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Image restoration requires a careful balance between noise suppression and structure preservation. While first-order total variation (TV) regularization effectively preserves edges, it often introduces staircase artifacts, whereas…

In the past decades, Computed Tomography (CT) has established itself as one of the most important imaging techniques in medicine. Today, the applicability of CT is only limited by the deposited radiation dose, reduction of which manifests…

We present two methods that combine image reconstruction and edge detection in computed tomography (CT) scans. Our first method is as an extension of the prominent filtered backprojection algorithm. In our second method we employ…

The total variation (TV) method is an image denoising technique that aims to reduce noise by minimizing the total variation of the image, which measures the variation in pixel intensities. The TV method has been widely applied in image…

Reconstruction of few-view x-ray Computed Tomography (CT) data is a highly ill-posed problem. It is often used in applications that require low radiation dose in clinical CT, rapid industrial scanning, or fixed-gantry CT. Existing analytic…

Low-dose CT (LDCT) imaging is desirable in many clinical applications to reduce X-ray radiation dose to patients. Inspired by deep learning (DL), a recent promising direction of model-based iterative reconstruction (MBIR) methods for LDCT…

Image restoration aims to recover the high-quality images from their degraded observations. Since most existing methods have been dedicated into single degradation removal, they may not yield optimal results on other types of degradations,…

In numerical magnetohydrodynamics (MHD), a major challenge is maintaining zero magnetic field-divergence (div-B). Constrained transport (CT) schemes can achieve this at high accuracy, but have generally been restricted to very specific…

This dissertation is devoted to provide advanced nonconvex nonsmooth variational models of (Magnetic Resonance Image) MRI reconstruction, efficient learnable image reconstruction algorithms and parameter training algorithms that improve the…

Deep neural networks have received considerable attention in clinical imaging, particularly with respect to the reduction of radiation risk. Lowering the radiation dose by reducing the photon flux inevitably results in the degradation of…

While Computerized Tomography (CT) images can help detect disease such as Covid-19, regular CT machines are large and expensive. Cheaper and more portable machines suffer from errors in geometry acquisition that downgrades CT image quality.…

Image restoration is a low-level vision task, most CNN methods are designed as a black box, lacking transparency and internal aesthetics. Although some methods combining traditional optimization algorithms with DNNs have been proposed, they…

Computing the gradient of a function provides fundamental information about its behavior. This information is essential for several applications and algorithms across various fields. One common application that require gradients are…

Masked Autoregressive (MAR) models promise better efficiency in visual generation than autoregressive (AR) models for the ability of parallel generation, yet their acceleration potential remains constrained by the modeling complexity of…

Purpose: Iterative projection reconstruction algorithms are currently the preferred reconstruction method in proton computed tomography (pCT). However, due to inconsistencies in the measured data arising from proton energy straggling and…

Ultrafast ultrasound (US) revolutionized biomedical imaging with its capability of acquiring full-view frames at over 1 kHz, unlocking breakthrough modalities such as shear-wave elastography and functional US neuroimaging. Yet, it suffers…

Long lasting efforts have been made to reduce radiation dose and thus the potential radiation risk to the patient for computed tomography acquisitions without severe deterioration of image quality. To this end, numerous reconstruction and…

Deep Learning (DL) methods can reconstruct highly accelerated magnetic resonance imaging (MRI) scans, but they rely on application-specific large training datasets and often generalize poorly to out-of-distribution data. Self-supervised…

Cardiovascular diseases (CVDs) remain the leading cause of mortality and morbidity worldwide. Both diagnosis and prognosis of these diseases benefit from high-quality imaging, which cardiac magnetic resonance imaging provides. CMR imaging…

Traditional model-based image reconstruction (MBIR) methods combine forward and noise models with simple object priors. Recent machine learning methods for image reconstruction typically involve supervised learning or unsupervised learning,…