Related papers: Total variation regularization for fMRI-based pred…
Total Variation (TV) based regularization has been widely applied in restoration problems due to its simple derivative filters based formulation and robust performance. While first order TV suffers from staircase effect, second order TV…
In this work, we introduce a function space setting for a wide class of structural/weighted total variation (TV) regularization methods motivated by their applications in inverse problems. In particular, we consider a regularizer that is…
Functional MRI (fMRI) has become the most common method for investigating the human brain. However, fMRI data present some complications for statistical analysis and modeling. One recently developed approach to these data focuses on…
Many methods for processing scalar and vector valued images, volumes and other data in the context of inverse problems are based on variational formulations. Such formulations require appropriate regularization functionals that model…
Purpose: Task-based assessment of image quality in undersampled magnetic resonance imaging provides a way of evaluating the impact of regularization on task performance. In this work, we evaluated the effect of total variation (TV) and…
In this paper, a new regularization term is proposed to solve mathematical image problems. By using difference operators in the four directions; horizontal, vertical and two diagonal directions, an estimation of derivative amplitude is…
This article is the second work in our series of papers dedicated to image processing models based on the fractional order total variation $TV^r$. In our first work of this series, we studied key analytic properties of these semi-norms.…
In this paper, we propose Total Variation Regularized Tensor-on-scalar Regression(TVTR), a novel method for estimating the association between a tensor outcome (a one dimensional or multidimensional array) and scalar predictors. While the…
In the past decade, sparsity-driven regularization has led to significant improvements in image reconstruction. Traditional regularizers, such as total variation (TV), rely on analytical models of sparsity. However, increasingly the field…
Radio frequency (RF) data contain richer information compared to other data types, such as envelope or B-mode, and employing RF data for training deep neural networks has attracted growing interest in ultrasound image processing. However,…
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…
Functional magnetic resonance imaging (fMRI) enables indirect detection of brain activity changes via the blood-oxygen-level-dependent (BOLD) signal. Conventional analysis methods mainly rely on the real-valued magnitude of these signals.…
A novel class of semi-norms, generalising the notion of the isotropic total variation $TV_{2}$ and the an-isotropic total variation $TV_{1}$ is introduced. A supervised learning method via bilevel optimisation is proposed for the…
Over the last decades, the total variation (TV) evolved to one of the most broadly-used regularisation functionals for inverse problems, in particular for imaging applications. When first introduced as a regulariser, higher-order…
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…
This paper presents a generative model for super-resolution in routine clinical magnetic resonance images (MRI), of arbitrary orientation and contrast. The model recasts the recovery of high resolution images as an inverse problem, in which…
Total variation (TV) is a widely used function for regularizing imaging inverse problems that is particularly appropriate for images whose underlying structure is piecewise constant. TV regularized optimization problems are typically solved…
An optimization framework is presented for minimizing the energy functional developed around a generalized equation governing physical systems such as fluid dynamics, particle transport, phase transition, and other related systems. The…
Total variation (TV) regularization is a popular reconstruction method for ill-posed imaging problems, and particularly useful for applications with piecewise constant targets. However, using TV for medical cone-beam computed X-ray…
Inferring the functional specificity of brain regions from functional Magnetic Resonance Images (fMRI) data is a challenging statistical problem. While the General Linear Model (GLM) remains the standard approach for brain mapping,…