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A fruitful approach for solving signal deconvolution problems consists of resorting to a frame-based convex variational formulation. In this context, parallel proximal algorithms and related alternating direction methods of multipliers have…
The parameter selection is crucial to regularization based image restoration methods. Generally speaking, a spatially fixed parameter for regularization item in the whole image does not perform well for both edge and smooth areas. A larger…
Motion degradation is a central problem in Magnetic Resonance Imaging (MRI). This work addresses the problem of how to obtain higher quality, super-resolved motion-free, reconstructions from highly undersampled MRI data. In this work, we…
Despite a variety of available techniques the issue of the proper regularization parameter choice for inverse problems still remains one of the biggest challenges. The main difficulty lies in constructing a rule, allowing to compute the…
Many imaging problems require computing spatial transformations induced by spatially varying intensity, feature, or density fields. Canonical examples include distortion correction, deformable image registration, atlas-based segmentation,…
Magnetic particle imaging (MPI) is an imaging modality exploiting the nonlinear magnetization behavior of (super-)paramagnetic nanoparticles to obtain a space- and often also time-dependent concentration of a tracer consisting of these…
Magnetic resonance imaging (MRI) reconstruction is a fundamental task aimed at recovering high-quality images from undersampled or low-quality MRI data. This process enhances diagnostic accuracy and optimizes clinical applications. In…
The importance of regularization has been well established in image reconstruction -- which is the computational inversion of imaging forward model -- with applications including deconvolution for microscopy, tomographic reconstruction,…
The choice of the parameter value for regularized inverse problems is critical to the results and remains a topic of interest. This article explores a criterion for selecting a good parameter value by maximizing the probability of the data,…
Magnetic resonance imaging (MRI) is central to the diagnosis of multiple sclerosis, where the identification of biomarkers such as the central vein sign benefits from high-resolution images. However, most clinical brain MRI scans are…
Fast and accurate reconstruction of magnetic resonance (MR) images from under-sampled data is important in many clinical applications. In recent years, deep learning-based methods have been shown to produce superior performance on MR image…
Beamforming in ultrasound imaging has significant impact on the quality of the final image, controlling its resolution and contrast. Despite its low spatial resolution and contrast, delay-and-sum is still extensively used nowadays in…
In many imaging applications where segmented features (e.g. blood vessels) are further used for other numerical simulations (e.g. finite element analysis), the obtained surfaces do not have fine resolutions suitable for the task. Increasing…
The recent introduction of portable, low-field MRI (LF-MRI) into the clinical setting has the potential to transform neuroimaging. However, LF-MRI is limited by lower resolution and signal-to-noise ratio, leading to incomplete…
The image reconstruction problem consists in finding an approximation of a function f starting from its Radon transform Rf. This problem arises in the ambit of medical imaging when one tries to reconstruct the internal structure of the…
We study the qualitative properties of optimal regularisation parameters in variational models for image restoration. The parameters are solutions of bilevel optimisation problems with the image restoration problem as constraint. A general…
We consider a bilevel optimization approach in function space for the choice of spatially dependent regularization parameters in TV image restoration models. First- and second-order optimality conditions for the bilevel problem are studied,…
An efficient computational approach for optimal reconstructing parameters of binary-type physical properties for models in biomedical applications is developed and validated. The methodology includes gradient-based multiscale optimization…
We went below the MRI acceleration factors (a.k.a., k-space undersampling) reported by all published papers that reference the original fastMRI challenge, and then considered powerful deep learning based image enhancement methods to…
This paper considers the model problem of reconstructing an object from incomplete frequency samples. Consider a discrete-time signal $f \in \C^N$ and a randomly chosen set of frequencies $\Omega$ of mean size $\tau N$. Is it possible to…