Related papers: A rate optimal procedure for sparse signal recover…
We attempt to recover an $n$-dimensional vector observed in white noise, where $n$ is large and the vector is known to be sparse, but the degree of sparsity is unknown. We consider three different ways of defining sparsity of a vector:…
Recovery of the sparsity pattern (or support) of an unknown sparse vector from a limited number of noisy linear measurements is an important problem in compressed sensing. In the high-dimensional setting, it is known that recovery with a…
This paper considers the noisy sparse phase retrieval problem: recovering a sparse signal $x \in \mathbb{R}^p$ from noisy quadratic measurements $y_j = (a_j' x )^2 + \epsilon_j$, $j=1, \ldots, m$, with independent sub-exponential noise…
Recovery of the sparsity pattern (or support) of an unknown sparse vector from a small number of noisy linear measurements is an important problem in compressed sensing. In this paper, the high-dimensional setting is considered. It is shown…
We present a novel approach for recovering a sparse signal from cross-correlated data. Cross-correlations naturally arise in many fields of imaging, such as optics, holography and seismic interferometry. Compared to the sparse signal…
In this paper, we consider the sparse phase retrieval problem, recovering an $s$-sparse signal $\bm{x}^{\natural}\in\mathbb{R}^n$ from $m$ phaseless samples $y_i=|\langle\bm{x}^{\natural},\bm{a}_i\rangle|$ for $i=1,\ldots,m$. Existing…
We investigate the sparse recovery problem of reconstructing a high-dimensional non-negative sparse vector from lower dimensional linear measurements. While much work has focused on dense measurement matrices, sparse measurement schemes are…
In this paper, we study the sample complexity and develop efficient optimal algorithms for 1-bit phase retrieval: recovering a signal $\mathbf{x}\in\mathbb{R}^n$ from $m$ phaseless bits…
In a variety of fields, in particular those involving imaging and optics, we often measure signals whose phase is missing or has been irremediably distorted. Phase retrieval attempts to recover the phase information of a signal from the…
Simultaneously performing variable selection and inference in high-dimensional regression models is an open challenge in statistics and machine learning. The increasing availability of vast amounts of variables requires the adoption of…
Controlling the False Discovery Rate (FDR) in a variable selection procedure is critical for reproducible discoveries, and it has been extensively studied in sparse linear models. However, it remains largely open in scenarios where the…
Conventional sparse phase retrieval schemes can recover sparse signals from the magnitude of linear measurements only up to a global phase ambiguity. This work proposes a novel approach that instead utilizes the magnitude of affine…
In this paper, we discuss application of iterative Stochastic Optimization routines to the problem of sparse signal recovery from noisy observation. Using Stochastic Mirror Descent algorithm as a building block, we develop a multistage…
As technology grows, higher frequency signals are required to be processed in various applications. In order to digitize such signals, conventional analog to digital convertors are facing implementation challenges due to the higher sampling…
The problem of signal recovery from its Fourier transform magnitude is of paramount importance in various fields of engineering and has been around for over 100 years. Due to the absence of phase information, some form of additional…
Signal modeling lies at the core of numerous signal and image processing applications. A recent approach that has drawn considerable attention is sparse representation modeling, in which the signal is assumed to be generated as a…
While data-driven confounder selection requires careful consideration, it is frequently employed in observational studies. Widely recognized criteria for confounder selection include the minimal-set approach, which involves selecting…
We consider the problem of sparse signal recovery from noisy measurements. Many of frequently used recovery methods rely on some sort of tuning depending on either noise or signal parameters. If no estimates for either of them are…
Compressed sensing deals with the recovery of sparse signals from linear measurements. Without any additional information, it is possible to recover an $s$-sparse signal using $m \gtrsim s \log(d/s)$ measurements in a robust and stable way.…
Controlling the false discovery rate (FDR) in high-dimensional variable selection requires balancing rigorous error control with statistical power. Existing methods with provable guarantees are often overly conservative, creating a…