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The Einstein-Podolsky-Rosen~(EPR) model is an analogous model of the anti-ferromagnetic Heisenberg model or the equivalent quantum maximum-cut problem, proposed by R. King two years ago. Adjacent qubits in the model prefer symmetric…
Large kernel convolutions offer a scalable alternative to vision transformers for high-resolution 3D volumetric analysis, yet naively increasing kernel size often leads to optimization instability. Motivated by the spatial bias inherent in…
Efforts to automate the reconstruction of neural circuits from 3D electron microscopic (EM) brain images are critical for the field of connectomics. An important computation for reconstruction is the detection of neuronal boundaries. Images…
The Expectation-Maximization algorithm is perhaps the most broadly used algorithm for inference of latent variable problems. A theoretical understanding of its performance, however, largely remains lacking. Recent results established that…
This paper introduces a Bayesian image segmentation algorithm based on finite mixtures. An EM algorithm is developed to estimate parameters of the Gaussian mixtures. The finite mixture is a flexible and powerful probabilistic modeling tool.…
A common task in cryo-electron microscopy (cryo-EM) data processing is to compare three-dimensional density maps of macromolecules. In this paper, we propose an algorithm for aligning three-dimensional density maps that exploits common…
In this project, we study the hidden Markov random field (HMRF) model and its expectation-maximization (EM) algorithm. We implement a MATLAB toolbox named HMRF-EM-image for 2D image segmentation using the HMRF-EM framework. This toolbox…
Kernel dimensionality reduction (KDR) algorithms find a low dimensional representation of the original data by optimizing kernel dependency measures that are capable of capturing nonlinear relationships. The standard strategy is to first…
In this paper, we outline the use of Mixture Models in density estimation of large astronomical databases. This method of density estimation has been known in Statistics for some time but has not been implemented because of the large…
We obtain upper bounds for the estimation error of Kernel Ridge Regression (KRR) for all non-negative regularization parameters, offering a geometric perspective on various phenomena in KRR. As applications: 1. We address the multiple…
Efficient scene representations are essential for many computer graphics applications. A general unified representation that can handle both surfaces and volumes simultaneously, remains a research challenge. Inspired by recent methods for…
Biclustering algorithms partition data and covariates simultaneously, providing new insights in several domains, such as analyzing gene expression to discover new biological functions. This paper develops a new model-free biclustering…
Kernel techniques are among the most popular and flexible approaches in data science allowing to represent probability measures without loss of information under mild conditions. The resulting mapping called mean embedding gives rise to a…
In traditional reversible data hiding (RDH) methods, researchers pay attention to enlarge the embedding capacity (EC) and to reduce the embedding distortion (ED). Recently, a completely novel RDH algorithm was developed to embed secret data…
Current deep image super-resolution (SR) approaches aim to restore high-resolution images from down-sampled images or by assuming degradation from simple Gaussian kernels and additive noises. However, these techniques only assume crude…
Kernel ridge regression (KRR) is a standard method for performing non-parametric regression over reproducing kernel Hilbert spaces. Given $n$ samples, the time and space complexity of computing the KRR estimate scale as $\mathcal{O}(n^3)$…
A single-particle cryo-electron microscopy (cryo-EM) measurement, called a micrograph, consists of multiple two-dimensional tomographic projections of a three-dimensional (3-D) molecular structure at unknown locations, taken under unknown…
Mixed linear regression involves the recovery of two (or more) unknown vectors from unlabeled linear measurements; that is, where each sample comes from exactly one of the vectors, but we do not know which one. It is a classic problem, and…
We consider a symmetric mixture of linear regressions with random samples from the pairwise comparison design, which can be seen as a noisy version of a type of Euclidean distance geometry problem. We analyze the expectation-maximization…
A novel and highly efficient computational framework for reconstructing binary-type images suitable for models of various complexity seen in diverse biomedical applications is developed and validated. Efficiency in computational speed and…