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In some super-resolution techniques, adjacent points are illuminated at different times. Thereby, their locations and light intensities can be detected even if the images are very blurred due to diffraction. According to conventional…
Manifold hypothesis states that data points in high-dimensional space actually lie in close vicinity of a manifold of much lower dimension. In many cases this hypothesis was empirically verified and used to enhance unsupervised and…
Despite its reduced complexity, lattice reduction-aided decoding exhibits a widening gap to maximum-likelihood (ML) performance as the dimension increases. To improve its performance, this paper presents randomized lattice decoding based on…
Undersampled images, such as those produced by the HST WFPC-2, misrepresent fine-scale structure intrinsic to the astronomical sources being imaged. Analyzing such images is difficult on scales close to their resolution limits and may…
Bayesian shrinkage methods have generated a lot of recent interest as tools for high-dimensional regression and model selection. These methods naturally facilitate tractable uncertainty quantification and incorporation of prior information.…
In medical imaging analysis, deep learning has shown promising results. We frequently rely on volumetric data to segment medical images, necessitating the use of 3D architectures, which are commended for their capacity to capture interslice…
A method for direct phase difference reconstruction using single-shot dual-wavelength off-axis digital holography is presented. This approach enables direct imaging of samples with high steps without the need to reconstruct phase images at…
Score-based algorithms that learn the structure of Bayesian networks can be used for both exact and approximate solutions. While approximate learning scales better with the number of variables, it can be computationally expensive in the…
We show that there are sampling projections on arbitrary $n$-dimensional subspaces of $B(D)$ with at most $2n$ samples and norm of order $\sqrt{n}$, where $B(D)$ is the space of complex-valued bounded functions on a set $D$. This gives a…
Recovering images corrupted by multiplicative noise is a well known challenging task. Motivated by the success of multiscale hierarchical decomposition methods (MHDM) in image processing, we adapt a variety of both classical and new…
A learning-based 3D reconstruction method for long-span bridges is proposed in this paper. 3D reconstruction generates a 3D computer model of a real object or scene from images, it involves many stages and open problems. Existing…
We study Markov Chain Monte Carlo (MCMC) methods operating in primary sample space and their interactions with multiple sampling techniques. We observe that incorporating the sampling technique into the state of the Markov Chain, as done in…
Maximum Mean Discrepancy (MMD) has been widely used in the areas of machine learning and statistics to quantify the distance between two distributions in the $p$-dimensional Euclidean space. The asymptotic property of the sample MMD has…
Despite the increased brilliance of the new generation synchrotron sources, there is still a challenge with high-resolution scanning of very thick and absorbing samples, such as the whole mouse brain stained with heavy elements, and,…
Super-resolution reconstruction techniques entail the utilization of software algorithms to transform one or more sets of low-resolution images captured from the same scene into high-resolution images. In recent years, considerable…
A detailed analysis of ptychography for 3D phase reconstructions of thick specimens is performed. We introduce multi-focus ptychography, which incorporates a 4D-STEM defocus series to enhance the quality of 3D reconstructions along the beam…
Supervised manifold learning methods learn data representations by preserving the geometric structure of data while enhancing the separation between data samples from different classes. In this work, we propose a theoretical study of…
Markov Chain Monte Carlo (MCMC) techniques have long been studied in computational geometry subjects whereabouts the problems to be studied are complex geometric objects which by their nature require optimized techniques to be deployed or…
In order to determine the 3D structure of a thick sample, researchers have recently combined ptychography (for high resolution) and tomography (for 3D imaging) in a single experiment. 2-step methods are usually adopted for reconstruction,…
The field of quantum information has been growing fast over the past decade. Optical quantum computation, based on the concepts of KLM and cluster states, has witnessed experimental realizations of larger and more complex systems in terms…