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The problem of phase retrieval has been intriguing researchers for decades due to its appearance in a wide range of applications. The task of a phase retrieval algorithm is typically to recover a signal from linear phase-less measurements.…

A theory is presented (and supported by numerical simulations) for phase-coherent reflection of light by a disordered medium which either absorbs or amplifies radiation. The distribution of reflection eigenvalues is shown to be the Laguerre…

Regularization by denoising (RED) is a powerful framework for solving imaging inverse problems. Most RED algorithms are iterative batch procedures, which limits their applicability to very large datasets. In this paper, we address this…

Alternating minimization, or Fienup methods, have a long history in phase retrieval. We provide new insights related to the empirical and theoretical analysis of these algorithms when used with Fourier measurements and combined with convex…

We introduce Autoregressive Retrieval Augmentation (AR-RAG), a novel paradigm that enhances image generation by autoregressively incorporating knearest neighbor retrievals at the patch level. Unlike prior methods that perform a single,…

As a powerful statistical image modeling technique, sparse representation has been successfully used in various image restoration applications. The success of sparse representation owes to the development of l1-norm optimization techniques,…

Modern large-scale recommender systems employ multi-stage ranking funnel (Retrieval, Pre-ranking, Ranking) to balance engagement and computational constraints (latency, CPU). However, the initial retrieval stage, often relying on efficient…

We develop a behavioural theory of reflective parallel algorithms (RAs), i.e. synchronous parallel algorithms that can modify their own behaviour. The theory comprises a set of postulates defining the class of RAs, an abstract machine…

This paper presents Randomized AutoRegressive modeling (RAR) for visual generation, which sets a new state-of-the-art performance on the image generation task while maintaining full compatibility with language modeling frameworks. The…

Recovering a signal from its Fourier magnitude is referred to as phase retrieval, which occurs in different fields of engineering and applied physics. This paper gives a new characterization of the phase retrieval problem. Particularly…

In this paper we propose the Iterative Amortized Hierarchical Variational Autoencoder (IA-HVAE), which expands on amortized inference with a hybrid scheme containing an initial amortized guess and iterative refinement with decoder…

Promoted by the advent of coherent synchrotron light sources, phase contrast tomography allows to resolve three-dimensional variations of an unknown sample's complex refractive index from scattering intensities recorded at different…

We present an algorithm for holographic shaping of partially coherent light, bridging the gap between traditional coherent and geometric optical approaches. The description of partially coherent light relies on a mode expansion formalism,…

The explicit low-rank regularization, e.g., nuclear norm regularization, has been widely used in imaging sciences. However, it has been found that implicit regularization outperforms explicit ones in various image processing tasks. Another…

We consider the problem of estimating a signal from noisy circularly-translated versions of itself, called multireference alignment (MRA). One natural approach to MRA could be to estimate the shifts of the observations first, and infer the…

The ability of widely distributed radar systems to capture diverse spatial scattering properties substantially improves radar imaging performance. Traditional imaging methods leverage regularized optimization techniques to reconstruct…

We present a new method for real- and complex-valued image reconstruction from two intensity measurements made in the Fourier plane: the Fourier magnitude of the unknown image, and the intensity of the interference pattern arising from…

Estimating the direction of arrival (DOA) of sources is an important problem in aerospace and vehicular communication, localization and radar. In this paper, we consider a challenging multi-source DOA estimation task, where the receiving…

Retrieval-Augmented Generation (RAG) improves factual grounding by incorporating external knowledge into language model generation. However, when retrieved context is noisy, unreliable, or inconsistent with the model's parametric knowledge,…

Phase retrieval has been an attractive but difficult problem rising from physical science, and there has been a gap between state-of-the-art theoretical convergence analyses and the corresponding efficient retrieval methods. Firstly, these…