Related papers: Rapid evaluation of the spectral signal detection …
The present paper implements a complex analytic method to recover the spectrum of a matrix perturbed by either the addition or the multiplication of a random matrix noise, under the assumption that the distribution of the noise is unitarily…
Super-resolution is a fundamental task in imaging, where the goal is to extract fine-grained structure from coarse-grained measurements. Here we are interested in a popular mathematical abstraction of this problem that has been widely…
Results on the spectral behavior of random matrices as the dimension increases are applied to the problem of detecting the number of sources impinging on an array of sensors. A common strategy to solve this problem is to estimate the…
Consider an $n \times p$ data matrix $X$ whose rows are independently sampled from a population with covariance $\Sigma$. When $n,p$ are both large, the eigenvalues of the sample covariance matrix are substantially different from those of…
The interplay between computational efficiency and statistical accuracy in high-dimensional inference has drawn increasing attention in the literature. In this paper, we study computational and statistical boundaries for submatrix…
We propose a novel estimation procedure for certain spectral distributions associated with a class of high dimensional linear time series. The processes under consideration are of the form $X_t = \sum_{\ell=0}^\infty \mathbf{A}_\ell…
Spectrum sensing enables cognitive radio systems to detect unused portions of the radio spectrum and then use them while avoiding interferences to the primary users. Energy detection is one of the most used techniques for spectrum sensing…
We study the statistical decision process of detecting the low-rank signal from various signal-plus-noise type data matrices, known as the spiked random matrix models. We first show that the principal component analysis can be improved by…
Line spectral estimation is a classical signal processing problem that aims to estimate the line spectra from their signal which is contaminated by deterministic or random noise. Despite a large body of research on this subject, the…
This paper studies the problem of line spectral estimation in the continuum of a bounded interval with one snapshot of array measurement. The single-snapshot measurement data is turned into a Hankel data matrix which admits the Vandermonde…
In this paper, we derive the analytical behavior of the limiting spectral distribution of non-central covariance matrices of the "general information-plus-noise" type, as studied in [14]. Through the equation defining its Stieltjes…
A previous signal processing algorithm that aimed to enhance spectral changes (SCE) over time showed benefit for hearing-impaired (HI) listeners to recognize speech in background noise. In this work, the previous SCE was manipulated to…
Signal-to-noise ratio (SNR) statistics play a central role in many applications. A common situation where SNR is studied is when a continuous time signal is sampled at a fixed frequency with some noise in the background. While estimation…
Anomaly detection in massive networks has numerous theoretical and computational challenges, especially as the behavior to be detected becomes small in comparison to the larger network. This presentation focuses on recent results in three…
The distance transform (DT) and its many variations are ubiquitous tools for image processing and analysis. In many imaging scenarios, the images of interest are corrupted by noise. This has a strong negative impact on the accuracy of the…
Terahertz Time Domain Spectroscopy (THz-TDS) systems have emerged as mature technologies with significant potential across various research fields and industries. However, the lack of standardized methods for signal and noise estimation and…
Recent work has generalized several results concerning the well-understood spiked Wigner matrix model of a low-rank signal matrix corrupted by additive i.i.d. Gaussian noise to the inhomogeneous case, where the noise has a variance profile.…
For submillimeter spectroscopy with ground-based single-dish telescopes, removing noise contribution from the Earth's atmosphere and the instrument is essential. For this purpose, here we propose a new method based on a data-scientific…
In the study of condensed matter physics, spectral information plays an important role for understand the mechanism of materials. However, it is difficult to obtain the spectrum directly through experiments or simulation. For example, the…
In this paper, a signal detection method based on the denoise diffusion model (DM) is proposed, which outperforms the maximum likelihood (ML) estimation method that has long been regarded as the optimal signal detection technique.…