Related papers: Hypercomplex Phase Retrieval

Hyperspectral image (HSI) super-resolution is commonly used to overcome the hardware limitations of existing hyperspectral imaging systems on spatial resolution. It fuses a low-resolution (LR) HSI and a high-resolution (HR) conventional…

Compressive sensing has shown significant promise in biomedical fields. It reconstructs a signal from sub-Nyquist random linear measurements. Classical methods only exploit the sparsity in one domain. A lot of biomedical signals have…

We describe dimensionally constrained symbolic regression which has been developed for mass measurement in certain classes of events in high-energy physics (HEP). With symbolic regression, we can derive equations that are well known in HEP.…

Recovering an unknown complex signal from the magnitude of linear combinations of the signal is referred to as phase retrieval. We present an exact performance analysis of a recently proposed convex-optimization-formulation for this…

Hyperspectral imaging, also known as image spectrometry, is a landmark technique in geoscience and remote sensing (RS). In the past decade, enormous efforts have been made to process and analyze these hyperspectral (HS) products mainly by…

Complex field imaging, which captures both the amplitude and phase information of input optical fields or objects, can offer rich structural insights into samples, such as their absorption and refractive index distributions. However,…

Signal recovery is one of the key techniques of Compressive sensing (CS). It reconstructs the original signal from the linear sub-Nyquist measurements. Classical methods exploit the sparsity in one domain to formulate the L0 norm…

Signal models formed as linear combinations of few atoms from an over-complete dictionary or few frame vectors from a redundant frame have become central to many applications in high dimensional signal processing and data analysis. A core…

We consider a recently proposed convex formulation, known as the PhaseMax method, for solving the phase retrieval problem. Using the replica method from statistical mechanics, we analyze the performance of PhaseMax in the high-dimensional…

The phase retrieval problem in the classical setting is to reconstruct real/complex functions from the magnitudes of their Fourier/frame measurements. In this paper, we consider a new phase retrieval paradigm in the…

The Topological Signal Processing (TSP) framework has been recently developed to analyze signals defined over simplicial complexes, i.e. topological spaces represented by finite sets of elements that are closed under inclusion of subsets…

We propose a new algorithm to learn a dictionary for reconstructing and sparsely encoding signals from measurements without phase. Specifically, we consider the task of estimating a two-dimensional image from squared-magnitude measurements…

Phase retrieval aims to recover a signal from magnitude or power spectra measurements. It is often addressed by considering a minimization problem involving a quadratic cost function. We propose a different formulation based on Bregman…

In recent years, the mathematical and algorithmic aspects of the phase retrieval problem have received considerable attention. Many papers in this area mention crystallography as a principal application. In crystallography, the signal to be…

In this paper, we introduce HPR-QP, a dual Halpern Peaceman-Rachford (HPR) method designed for solving large-scale convex composite quadratic programming. One distinctive feature of HPR-QP is that, instead of working with the primal…

We propose a novel approach and algorithm based on two preliminary tests of the optical system elements to enhance the super-resolved complex-valued imaging. The approach is developed for inverse phase imaging in a single-shot lensless…

This paper investigates the sparse phase retrieval problem, which aims to recover a sparse signal from a system of quadratic measurements. In this work, we propose a novel non-convex algorithm, termed Gradient Hard Thresholding Pursuit…

Hyperspectral imaging offers new perspectives for diverse applications, ranging from the monitoring of the environment using airborne or satellite remote sensing, precision farming, food safety, planetary exploration, or astrophysics.…

Phase retrieval, a long-established challenge for recovering a complex-valued signal from its Fourier intensity measurements, has attracted significant interest because of its far-flung applications in optical imaging. To enhance accuracy,…

In many signal processing problems, it may be fruitful to represent the signal under study in a frame. If a probabilistic approach is adopted, it becomes then necessary to estimate the hyper-parameters characterizing the probability…