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Low-dose tomography is highly preferred in medical procedures for its reduced radiation risk when compared to standard-dose Computed Tomography (CT). However, the lower the intensity of X-rays, the higher the acquisition noise and hence the…
We propose a second-order total generalized variation (TGV) regularization for the reconstruction of the initial condition in variational data assimilation problems. After showing the equivalence between TGV regularization and the Bayesian…
Among all tissue imaging modalities, photo-acoustic tomography (PAT) has been getting increasing attention in the recent past due to the fact that it has high contrast, high penetrability, and has capability of retrieving high resolution.…
The conjugate gradient (CG) method is commonly used for the rapid solution of least squares problems. In image reconstruction, the problem can be ill-posed and also contaminated by noise; due to this, approaches such as regularization…
Hyperspectral image (HSI) denoising aims to restore clean HSI from the noise-contaminated one. Noise contamination can often be caused during data acquisition and conversion. In this paper, we propose a novel spatial-spectral total…
Total Variation (TV) and related extensions have been popular in image restoration due to their robust performance and wide applicability. While the original formulation is still relevant after two decades of extensive research, its…
The reconstruction of images from their corresponding noisy Radon transform is a typical example of an ill-posed linear inverse problem as arising in the application of computerized tomography (CT). As the (naive) solution does not depend…
We propose two new variational models aimed to outperform the popular total variation (TV) model for image restoration with L$_2$ and L$_1$ fidelity terms. In particular, we introduce a space-variant generalization of the TV regularizer,…
A standard dose of radioactive tracer must be delivered into the patients body to obtain high-quality Positron Emission Tomography (PET) images for diagnostic purposes, which raises the risk of radiation harm. A reduced tracer dose, on the…
Total variation (TV) regularization is popular in image restoration and reconstruction due to its ability to preserve image edges. To date, most research activities on TV models concentrate on image restoration from blurry and noisy…
This article proposes a novel regularization method, named Geometric Spatio-Spectral Total Variation (GeoSSTV), for hyperspectral (HS) image denoising and destriping. HS images are inevitably affected by various types of noise due to the…
Objective: Positron Emission Tomography (PET) has been a commonly used imaging modality in broad clinical applications. One of the most important tradeoffs in PET imaging is between image quality and radiation dose: high image quality comes…
Large high-quality medical image datasets are difficult to acquire but necessary for many deep learning applications. For positron emission tomography (PET), reconstructed image quality is limited by inherent Poisson noise. We propose a…
In this paper we propose a new approach for tomographic reconstruction with spatially varying regularization parameter. Our work is based on the SA-TV image restoration model proposed in [3] where an automated parameter selection rule for…
We consider inverse problems with large null spaces, which arise in important applications such as in inverse ECG and EEG procedures. Standard regularization methods typically produce solutions in or near the orthogonal complement of the…
We present a new vectorial total variation method that addresses the problem of color consistent image filtering. Our approach is inspired from the double-opponent cell representation in the human visual cortex. Existing methods of…
In this paper, we propose a novel variational model for decomposing images into their respective cartoon and texture parts. Our model characterizes certain non-local features of any Bounded Variation (BV) image by its Total Symmetric…
Positron Emission Tomography (PET) is an essential technique in many clinical applications that allows for quantitative imaging at the molecular level. This study aims to develop a denoising method using novel dilated convolutional neural…
Positron Emission Tomography (PET) is a vital imaging modality widely used in clinical diagnosis and preclinical research but faces limitations in image resolution and signal-to-noise ratio due to inherent physical degradation factors.…
Total variation (TV) is a powerful regularization method that has been widely applied in different imaging applications, but is difficult to apply to diffuse optical tomography (DOT) image reconstruction (inverse problem) due to complex and…