Related papers: On the Phase Transition of Corrupted Sensing
Recent research indicates that many convex optimization problems with random constraints exhibit a phase transition as the number of constraints increases. For example, this phenomenon emerges in the $\ell_1$ minimization method for…
Compressed sensing deals with efficient recovery of analog signals from linear encodings. This paper presents a statistical study of compressed sensing by modeling the input signal as an i.i.d. process with known distribution. Three classes…
We study a spectral initialization method that serves a key role in recent work on estimating signals in nonconvex settings. Previous analysis of this method focuses on the phase retrieval problem and provides only performance bounds. In…
Demixing refers to the challenge of identifying two structured signals given only the sum of the two signals and prior information about their structures. Examples include the problem of separating a signal that is sparse with respect to…
Convexity splitting like schemes with improved accuracy are proposed for a phase field model for surface diffusion. The schemes are developed to enable large scale simulations in three spatial dimensions describing experimentally observed…
We review connections between phase transitions in high-dimensional combinatorial geometry and phase transitions occurring in modern high-dimensional data analysis and signal processing. In data analysis, such transitions arise as abrupt…
Sparse support recovery (SSR) is an important part of the compressive sensing (CS). Most of the current SSR methods are with the full information measurements. But in practice the amplitude part of the measurements may be seriously…
High-dimensional linear regression under heavy-tailed noise or outlier corruption is challenging, both computationally and statistically. Convex approaches have been proven statistically optimal but suffer from high computational costs,…
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…
Convex splitting is a powerful technique in quantum information theory used in proving the achievability of numerous information-processing protocols such as quantum state redistribution and quantum network channel coding. In this work, we…
We propose a robust and efficient approach to the problem of compressive phase retrieval in which the goal is to reconstruct a sparse vector from the magnitude of a number of its linear measurements. The proposed framework relies on…
In Bayesian statistics, horseshoe prior has attracted increasing attention as an approach to the sparse estimation. The estimation accuracy of compressed sensing with the horseshoe prior is evaluated by statistical mechanical method. It is…
In this paper we analyze a quartic tensor model with one interaction for a tensor of arbitrary rank. This model has a critical point where a continuous limit of infinitely refined random geometries is reached. We show that the critical…
It is known that arrays of trapped ions can be used to efficiently simulate a variety of many-body quantum systems. Here, we show how it is possible to build a model representing a spin chain interacting with bosons which is exactly…
We consider the level-sets of continuous Gaussian fields on $\mathbb{R}^d$ above a certain level $-\ell\in \mathbb{R}$, which defines a percolation model as $\ell$ varies. We assume that the covariance kernel satisfies certain regularity,…
In this note we study the phase transition for percolation on quasi-transitive graphs with quasi-transitively inhomogeneous edge-retention probabilities. A quasi-transitive graph is an infinite graph with finitely many different "types" of…
We consider a layered superconductor with a complex order parameter whose phase switches sign from one layer to the next. This system is shown to exhibit gapless superconductivity for sufficiently large interlayer pairing or interlayer…
The transition between gapped (semiconducting) and gapless (metallic) phases and tunability of bandgap in materials is a very lucrative yet considerably challenging goal for new-age device preparation. For bulk materials and for…
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…
Many-body open quantum systems balance internal dynamics against decoherence from interactions with an environment. Here, we explore this balance via random quantum circuits implemented on a trapped ion quantum computer, where the system…