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In this paper, we introduce novel fast matrix inversion algorithms that leverage triangular decomposition and recurrent formalism, incorporating Strassen's fast matrix multiplication. Our research places particular emphasis on triangular…
In this work, an inverse problem on the determination of multiple coefficients arising from the time-domain diffuse optical tomography with fluorescence (DOT-FDOT) is investigated. We simultaneously recover the distribution of background…
Iterative sketching and sketch-and-precondition are randomized algorithms used for solving overdetermined linear least-squares problems. When implemented in exact arithmetic, these algorithms produce high-accuracy solutions to least-squares…
Photoemission orbital tomography provides direct access from laboratory measurements to the real-space molecular orbitals of well-ordered organic semiconductor layers. Specifically, the application of phase retrieval algorithms to…
This paper introduces a fast algorithm, applicable throughout the electromagnetic spectrum, for the numerical solution of problems of scattering by periodic surfaces in two-dimensional space. The proposed algorithm remains highly accurate…
The boundary integral method is an efficient approach for solving time-harmonic acoustic obstacle scattering problems. The main computational task is the evaluation of an oscillatory boundary integral at each discretization point of the…
In computer vision, the estimation of the fundamental matrix is a basic problem that has been extensively studied. The accuracy of the estimation imposes a significant influence on subsequent tasks such as the camera trajectory…
Iterative phase retrieval algorithms are widely used in digital optics for their efficiency and simplicity. Conventionally, these algorithms do not consider aberrations as they assume an ideal, aberration-free optical system. Here, we…
An algorithm to efficiently compute the moments of volumetric images is disclosed. The approach demonstrates a reduction in processing time by reducing the computational complexity significantly. Specifically, the algorithm reduces…
We present a framework for accelerated iterative reconstructions using a fast and approximate forward model that is based on k-space methods for photoacoustic tomography. The approximate model introduces aliasing artefacts in the gradient…
This paper proposes a fast multi-band image fusion algorithm, which combines a high-spatial low-spectral resolution image and a low-spatial high-spectral resolution image. The well admitted forward model is explored to form the likelihoods…
Incorporating a deep generative model as the prior distribution in inverse problems has established substantial success in reconstructing images from corrupted observations. Notwithstanding, the existing optimization approaches use gradient…
Deep learning methods for accelerated MRI achieve state-of-the-art results but largely ignore additional speedups possible with noncartesian sampling trajectories. To address this gap, we created a generative diffusion model-based…
Image inverse problems have numerous applications, including image processing, super-resolution, and computer vision, which are important areas in image science. These application models can be seen as a three-function composite…
This paper studies inverse problems in quantitative photoacoustic tomography with additional optical current data supplemented from diffuse optical tomography. We propose a three-stage image reconstruction method for the simultaneous…
Ptychography is a powerful computational imaging technique that transforms a collection of low-resolution images into a high-resolution sample reconstruction. Unfortunately, algorithms that are currently used to solve this reconstruction…
A novel approach is given to overcome the computational challenges of the full-matrix Adaptive Gradient algorithm (Full AdaGrad) in stochastic optimization. By developing a recursive method that estimates the inverse of the square root of…
Photo-acoustic tomography (PAT) aims to leverage the photo-acoustic coupling between optical absorption of light sources and ultrasound (US) emission to obtain high contrast reconstructions of optical parameters with the high resolution of…
Compared to standard tomographic reconstruction, iterative approaches offer the possibility to account for extraneous experimental influences, which allows for a suppression of related artifacts. However, the inclusion of corresponding…
Real life signals are in general non--stationary and non--linear. The development of methods able to extract their hidden features in a fast and reliable way is of high importance in many research fields. In this work we tackle the problem…