Related papers: Benchmarking Iterative Projection Algorithms for P…
In this paper we analyse convergence of projected fixed-point iteration on a Riemannian manifold of matrices with fixed rank. As a retraction method we use `projector splitting scheme'. We prove that the projector splitting scheme converges…
Bit retrieval, the problem of determining a binary sequence from its cyclic autocorrelation, is a special case of the phase retrieval problem. Algorithms for phase retrieval are extensively used in several scientific disciplines, and yet,…
Partially observable Markov decision processes (POMDPs) have recently become popular among many AI researchers because they serve as a natural model for planning under uncertainty. Value iteration is a well-known algorithm for finding…
Scanning transmission electron microscopy (STEM) has been extensively used for imaging complex materials down to atomic resolution. The most commonly employed STEM modality, annular dark-field imaging, produces easily-interpretable…
We study the Kaczmarz methods for solving systems of quadratic equations, i.e., the generalized phase retrieval problem. The methods extend the Kaczmarz methods for solving systems of linear equations by integrating a phase selection…
We consider a variant of the phase retrieval problem, where vectors are replaced by unitary matrices, i.e., the unknown signal is a unitary matrix U, and the measurements consist of squared inner products |Tr(C*U)|^2 with unitary matrices C…
Exploring the idea 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 phaseless…
An iterative method is derived for image reconstruction. Among other attributes, this method allows constraints unrelated to the radiation measurements to be incorporated into the reconstructed image. A comparison is made with the widely…
Phase retrieval is in general a non-convex and non-linear task and the corresponding algorithms struggle with the issue of local minima. We consider the case where the measurement samples within typically very small and disconnected subsets…
In many applications of tomography, the acquired projections are either limited in number or contain a significant amount of noise. In these cases, standard reconstruction methods tend to produce artifacts that can make further analysis…
We introduce a kind of partial observability to the projective simulation (PS) learning method. It is done by adding a belief projection operator and an observability parameter to the original framework of the efficiency of the PS model. I…
We develop a novel, fundamental and surprisingly simple randomized iterative method for solving consistent linear systems. Our method has six different but equivalent interpretations: sketch-and-project, constrain-and-approximate, random…
Iterative methods for tomographic image reconstruction have great potential for enabling high quality imaging from low-dose projection data. The computational burden of iterative reconstruction algorithms, however, has been an impediment in…
We study algorithms for solving quadratic systems of equations based on optimization methods over polytopes. Our work is inspired by a recently proposed convex formulation of the phase retrieval problem, which estimates the unknown signal…
The classical problem of phase retrieval arises in various signal acquisition systems. Due to the ill-posed nature of the problem, the solution requires assumptions on the structure of the signal. In the last several years, sparsity and…
Phase-retrieval techniques aim to recover the original signal from just the modulus of its Fourier transform, which is usually much easier to measure than its phase, but the standard iterative techniques tend to fail if only part of the…
Results about existence and uniqueness of solutions of initial value problem for certain types of partial differential equations are recalled as well as iterative scheme and an error estimate for approximate solutions obtained using this…
We study theoretical limits of \emph{descending} phase retrieval algorithms. Utilizing \emph{Random duality theory} (RDT) we develop a generic program that allows statistical characterization of various algorithmic performance metrics.…
In this paper, we consider the phase recovery problem, where a complex signal vector has to be estimated from the knowledge of the modulus of its linear projections, from a naive variational Bayesian point of view. In particular, we derive…
We improve a phase retrieval approach that uses correlation-based measurements with compactly supported measurement masks [27]. The improved algorithm admits deterministic measurement constructions together with a robust, fast recovery…