相关论文: Error estimation in the direct state tomography

In this paper, we study the Tikhonov regularization scheme in Hilbert scales for the nonlinear statistical inverse problem with a general noise. The regularizing norm in this scheme is stronger than the norm in Hilbert space. We focus on…

Synthetic transmit aperture (STA) imaging can achieve optimal lateral resolution in the full field of view, at the cost of low frame rate (FR) and low signal-to-noise ratio (SNR). In our previous studies, compressed sensing based synthetic…

This paper addresses the problem of resilient state estimation and attack reconstruction for bounded-error nonlinear discrete-time systems with nonlinear observations/ constraints, where both sensors and actuators can be compromised by…

We propose a novel direct sampling method (DSM) for the effective and stable inversion of the Radon transform. The DSM is based on a generalization of the important almost orthogonality property in classical DSMs to fractional order Sobolev…

An important theme in modern inverse problems is the reconstruction of time-dependent data from only finitely many measurements. To obtain satisfactory reconstruction results in this setting it is essential to strongly exploit temporal…

Accurate quantum tomography is a vital tool in both fundamental and applied quantum science. It is a task that involves processing a noisy measurement record in order to construct a reliable estimate of an unknown quantum state, and is…

Reconstruction of density matrices is important in NMR quantum computing. An analysis is made for a 2-qubit system by using the error matrix method. It is found that the state tomography method determines well the parameters that are…

We address the channel estimation (CE) problem in reconfigurable intelligent surface (RIS) aided orthogonal frequency-division multiplexing (OFDM) systems by proposing a dual-structure and multi-dimensional transformations (DS-MDT)…

We tackle the problem of automatic calibration of radially distorted cameras in challenging conditions. Accurately determining distortion parameters typically requires either 1) solving the full Structure from Motion (SfM) problem involving…

We introduce a new method to estimate unknown pure $d$-dimensional quantum states using the probability distributions associated with only three measurement bases. Measurement results of $2d$ projectors are employed to generate a set of…

The Image-Based Rendering (IBR) approach using Shearlet Transform (ST) is one of the most effective methods for Densely-Sampled Light Field (DSLF) reconstruction. The ST-based DSLF reconstruction typically relies on an iterative…

Ordinary Differential Equations are widespread tools to model chemical, physical, biological process but they usually rely on parameters which are of critical importance in terms of dynamic and need to be estimated directly from the data.…

We compare the two main techniques used for estimating the state of a physical system from unknown measurements: standard detector tomography and data-pattern tomography. Adopting linear inversion as a fair benchmark, we show that the…

Debugging quantum states transformations is an important task of modern quantum computing. The use of quantum tomography for these purposes significantly expands the range of possibilities. However, the presence of preparation and…

Four-dimensional scanning transmission electron microscopy (4D-STEM) is one of the most rapidly growing modes of electron microscopy imaging. The advent of fast pixelated cameras and the associated data infrastructure have greatly…

The ability to uniquely identify a quantum state is integral to quantum science, but for non-orthogonal states, quantum mechanics precludes deterministic, error-free discrimination. However, using the non-deterministic protocol of…

In this work, we demonstrate that the ptychographic phase problem can be solved in a live fashion during scanning, while data is still being collected. We propose a generally applicable modification of the widespread projection-based…

Given a set of samples, a few of them being possibly saturated, we propose an efficient algorithm in order to cancel saturation while reconstructing band-limited signals. Our method satisfies a minimum-loss constraint and relies on…

4D time-space reconstruction of dynamic events or deforming objects using X-ray computed tomography (CT) is an important inverse problem in non-destructive evaluation. Conventional back-projection based reconstruction methods assume that…

A reliable model order reduction process for parametric analysis in electromagnetics is detailed. Special emphasis is placed on certifying the accuracy of the reduced-order model. For this purpose, a sharp state error estimator is proposed.…