Related papers: Minimax Analysis of Estimation Problems in Coheren…

The image reconstruction of partially coherent light is interpreted as the quantum state reconstruction. The efficient method based on maximum-likelihood estimation is proposed to acquire information from registered intensity measurements…

We want to reconstruct a signal based on inhomogeneous data (the amount of data can vary strongly), using the model of regression with a random design. Our aim is to understand the consequences of inhomogeneity on the accuracy of estimation…

All techniques for denoising involve a notion of a true (noise-free) image, and a hypothesis space. The hypothesis space may reconstruct the image directly as a grayscale valued function, or indirectly by its Fourier or wavelet spectrum.…

Optical coherence tomography (OCT) is a widely used imaging technique in the micrometer regime, which gained accelerating interest in medical imaging in the last twenty years. In up-to-date OCT literature [5,6] certain simplifying…

We study the problem of designing minimax procedures in linear regression under the quantile risk. We start by considering the realizable setting with independent Gaussian noise, where for any given noise level and distribution of inputs,…

Performance of regularized least-squares estimation in noisy compressed sensing is analyzed in the limit when the dimensions of the measurement matrix grow large. The sensing matrix is considered to be from a class of random ensembles that…

In high dimension, it is customary to consider Lasso-type estimators to enforce sparsity. For standard Lasso theory to hold, the regularization parameter should be proportional to the noise level, yet the latter is generally unknown in…

In large-scale systems, complex internal relationships are often present. Such interconnected systems can be effectively described by low rank stochastic processes. When identifying a predictive model of low rank processes from sampling…

Estimation of Markov Random Field and covariance models from high-dimensional data represents a canonical problem that has received a lot of attention in the literature. A key assumption, widely employed, is that of {\em sparsity} of the…

Non-invasive imaging plays a crucial role in the early detection, diagnosis, and treatment of numerous medical conditions. This article discusses recent advancements in coherent imaging techniques.The article begins by discussing the…

Machine learning (ML) systems for medical imaging have demonstrated remarkable diagnostic capabilities, but their susceptibility to biases poses significant risks, since biases may negatively impact generalization performance. In this…

Holographic coherent X-ray imaging enables nanoscale imaging of biological cells and tissues, rendering both phase and absorption contrast, i.e. real and imaginary parts of the refractive index. Unlike the standard model, which assumes a…

This work is concerned with the estimation of multidimensional regression and the asymptotic behaviour of the test involved in selecting models. The main problem with such models is that we need to know the covariance matrix of the noise to…

Imaging is an important means by which information is gathered regarding the physical world. Spatial resolution and signal-to-noise ratio are underpinning concepts. There is a paucity of rigorous definitions for these quantities, which are…

The comprehensive integration of machine learning healthcare models within clinical practice remains suboptimal, notwithstanding the proliferation of high-performing solutions reported in the literature. A predominant factor hindering…

Multi-rater medical image segmentation captures the inherent ambiguity of clinical interpretation, where diagnostic boundaries vary across experts and imaging devices. Existing approaches often reduce this diversity to consensus labels or…

We propose an adaptive training scheme for unsupervised medical image registration. Existing methods rely on image reconstruction as the primary supervision signal. However, nuisance variables (e.g. noise and covisibility), violation of the…

Implicit neural representations (INRs) have gained prominence as a powerful paradigm in scene reconstruction and computer graphics, demonstrating remarkable results. By utilizing neural networks to parameterize data through implicit…

Here the role and influence of aberrations in optical imaging systems employing partially coherent complex scalar fields is studied. Imaging systems require aberrations to yield contrast in the output image. For linear shift-invariant…

Coherent diffractive imaging is unique as the only route for achieving diffraction-limited spatial resolution in the extreme ultraviolet and X-ray regions, limited only by the wavelength of the light. Recently, advances in coherent short…