arXiv subjects

Bing Gao

Publications and source records attributed to Bing Gao.

15 recordsLinked to original sources

arXiv2026

The Fusion Frame Phase Retrieval

The phase retrieval problem involves reconstructing a function or signal solely from the magnitude of linear measurements. Most theoretical analyses of phase retrieval algorithms rely on i.i.d. Gaussian random measurements or sub-Gaussian random measurements. In this paper, our focus is on the fusion frame phase retrieval problem, where the sampling matrices are i.i.d. rank-$r$ orthogonal projections drawn from the Haar measure. We present concentration inequalities for functions on the set of rank-$r$ orthogonal projection matrices. These inequalities are crucial for the theoretical analysis of the fusion frame phase retrieval problem. Based on these inequalities, we demonstrate that gradient descent, combined with a two-stage initialization, achieves linear convergence to the target signal up to a global phase with a measurement complexity of $O(d\log^2 d)$ when the rank $r = O(1)$. We verify this convergence through numerical results.

cs.IT↗

arXiv2026

Accelerating Multi-Scale Deformable Attention Using Near-Memory-Processing Architecture

Multi Scale Deformable Attention (MSDAttn) has become a fundamental component in various vision tasks due to its effective multi scale grid sampling (MSGS). However, its reliance on random sampling results in highly irregular memory access patterns, making it a memory intensive operation inefficient for GPUs. Near memory processing (NMP) offers a promising solution for accelerating memory bound kernels, yet existing NMP based attention accelerators remain suboptimal for MSDAttn due to incompatible load balancing and data reuse strategies. Specifically, current NMP solutions uniformly distribute processing elements (PEs) across all banks, leading to significant PE underutilization and excessive cross bank data transfers. Moreover, most rely on locality based reuse, which fails under MSDAttn's unpredictable sampling patterns. To address these challenges, this paper presents DANMP, a hardware software co designed NMP based MSDAttn accelerator. On the hardware side, DANMP adopts non uniform NMP integration to handle unbalanced workloads, allocating PEs only in select banks for hot entries, while cold data are processed at the bank group level reducing PE idleness and cross bank transfers. On the software side, it introduces a clustering and packing (CAP) method that leverages clustering to improve temporal locality in query processing, enhancing data reuse. Finally, we implement host NMP co optimization techniques, including an optimized programming model, customized instructions, and a tailored dataflow. Experiments on object detection inference show that DANMP achieves 97.43x speedup and 208.47x energy efficiency improvement over NVIDIA A6000 GPU.

cs.AR↗

arXiv2026

Distinguishing Hot-Electron and Optomechanical Pathways at Metal-Molecule Interfaces

Energy and charge transfer between molecules and metal surfaces underpin heterogeneous catalysis, surface-enhanced spectroscopies and plasmon-driven chemistry, yet the microscopic origins of vibrational excitation at metal interfaces remain unresolved. Here we use temperature-dependent surface-enhanced Raman scattering (SERS) to directly distinguish plasmon-vibration optomechanical coupling from hot-electron-driven excitation.By probing thionine adsorbed on gold nanostructures at 295 K and 3.5 K, we show that pronounced anti-Stokes scattering at cryogenic temperature arises from optical pumping of vibrational populations, whereas room-temperature spectra are governed by thermal population. Bromide co-adsorbates play a decisive role by guiding molecular alignment, inducing surface atom displacements, and enabling transient adsorption geometries that activate otherwise Raman-inactive vibrational modes. In the absence of bromide, distinct excitation pathways emerge, reflecting competition between optomechanical coupling and charge-transfer processes associated with molecular polarization along the optical field or orientation relative to the metal surface. These results establish molecular optomechanics as a sensitive probe of surface-molecule interactions and demonstrate how anion-mediated surface dynamics regulate energy flow at plasmonic interfaces.

cond-mat.mes-hall↗

arXiv2025

Convergence analysis of Wirtinger Flow for Poisson phase retrieval

This paper presents a rigorous theoretical convergence analysis of the Wirtinger Flow (WF) algorithm for Poisson phase retrieval, a fundamental problem in imaging applications. Unlike prior analyses that rely on truncation or additional adjustments to handle outliers, our framework avoids eliminating measurements or introducing extra computational steps, thereby reducing overall complexity. We prove that WF achieves linear convergence to the true signal under noiseless conditions and remains robust and stable in the presence of bounded noise for Poisson phase retrieval. Additionally, we propose an incremental variant of WF, which significantly improves computational efficiency and guarantees convergence to the true signal with high probability under suitable conditions.

math.NA↗

arXiv2024

On ergodic optimization for unimodal maps

In this article, we show that for a typical non-uniformly expanding unimodal map, the unique maximizing measure of a generic Lipschitz function is supported on a periodic orbit.

math.DS↗

arXiv2022

Affine Phase Retrieval via Second-Order Methods

In this paper, we study the affine phase retrieval problem, which aims to recover signals from the magnitudes of affine measurements. We develop second-order optimization methods based on Newton and Gauss-Newton iterations and establish that, under specific a priori conditions, the problem exhibits strong convexity. Theoretically, we prove that the Newton method with resampling achieves global quadratic convergence in the noiseless setting for both Gaussian measurements and admissible coded diffraction patterns (CDPs). Furthermore, we demonstrate that the same theoretical framework naturally extends to the Gauss-Newton method, implying its quadratic convergence. To validate our theoretical findings, we conduct extensive numerical experiments. The results confirm the quadratic convergence of second-order methods, while their computational efficiency remains comparable to that of first-order methods. Additionally, our experiments demonstrate that second-order methods achieve exact recovery with relatively few measurements, highlighting their practical feasibility and robustness.

cs.IT↗

arXiv2021

A Random Active Set Method for Strictly Convex Quadratic Problem with Simple Bounds

Active set method aims to find the correct active set of the optimal solution and it is a powerful method for solving strictly convex quadratic problem with bound constraints. To guarantee the finite step convergence, the existing active set methods all need strict conditions or some additional strategies, which greatly affect the efficiency of the algorithm. In this paper, we propose a random active set method which introduces randomness in the update of active set. We prove that it can converge in finite iterations with probability one without any conditions on the problem or any additional strategies. Numerical results show that the algorithm obtains the correct active set within a few iterations, and compared with the existing methods, it has better robustness and efficiency.

math.OC↗

arXiv2020

Perturbed Amplitude Flow for Phase Retrieval

In this paper, we propose a new non-convex algorithm for solving the phase retrieval problem, i.e., the reconstruction of a signal $ \vx\in\H^n $ ($\H=\R$ or $\C$) from phaseless samples $ b_j=\abs{\langle \va_j, \vx\rangle } $, $ j=1,\ldots,m $. The proposed algorithm solves a new proposed model, perturbed amplitude-based model, for phase retrieval and is correspondingly named as {\em Perturbed Amplitude Flow} (PAF). We prove that PAF can recover $c\vx$ ($\abs{c} = 1$) under $\mathcal{O}(n)$ Gaussian random measurements (optimal order of measurements). Starting with a designed initial point, our PAF algorithm iteratively converges to the true solution at a linear rate for both real and complex signals. Besides, PAF algorithm needn't any truncation or re-weighted procedure, so it enjoys simplicity for implementation. The effectiveness and benefit of the proposed method are validated by both the simulation studies and the experiment of recovering natural images.

math.NA↗

arXiv2020

On fair entropy of the tent family

The notions of fair measure and fair entropy were introduced by Misiurewicz and Rodrigues recently, and discussed in detail for piecewise monotone interval maps. In particular, they showed that the fair entropy $h(a)$ of the tent map $f_a$, as a function of the parameter $a=\exp(h_{top}(f_a))$, is continuous and strictly increasing on $[\sqrt{2},2]$. In this short note, we extend the last result and characterize regularity of the function $h$ precisely. We prove that $h$ is $\frac{1}{2}$-Hölder continuous on $[\sqrt{2},2]$ and identify its best Hölder exponent on each subinterval of $[\sqrt{2},2]$. On the other hand, parallel to a recent result on topological entropy of the quadratic family due to Dobbs and Mihalache, we give a formula of pointwise Hölder exponents of $h$ at parameters chosen in an explicitly constructed set of full measure. This formula particularly implies that the derivative of $h$ vanishes almost everywhere.

math.DS↗

arXiv2019

Phase retrieval for sub-Gaussian measurements

Generally, phase retrieval problem can be viewed as the reconstruction of a function/signal from only the magnitude of the linear measurements. These measurements can be, for example, the Fourier transform of the density function. Computationally the phase retrieval problem is very challenging. Many algorithms for phase retrieval are based on i.i.d. Gaussian random measurements. However, Gaussian random measurements remain one of the very few classes of measurements. In this paper, we develop an efficient phase retrieval algorithm for sub-gaussian random frames. We provide a general condition for measurements and develop a modified spectral initialization. In the algorithm, we first obtain a good approximation of the solution through the initialization, and from there we useWirtinger Flow to solve for the solution. We prove that the algorithm converges to the global minimizer linearly.

math.OC↗

arXiv2016

Phase Retrieval From the Magnitudes of Affine Linear Measurements

In this paper, we consider the phase retrieval problem in which one aims to recover a signal from the magnitudes of affine measurements. Let $\{{\mathbf a}_j\}_{j=1}^m \subset {\mathbb H}^d$ and ${\mathbf b}=(b_1, \ldots, b_m)^\top\in{\mathbb H}^m$, where ${\mathbb H}={\mathbb R}$ or ${\mathbb C}$. We say $\{{\mathbf a}_j\}_{j=1}^m$ and $\mathbf b$ are affine phase retrievable for ${\mathbb H}^d$ if any ${\mathbf x}\in{\mathbb H}^d$ can be recovered from the magnitudes of the affine measurements $\{|<{\mathbf a}_j,{\mathbf x}>+b_j|,\, 1\leq j\leq m\}$. We develop general framework for affine phase retrieval and prove necessary and sufficient conditions for $\{{\mathbf a}_j\}_{j=1}^m$ and $\mathbf b$ to be affine phase retrievable. We establish results on minimal measurements and generic measurements for affine phase retrieval as well as on sparse affine phase retrieval. In particular, we also highlight some notable differences between affine phase retrieval and the standard phase retrieval in which one aims to recover a signal $\mathbf x$ from the magnitudes of its linear measurements. In standard phase retrieval, one can only recover $\mathbf x$ up to a unimodular constant, while affine phase retrieval removes this ambiguity. We prove that unlike standard phase retrieval, the affine phase retrievable measurements $\{{\mathbf a}_j\}_{j=1}^m$ and $\mathbf b$ do not form an open set in ${\mathbb H}^{m\times d}\times {\mathbb H}^m$. Also in the complex setting, the standard phase retrieval requires $4d-O(\log_2d)$ measurements, while the affine phase retrieval only needs $m=3d$ measurements.

cs.IT↗

arXiv2016

Phaseless Rcovery using Gauss-Newton Method

In this paper, we develop a concrete algorithm for phase retrieval, which we refer to as Gauss-Newton algorithm. In short, this algorithm starts with a good initial estimation, which is obtained by a modified spectral method, and then update the iteration point by a Gauss-Newton iteration step. We prove that a re-sampled version of this algorithm quadratically converges to the solution for the real case with the number of random measurements being nearly minimal. Numerical experiments also show that Gauss-Newton method has better performance over the other algorithms.

cs.IT↗

arXiv2016

The $ \ell_1 $-analysis with redundant dictionary in phase retrieval

This article presents new results concerning the recovery of a signal from magnitude only measurements where the signal is not sparse in an orthonormal basis but in a redundant dictionary. To solve this phaseless problem, we analyze the $ \ell_1 $-analysis model. Firstly we investigate the noiseless case with presenting a null space property of the measurement matrix under which the $ \ell_1 $-analysis model provide an exact recovery. Secondly we introduce a new property (S-DRIP) of the measurement matrix. By solving the $ \ell_1 $-analysis model, we prove that this property can guarantee a stable recovery of real signals that are nearly sparse in highly overcomplete dictionaries.

math.NA↗

arXiv2015

Stable Signal Recovery from Phaseless Measurements

The aim of this paper is to study the stability of the $\ell_1$ minimization for the compressive phase retrieval and to extend the instance-optimality in compressed sensing to the real phase retrieval setting. We first show that the $m={\mathcal O}(k\log(N/k))$ measurements is enough to guarantee the $\ell_1$ minimization to recover $k$-sparse signals stably provided the measurement matrix $A$ satisfies the strong RIP property. We second investigate the phaseless instance-optimality with presenting a null space property of the measurement matrix $A$ under which there exists a decoder $Δ$ so that the phaseless instance-optimality holds. We use the result to study the phaseless instance-optimality for the $\ell_1$ norm. The results build a parallel for compressive phase retrieval with the classical compressive sensing.

math.FA↗

arXiv2012

Summability implies Collet-Eckmann almost surely

We provide a strengthened version of the famous Jakobson's theorem. Consider an interval map $f$ satisfying a summability condition. For a generic one-parameter family $f_t$ of maps with $f_0=f$, we prove that $t=0$ is a Lebesgue density point of the set of parameters for which $f_t$ satisfies both the Collect-Eckmann condition and a strong polynomial recurrence condition.

math.DS↗