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Electrical impedance tomography (EIT) is a noninvasive imaging method whereby electrical measurements on the boundary of a conductive medium (the data) are taken according to a prescribed protocol set and inverted to map the internal…
One of the most effective ways to treat liver cancer is to perform precise liver resection surgery, the key step of which includes precise digital image segmentation of the liver and its tumor. However, traditional liver parenchymal…
In X-ray Computed Tomography (CT), projections from many angles are acquired and used for 3D reconstruction. To make CT suitable for in-line quality control, reducing the number of angles while maintaining reconstruction quality is…
Quantitative cancer image analysis relies on the accurate delineation of tumours, a very specialised and time-consuming task. For this reason, methods for automated segmentation of tumours in medical imaging have been extensively developed…
We review a resistor network approach to the numerical solution of the inverse problem of electrical impedance tomography (EIT). The networks arise in the context of finite volume discretizations of the elliptic equation for the electric…
In this paper we investigate and compare different gradient algorithms designed for the domain expression of the shape derivative. Our main focus is to examine the usefulness of kernel reproducing Hilbert spaces for PDE constrained shape…
In computed tomography (CT), the forward model consists of a linear Radon transform followed by an exponential nonlinearity based on the attenuation of light according to the Beer-Lambert Law. Conventional reconstruction often involves…
Optimizing shapes and topology of physical devices is crucial for both scientific and technological advancements, given its wide-ranging implications across numerous industries and research areas. Innovations in shape and topology…
Bayesian experimental design (BED) is to answer the question that how to choose designs that maximize the information gathering. For implicit models, where the likelihood is intractable but sampling is possible, conventional BED methods…
Wavefront shaping systems aim to image deep into scattering tissue by reshaping incoming and outgoing light to correct aberrations caused by tissue inhomogeneity However, the desired modulation depends on the unknown tissue structure and…
A challenge in high-dimensional inverse problems is developing iterative solvers to find the accurate solution of regularized optimization problems with low computational cost. An important example is computed tomography (CT) where both…
Cone-beam computed tomography (CBCT) systems, with their flexibility, present a promising avenue for direct point-of-care medical imaging, particularly in critical scenarios such as acute stroke assessment. However, the integration of CBCT…
We design and analyze a novel accelerated gradient-based algorithm for a class of bilevel optimization problems. These problems have various applications arising from machine learning and image processing, where optimal solutions of the two…
We propose a new compressive imaging method for reconstructing 2D or 3D objects from their scattered wave-field measurements. Our method relies on a novel, nonlinear measurement model that can account for the multiple scattering phenomenon,…
Breast cancer is a disease that threatens many women's life, thus, early and accurate detection plays a key role in reducing the mortality rate. Mammography stands as the reference technique for breast cancer screening; nevertheless, many…
The aim of Electrical Impedance Tomography (EIT) is to determine the electrical conductivity distribution inside a domain by applying currents and measuring voltages on its boundary. Mathematically, the EIT reconstruction task can be…
Multispectral transmission imaging provides strong benefits for early breast cancer screening. The frame accumulation method addresses the challenge of low grayscale and signal-to-noise ratio resulting from the strong absorption and…
Correcting scan-positional errors is critical in achieving electron ptychography with both high resolution and high precision. This is a demanding and challenging task due to the sheer number of parameters that need to be optimized. For…
Computed tomography (CT) has been developed as a non-destructive technique for observing minute internal images of samples. It has been difficult to obtain photo-realistic (clean or clear) CT images due to various unwanted artifacts…
We consider the projected gradient algorithm for the nonconvex best subset selection problem that minimizes a given empirical loss function under an $\ell_0$-norm constraint. Through decomposing the feasible set of the given sparsity…