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Image restoration is one of the most fundamental issues in imaging science. Total variation (TV) regularization is widely used in image restoration problems for its capability to preserve edges. In the literature, however, it is also well…
We extend a recently introduced deep unrolling framework for learning spatially varying regularisation parameters in inverse imaging problems to the case of Total Generalised Variation (TGV). The framework combines a deep convolutional…
This paper introduces a novel variational approach for image compression motivated by recent PDE-based approaches combining edge detection and Laplacian inpainting. The essential feature is to encode the image via a sparse vector field,…
Multispectral images (MSI) contain light information in different wavelengths of objects, which convey spectral-spatial information and help improve the performance of various image processing tasks. Numerous techniques have been created to…
The use of ray projections to reconstruct images is a common technique in medical imaging. Dealing with incomplete data is particularly important when a patient is vulnerable to potentially damaging radiation or is unable to cope with the…
Total variation(TV) regularization is applied to X-Ray computed tomography(CT) in an effort to reduce metal artifacts. Tikhonov regularization with $L^2$ data fidelity term and total variation regularization is augmented in this novel model…
We propose a novel discrete concept for the total generalized variation (TGV), which has originally been derived to reduce the staircasing effect in classical total variation (TV) regularization, in image denoising problems. We describe…
In this article, we study several reconstruction methods for the inverse source problem of photoacoustic tomography (PAT) with spatially variable sound speed and damping. The backbone of these methods is the adjoint operators, which we…
In this thesis, we offer a thorough investigation of different regularisation terms used in variational imaging problems, together with detailed optimisation processes of these problems. We begin by studying smooth problems and partially…
Diffuse Optical Tomography (DOT) is an emerging technology in medical imaging which employs light in the NIR spectrum to estimate the distribution of optical coefficients in biological tissues for diagnostic and monitoring purposes. DOT…
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…
This work is concerned with applying iterative image reconstruction, based on constrained total-variation minimization, to low-intensity X-ray CT systems that have a high sampling rate. Such systems pose a challenge for iterative image…
Previous work showed that total variation superiorization (TVS) improves reconstructed image quality in proton computed tomography (pCT). The structure of the TVS algorithm has evolved since then and this work investigated if this new…
Positron Emission Tomography (PET) imaging is a vital tool in medical diagnostics, offering detailed insights into molecular processes within the human body. However, PET images often suffer from complicated noise, which can obscure…
Various problems in computer vision and medical imaging can be cast as inverse problems. A frequent method for solving inverse problems is the variational approach, which amounts to minimizing an energy composed of a data fidelity term and…
We propose a model-based image reconstruction method for photoacoustic tomography(PAT) involving a novel form of regularization and demonstrate its ability to recover good quality images from significantly reduced size datasets. The…
Small compression noises, despite being transparent to human eyes, can adversely affect the results of many image restoration processes, if left unaccounted for. Especially, compression noises are highly detrimental to inverse operators of…
Spectral Computed Tomography (CT) is an emerging technology that enables to estimate the concentration of basis materials within a scanned object by exploiting different photon energy spectra. In this work, we aim at efficiently solving a…
In image denoising problems, one widely-adopted approach is to minimize a regularized data-fit objective function, where the data-fit term is derived from a physical image acquisition model. Typically the regularizer is selected with two…
In optoacoustic tomography, image reconstruction is often performed with incomplete or noisy data, leading to reconstruction errors. Significant improvement in reconstruction accuracy may be achieved in such cases by using nonlinear…