patterns that are acquired at equal intervals within a sample's half-wavelength axial shift. To address edge diffraction, as well as non-uniform illumination, a normalization operation is applied. As the twin-image disturbances when dealing with a single diffraction pattern, multi-plane configuration is employed. With all these strategies combined, we propose a flyscan THz multi-plane lensless imaging technique that enables subwavelength resolution, and high-quality, full-field, and rapid complex-valued THz imaging. Furthermore, we refine two algorithms for image reconstruction: one based on the regular multi-plane alternating projection and the other based on an optimization model with total variation regularization. We experimentally verify the proposed methods, achieving a lateral resolution of 88 µm (0.74λ) at 2.52 THz, and showcase its potential for biomedical applications by imaging a section of mouse brain tissue.

Enhancing photon-counting computed tomography reconstruction via subspace dictionary learning and spatial sparsity regularization.

Photon-counting computed tomography (CT) is an advanced imaging technique that enables multi-energy imaging from a single scan. However, the limited photon count assigned to narrow energy bins leads to increased quantum noise in the reconstructed spectral images. To address this issue, leveraging the prior information in the spectral images is essential. This study aimed to develop an efficient algorithm that enhances image reconstruction quality by reducing noise levels and preserving image details. To improve image reconstruction quality for photon-counting CT, we propose an algorithm based on the subspace-assisted multi-prior information, including global, nonlocal, and local priors, for spectral CT reconstruction. Specifically, the algorithm first maps spectral CT images, which exhibit global low-rank characteristics, to low-dimensional eigenimages using subspace decomposition. Then, similar image patches are extracted based on the manifold structure distance from highly correlated eigenimages in both spectral and spatial domains. These patches are stacked to form a nonlocal full-channel tensor group. Subsequently, non-convex structural sparsity is applied to this tensor group through adaptive dictionary learning, exploiting nonlocal similarity. Finally, the alternating direction method of multipliers (ADMM) is applied to solve the optimization model iteratively. The simulated walnut and real mouse data were applied to validate the effectiveness of the proposed method. In the simulation experiments, the proposed method reduced the root mean square error (RMSE) by 87.74%, 86.88%, 67.01%, 46.42%, and 13.51% compared to the respective state-of-the-art five comparison methods. The time taken for one iteration of the proposed algorithm was as low as 32.57 seconds, which was 92.07% less than framelet tensor nuclear norm [framelet tensor sparsity with block-matching method (FTNN)] method and 74.13% less than total variation regularization [tensor nonlocal similarity and local TV sparsity method (ITS_TV)] method, the other two tensor block-matching (BM)-based comparison methods. The material decomposition results in real mouse data further validated the accuracy of the proposed method for different materials. The experimental results indicate that the proposed algorithm effectively reduces computational costs while improving the accuracy of image reconstruction and material decomposition, showing promising advantages over the compared method.

A New Cross-Space Total Variation Regularization Model for Color Image Restoration With Quaternion Blur Operator

A New Cross-Space Total Variation Regularization Model for Color Image Restoration With Quaternion Blur Operator

Superimposed Wavefront Imaging of Diffraction-enhanced X-rays: sparsity-aware CT reconstruction from limited-view projections.

In this paper, we describe an algebraic reconstruction algorithm with a total variation regularization (ART + TV) based on the Superimposed Wavefront Imaging of Diffraction-enhanced X-rays (SWIDeX) method to effectively reduce the number of projections required for differential phase-contrast CT reconstruction. SWIDeX is a technique that uses a Laue-case Si analyzer with closely spaced scintillator to generate second derivative phase-contrast images with high contrast of a subject. When the projections obtained by this technique are reconstructed, a Laplacian phase-contrast tomographic image with higher sparsity than the original physical distribution of the subject can be obtained. In the proposed method, the Laplacian image is first obtained by applying ART + TV, which is expected to reduce the projection with higher sparsity, to the projection obtained from SWIDeX with a limited number of views. Then, by solving Poisson's equation for the Laplacian image, a tomographic image representing the refractive index distribution is obtained. Simulations and actual X-ray experiments were conducted to demonstrate the effectiveness of the proposed method in projection reduction. In the simulation, image quality was maintained even when the number of projections was reduced to about 1/10 of the originally required views, and in the actual experiment, biological tissue structure was maintained even when the number of projections was reduced to about 1/30. SWIDeX can visualize the internal structures of biological tissues with very high contrast, and the proposed method will be useful for CT reconstruction from large projection data with a wide field of view and high spatial resolution.

A retinex inspired deep image prior model for despeckling and deblurring of aerial and satellite images using proximal gradient method

ABSTRACT Unsupervised learning models, particularly in the remote sensing domain, have gained significant attention in recent years. Various degradations in the satellite images, primarily occurring during acquisition, pose a substantial hurdle in obtaining reliable ground truth and extensive training data. The Deep Image Prior model (DIP) addresses these issues by performing restoration tasks using a single image, relying on the implicit regularization inherent in the network architecture. In this paper, we propose a novel approach, integrating the DIP model within the retinex framework to restore aerial and satellite images from the Gamma distributed speckles and linear shift-invariant Gaussian blur along with contrast enhancement using the alternating proximal gradient descent ascent (PGDA) method. Our proposed methodology combines implicit regularization with explicit total variational (TV) regularization, incorporating automated estimation of local regularization parameters. The data-fidelity component in the optimization function is formulated using the Bayesian Maximum A posteriori (MAP) estimate, assuming the speckles follow the Gamma distribution. Demonstration of despeckling and deblurring alone and in addition as a combined task is carried out on aerial and Synthetic Aperture Radar (SAR) images with different resolutions and polarization from various sources. Results obtained are compared with various state-of-the-art despeckling and deblurring models using distinct image quality metrics such as Equivalent Number of Looks (ENL), Contrast to Noise Ratio (CNR), Edge Preserving Index (EPI), Entropy, Global Contrast Factor (GCF), Natural Image Quality Evaluator (NIQE), Blind/Referenceless Image Spatial Quality Evaluator (BRISQUE) and Bradley-Terry (B-T) score based on the various factors. The quality of restored images depicted superior performance of the proposed method over the existing models under study.

Blind Infrared Remote-Sensing Image Deblurring Algorithm via Edge Composite-Gradient Feature Prior and Detail Maintenance

The problem of blind image deblurring remains a challenging inverse problem, due to the ill-posed nature of estimating unknown blur kernels and latent images within the Maximum A Posteriori (MAP) framework. To address this challenge, traditional methods often rely on sparse regularization priors to mitigate the uncertainty inherent in the problem. In this paper, we propose a novel blind deblurring model based on the MAP framework that leverages Composite-Gradient Feature (CGF) variations in edge regions after image blurring. This prior term is specifically designed to exploit the high sparsity of sharp edge regions in clear images, thereby effectively alleviating the ill-posedness of the problem. Unlike existing methods that focus on local gradient information, our approach focuses on the aggregation of edge regions, enabling better detection of both sharp and smoothed edges in blurred images. In the blur kernel estimation process, we enhance the accuracy of the kernel by assigning effective edge information from the blurred image to the smoothed intermediate latent image, preserving critical structural details lost during the blurring process. To further improve the edge-preserving restoration, we introduce an adaptive regularizer that outperforms traditional total variation regularization by better maintaining edge integrity in both clear and blurred images. The proposed variational model is efficiently implemented using alternating iterative techniques. Extensive numerical experiments and comparisons with state-of-the-art methods demonstrate the superior performance of our approach, highlighting its effectiveness and real-world applicability in diverse image-restoration tasks.

Unsupervised Bayesian generation of synthetic CT from CBCT using patient-specific score-based prior.

Cone-beam computed tomography (CBCT) scans, performed fractionally (e.g., daily or weekly), are widely utilized for patient alignment in the image-guided radiotherapy (IGRT) process, thereby making it a potential imaging modality for the implementation of adaptive radiotherapy (ART) protocols. Nonetheless, significant artifacts and incorrect Hounsfield unit (HU) values hinder their application in quantitative tasks such as target and organ segmentations and dose calculation. Therefore, acquiring CT-quality images from the CBCT scans is essential to implement online ART in clinical settings. This work aims to develop an unsupervised learning method using the patient-specific diffusion model for CBCT-based synthetic CT (sCT) generation to improve the image quality of CBCT. The proposed method is in an unsupervised framework that utilizes a patient-specific score-based model as the image prior alongside a customized total variation (TV) regularization to enforce coherence across different transverse slices. The score-based model is unconditionally trained using the same patient's planning CT (pCT) images to characterize the manifold of CT-quality images and capture the unique anatomical information of the specific patient. The efficacy of the proposed method was assessed on images from anatomical sites including head and neck (H&N) cancer, pancreatic cancer, and lung cancer. The performance of the proposed CBCT correction method was evaluated using quantitative metrics, including mean absolute error (MAE), non-uniformity (NU), and structural similarity index measure (SSIM). Additionally, the proposed algorithm was benchmarked against other unsupervised learning-based CBCT correction algorithms. The proposed method significantly reduced various kinds of CBCT artifacts in the studies of H&N, pancreatic, and lung cancer patients. In the lung stereotactic body radiation therapy (SBRT) patient study, the MAE, NU, and SSIM were improved from 47 HU, 45 HU, and 0.58 in the original CBCT images to 13 HU, 14dB, and 0.67 in the generated sCT images. Compared to other unsupervised learning-based algorithms, the proposed method demonstrated superior performance in artifact reduction. The proposed unsupervised method can generate sCT from CBCT with reduced artifacts and precise HU values, enabling CBCT-guided segmentation and replanning for online ART.

Low Light Image Enhancement Using Python

ABSTRACT----The poor signal-to-noise ratio (SNR) in low-light photos frequently results in significant sensor noise. Moreover, the noise is non-Gaussian and signal-dependent. We propose a novel denoising technique to tackle the issue by combining weighted total variation (TV) regularization with a Poisson noise model. The weighted Total Variation (T V) regularization effectively eliminates noise while preserving details, whereas the Poisson noise model retains the nature of the noise. Our suggested strategy performs better on NIQE scores than the most advanced techniques. KEYWORDS----COOPERATIVE Intelligent Transport Systems (C-ITS), Convolutional Neural Network (CNN), Image Collection, CNN+Pyramid Model, Signal to Noise Ratio (SNR), Total Variation (TV) Image Segmentation Histogram Analysis, Image Processing, Image Filtering, Image Enhancement

Magnetic Resonance Image Restoration by Utilizing Fractional-Order Total Variation and Recursive Filtering

Total variation-based methods are effective for magnetic resonance image restoration. To eliminate impulse noise, the l_0-norm total variation model is a proven approach. However, traditional total variation image restoration often results in staircase artifacts, especially at high noise levels. In this paper, we propose an innovative magnetic resonance image restoration model that integrates fractional-order regularization and filtering techniques. Specifically, the first term uses the l_0-norm as the data fidelity term to effectively remove impulse noise. The second term introduces a fractional-order total variation regularizer, which preserves structural information while reducing staircase artifacts during deblurring. Due to its limitations in texture detail recovery, we employ recursive filtering for high-quality edge-preserving filtering. Finally, we solve the optimization model using the alternating direction method of multipliers. Experimental results demonstrate the effectiveness of our method in restoring magnetic resonance images.

On the existence of solutions to adversarial training in multiclass classification

Abstract Adversarial training is a min-max optimization problem that is designed to construct robust classifiers against adversarial perturbations of data. We study three models of adversarial training in the multiclass agnostic-classifier setting. We prove the existence of Borel measurable robust classifiers in each model and provide a unified perspective of the adversarial training problem, expanding the connections with optimal transport initiated by the authors in their previous work [21]. In addition, we develop new connections between adversarial training in the multiclass setting and total variation regularization. As a corollary of our results, we provide an alternative proof of the existence of Borel measurable solutions to the agnostic adversarial training problem in the binary classification setting.

Improving Xenon-129 lung ventilation image SNR with deep-learning based image reconstruction.

To evaluate the feasibility and utility of a deep learning (DL)-based reconstruction for improving the SNR of hyperpolarized 129Xe lung ventilation MRI. 129Xe lung ventilation MRI data acquired from patients with asthma and/or chronic obstructive pulmonary disease (COPD) were retrospectively reconstructed with a commercial DL reconstruction pipeline at five different denoising levels. Quantitative imaging metrics of lung ventilation including ventilation defect percentage (VDP) and ventilation heterogeneity index (VHI) were compared between each set of DL-reconstructed images and alternative denoising strategies including: filtering, total variation denoising and higher-order singular value decomposition. Structural similarity between the denoised and original images was assessed. In a prospective study, the feasibility of using SNR gains from DL reconstruction to allow natural-abundance xenon MRI was evaluated in healthy volunteers. 129Xe ventilation image SNR was improved with DL reconstruction when compared with conventionally reconstructed images. In patients with asthma and/or COPD, DL-reconstructed images exhibited a slight positive bias in ventilation defect percentage (1.3% at 75% denoising) and ventilation heterogeneity index (˜1.4) when compared with conventionally reconstructed images. Additionally, DL-reconstructed images preserved structural similarity more effectively than data denoised using alternative approaches. DL reconstruction greatly improved image SNR (greater than threefold), to a level that 129Xe ventilation imaging using natural-abundance xenon appears feasible. DL-based image reconstruction significantly improves 129Xe ventilation image SNR, preserves structural similarity, and leads to a minor bias in ventilation metrics that can be attributed to differences in the image sharpness. This tool should help facilitate cost-effective 129Xe ventilation imaging with natural-abundance xenon in the future.

A hybrid overlapping group sparsity denoising model with fractional-order total variation and non-convex regularizer

A hybrid overlapping group sparsity denoising model with fractional-order total variation and non-convex regularizer

Long-range fourier ptychographic imaging of the object in multidimensional motion

Fourier Ptychographic (FP) is a cutting-edge technique for achieving high resolution in long-range imaging, holding significant research value. However, most of the research on FP has been limited to high-resolution imaging of stationary objects, considerably narrowing the scope of its applications. In real-world scenarios, the object may move in three dimensions and rotate during the image acquisition process. To address such scenarios, this paper proposes a method for achieving FP of the object in multidimensional motion using a single camera. Starting from the principles of Fourier optics and diffraction, the paper calculates the effects of an object's movement in different dimensions on the light field. The Fourier-Mellin algorithm is to be applied to deduce changes in the light field from captured intensity images and align all collected data under a chosen reference light field. During image reconstruction, we propose an additional phase retrieval algorithm that integrates total variation regularization to address aperture offset issues. The paper validates the proposed method's effectiveness through simulations and experiments. FP is successfully applied to objects in multidimensional motion. The method also doubles the imaging system's resolution.