相关论文: On the Phase Transition of Corrupted Sensing
This paper develops a novel framework for phase retrieval, a problem which arises in X-ray crystallography, diffraction imaging, astronomical imaging and many other applications. Our approach combines multiple structured illuminations…
Motivated by the fact that 2-dimensional data have become popularly used in many applications without being much considered its integrity checking. We introduce the problem of detecting a corrupted area in a 2-dimensional space, and…
In this paper, we present sufficient conditions ensuring that the sum of the image of quadratic functions and the nonnegative orthant is convex. The hidden convexity of the trust-region problem with linear inequality constraints is…
We observed a phase transition-like behavior that is marked by the onset of the realization of the connectivity between two sites on a two-dimensional cross-section of a three-dimensional percolation cluster. This was found using…
This paper studies the problem of shuffled linear regression, where the correspondence between predictors and responses in a linear model is obfuscated by a latent permutation. Specifically, we consider the model $y = \Pi_* X \beta_* + w$,…
This work investigates the problem of signal recovery from undersampled noisy sub-Gaussian measurements under the assumption of a synthesis-based sparsity model. Solving the $\ell^1$-synthesis basis pursuit allows for a simultaneous…
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…
Quantum phase transitions occur when quantum fluctuation destroys order at zero temperature. With an increase in temperature, normally the thermal fluctuation wipes out any signs of this transition. Here we identify a physical quantity that…
Quadratic systems with lossless quadratic terms arise in many applications, including models of atmosphere and incompressible fluid flows. Such systems have a trapping region if all trajectories eventually converge to and stay within a…
The measurement problem for the optical phase has been traditionally attacked for noiseless schemes or in the presence of amplitude or detection noise. Here we address estimation of phase in the presence of phase diffusion and evaluate the…
The convergence rate is analyzed for the SpaSRA algorithm (Sparse Reconstruction by Separable Approximation) for minimizing a sum $f (\m{x}) + \psi (\m{x})$ where $f$ is smooth and $\psi$ is convex, but possibly nonsmooth. It is shown that…
The large N limit of a one-dimensional infinite chain of random matrices is investigated. It is found that in addition to the expected Kosterlitz--Thouless phase transition this model exhibits an infinite series of phase transitions at…
A many body system in the vicinity of a first-order phase transition may get trapped in a local minimum of the free energy landscape. These so-called false-vacuum states may survive for exceedingly long times if the barrier for their decay…
Fidelity approach has been widely used to detect various types of quantum phase transitions, including some that are beyond the Landau symmetry breaking theory, in condensed matter models. However, challenges remain in locating the…
We address a phase estimation scheme using Gaussian states in the presence of non-Gaussian phase noise. At variance with previous analysis, we analyze situations in which the noise occurs before encoding phase information. In particular, we…
Recovery of signals with elements defined on the nodes of a graph, from compressive measurements is an important problem, which can arise in various domains such as sensor networks, image reconstruction and group testing. In some scenarios,…
Super-resolution overcoming the standard quantum limit has been intensively studied for quantum sensing applications of precision target detection over the last decades. Not only higher-order entangled photons but also phase-controlled…
Phase retrieval is an important problem with significant physical and industrial applications. In this paper, we consider the case where the magnitude of the measurement of an underlying signal is corrupted by Gaussian noise. We introduce a…
Poorly transparent barriers (e.g., reinforced walls, shielding panels, metallic or high-contrast dielectrics) strongly reflect incident radiation, limiting wireless power transfer (WPT) unless the barrier is structurally modified to support…
We theoretically investigate the quantum phase transition in the collective systems of qubits in a high-quality cavity, which is driven by a squeezed light. We show that the squeezed light induced symmetry breaking can result in quantum…