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Despite today's prevalence of ultrasound imaging in medicine, ultrasound signal-to-noise ratio is still affected by several sources of noise and artefacts. Moreover, enhancing ultrasound image quality involves balancing concurrent factors…
We consider the problem of 3D shape reconstruction from multi-modal data, given uncertain calibration parameters. Typically, 3D data modalities can be in diverse forms such as sparse point sets, volumetric slices, 2D photos and so on. To…
High-quality imaging in photoacoustic computed tomography (PACT) usually requires a high-channel count system for dense spatial sampling around the object to avoid aliasing-related artefacts. To reduce system complexity, various image…
Discrete inverse problems correspond to solving a system of equations in a stable way with respect to noise in the data. A typical approach to enforce uniqueness and select a meaningful solution is to introduce a regularizer. While for most…
In this tutorial, we combine the different scientific fields of information theory, thermodynamics, regularization theory and non-destructive imaging, especially for photoacoustic and photothermal imaging. The goal is to get a better…
Paganin's method for image reconstruction in propagation-based phase-contrast X-ray imaging and tomography has enjoyed broad acceptance in recent years, with over one thousand publications citing its use. The present paper discusses…
We propose a novel automatic parameter selection strategy for variational imaging problems under Poisson noise corruption. The selection of a suitable regularization parameter, whose value is crucial in order to achieve high quality…
We propose a compressive sensing algorithm that exploits geometric properties of images to recover images of high quality from few measurements. The image reconstruction is done by iterating the two following steps: 1) estimation of normal…
Indirect image registration is a promising technique to improve image reconstruction quality by providing a shape prior for the reconstruction task. In this paper, we propose a novel hybrid method that seeks to reconstruct high quality…
Most of today's state-of-the-art methods for perspective shape from shading are modelled in terms of partial differential equations (PDEs) of Hamilton-Jacobi type. To improve the robustness of such methods w.r.t. noise and missing data,…
We propose a new fast algorithm for solving one of the standard approaches to ill-posed linear inverse problems (IPLIP), where a (possibly non-smooth) regularizer is minimized under the constraint that the solution explains the observations…
Computational imaging plays a pivotal role in determining hidden information from sparse measurements. A robust inverse solver is crucial to fully characterize the uncertainty induced by these measurements, as it allows for the estimation…
Image reconstruction is an inverse problem that solves for a computational image based on sampled sensor measurement. Sparsely sampled image reconstruction poses addition challenges due to limited measurements. In this work, we propose an…
In this paper, we propose a new variational model for image reconstruction by minimizing the $L^1$ norm of the \emph{Weingarten map} of image surface $(x,y,f(x,y))$ for a given image $f:{\mathrm{\Omega}}\rightarrow \mathbb R$. We…
The need for tomographic reconstruction from sparse measurements arises when the measurement process is potentially harmful, needs to be rapid, or is uneconomical. In such cases, information from previous longitudinal scans of the same…
We propose to learn non-convex regularizers with a prescribed upper bound on their weak-convexity modulus. Such regularizers give rise to variational denoisers that minimize a convex energy. They rely on few parameters (less than 15,000)…
The problem of numerical differentiation can be thought of as an inverse problem by considering it as solving a Volterra equation. It is well known that such inverse integral problems are ill-posed and one requires regularization methods to…
Image denoising is a well-known and well studied problem, commonly targeting a minimization of the mean squared error (MSE) between the outcome and the original image. Unfortunately, especially for severe noise levels, such Minimum MSE…
Owing to the edge preserving ability and low computational cost of the total variation (TV), variational models with the TV regularization have been widely investigated in the field of multiplicative noise removal. The key points of the…
Training deep neural networks has become a common approach for addressing image restoration problems. An alternative for training a "task-specific" network for each observation model is to use pretrained deep denoisers for imposing only the…