相关论文: Robust Outlier Bound Condition to Phase Retrieval …

The problem of reconstructing a function from the magnitudes of its frame coefficients has recently been shown to be never uniformly stable in infinite-dimensional spaces [5]. This result also holds for frames that are possibly continuous…

We study the subgradient method for factorized robust signal recovery problems, including robust PCA, robust phase retrieval, and robust matrix sensing. The resulting objectives are nonsmooth and nonconvex, and can have unbounded sublevel…

This paper considers the robust phase retrieval problem, which can be cast as a nonsmooth and nonconvex optimization problem. We propose a new inexact proximal linear algorithm with the subproblem being solved inexactly. Our contributions…

In this paper, we investigate the theoretical guarantees of penalized $\lun$ minimization (also called Basis Pursuit Denoising or Lasso) in terms of sparsity pattern recovery (support and sign consistency) from noisy measurements with…

Suppose we wish to recover an n-dimensional real-valued vector x_0 (e.g. a digital signal or image) from incomplete and contaminated observations y = A x_0 + e; A is a n by m matrix with far fewer rows than columns (n << m) and e is an…

The phase retrieval problem asks to recover a natural signal $y_0 \in \mathbb{R}^n$ from $m$ quadratic observations, where $m$ is to be minimized. As is common in many imaging problems, natural signals are considered sparse with respect to…

Outlier-robust estimation is a fundamental problem and has been extensively investigated by statisticians and practitioners. The last few years have seen a convergence across research fields towards "algorithmic robust statistics", which…

The generalized phase retrieval problem over compact groups aims to recover a set of matrices -- representing an unknown signal -- from their associated Gram matrices. This framework generalizes the classical phase retrieval problem, which…

We consider the problem of signal reconstruction from quadratic measurements that are encoded as +1 or -1 depending on whether they exceed a predetermined positive threshold or not. Binary measurements are fast to acquire and inexpensive in…

We study the problem of recovering a hidden binary $k$-sparse $p$-dimensional vector $\beta$ from $n$ noisy linear observations $Y=X\beta+W$ where $X_{ij}$ are i.i.d. $\mathcal{N}(0,1)$ and $W_i$ are i.i.d. $\mathcal{N}(0,\sigma^2)$. A…

In the compressive phase retrieval problem, or phaseless compressed sensing, or compressed sensing from intensity only measurements, the goal is to reconstruct a sparse or approximately $k$-sparse vector $x \in \mathbb{R}^n$ given access to…

Consider the $n$-dimensional vector $y=X\be+\e$, where $\be \in \R^p$ has only $k$ nonzero entries and $\e \in \R^n$ is a Gaussian noise. This can be viewed as a linear system with sparsity constraints, corrupted by noise. We find a…

We consider outlier-robust and sparse estimation of linear regression coefficients, when the covariates and the noises are contaminated by adversarial outliers and noises are sampled from a heavy-tailed distribution. Our results present…

Quadratically-constrained basis pursuit has become a popular device in sparse regularization; in particular, in the context of compressed sensing. However, the majority of theoretical error estimates for this regularizer assume an a priori…

$3$D structure recovery from a collection of $2$D images requires the estimation of the camera locations and orientations, i.e. the camera motion. For large, irregular collections of images, existing methods for the location estimation…

Consider estimating a structured signal $\mathbf{x}_0$ from linear, underdetermined and noisy measurements $\mathbf{y}=\mathbf{A}\mathbf{x}_0+\mathbf{z}$, via solving a variant of the lasso algorithm: $\hat{\mathbf{x}}=\arg\min_\mathbf{x}\{…

We consider the problem of exact support recovery of sparse signals via noisy measurements. The main focus is the sufficient and necessary conditions on the number of measurements for support recovery to be reliable. By drawing an analogy…

We address the problem of blind gain and phase calibration of a sensor array from ambient noise. The key motivation is to ease the calibration process by avoiding a complex procedure setup. We show that computing the sample covariance…

We consider high dimensional sparse regression, and develop strategies able to deal with arbitrary -- possibly, severe or coordinated -- errors in the covariance matrix $X$. These may come from corrupted data, persistent experimental…

We consider the problem of reconstructing a function $f\in L^2(\mathbb{R})$ given phase-less samples of its Gabor transform, which is defined by $$\mathcal{G} f(x,\omega) := 2^{\frac14} \int_{\mathbb{R}} f(t) e^{-\pi (t-x)^2} e^{-2\pi i y…