Related papers: Separating signal from noise
In this paper, we establish sample complexity bounds for learning high-dimensional simplices in $\mathbb{R}^K$ from noisy data. Specifically, we consider $n$ i.i.d. samples uniformly drawn from an unknown simplex in $\mathbb{R}^K$, each…
Inferring networks from observed time series data presents a clear glimpse into the interconnections among nodes. Network inference models, when dealing with real-world open cases, especially in the presence of observational noise,…
The paper considers the phase retrieval problem in N-dimensional complex vector spaces. It provides two sets of deterministic measurement vectors which guarantee signal recovery for all signals, excluding only a specific subspace and a…
Separating a stochastic gravitational wave background (SGWB) from noise is a challenging statistical task. One approach to establishing a detection criterion for the SGWB is using Bayesian evidence. If the evidence ratio (Bayes factor)…
Lossy transmission over a relay channel in which the relay has access to correlated side information is considered. First, a joint source-channel decode-and-forward scheme is proposed for general discrete memoryless sources and channels.…
We consider the problem of pointwise estimation of multi-dimensional signals $s$, from noisy observations $(y_\tau)$ on the regular grid $\bZd$. Our focus is on the adaptive estimation in the case when the signal can be well recovered using…
The problem of recovering a structured signal from its linear measurements in the presence of speckle noise is studied. This problem appears in many imaging systems such as synthetic aperture radar and optical coherence tomography. The…
We consider the situation in which a transmitter attempts to communicate reliably over a discrete memoryless channel while simultaneously ensuring covertness (low probability of detection) with respect to a warden, who observes the signals…
In the standard Gaussian linear measurement model $Y=X\mu_0+\xi \in \mathbb{R}^m$ with a fixed noise level $\sigma>0$, we consider the problem of estimating the unknown signal $\mu_0$ under a convex constraint $\mu_0 \in K$, where $K$ is a…
This paper introduces a Bayesian framework to detect multiple signals embedded in noisy observations from a sensor array. For various states of knowledge on the communication channel and the noise at the receiving sensors, a marginalization…
Image noise can often be accurately fitted to a Poisson-Gaussian distribution. However, estimating the distribution parameters from a noisy image only is a challenging task. Here, we study the case when paired noisy and noise-free samples…
With the advent of massive data outputs at a regular rate, admittedly, signal processing technology plays an increasingly key role. Nowadays, signals are not merely restricted to physical sources, they have been extended to digital sources…
Several differentiating algorithms of the noisy signals are considered. The proposed wavelet based technique is compared with others based on the Fourier transform and the finite differences. The accuracy of the calculations for different…
Using random Gaussian vectors and an information-uncertainty relation, we give a proof that the coherent information is an achievable rate for entanglement transmission through a noisy quantum channel. The codes are random subspaces…
We consider the problem of recovering linear image of unknown signal belonging to a given convex compact signal set from noisy observation of another linear image of the signal. We develop a simple generic efficiently computable nonlinear…
The extraction of information carried by light plays an increasingly important role in optical communication, imaging, and detection. However, the information can only be successfully extracted when the light pulse is comparably strong,…
This paper studies the problem of recovering a signal vector and the corrupted noise vector from a collection of corrupted linear measurements through the solution of a l1 minimization, where the sensing matrix is a partial Fourier matrix…
In many applications sampled data are collected in irregular fashion or are partly lost or unavailable. In these cases it is required to convert irregularly sampled signals to regularly sampled ones or to restore missing data. In this…
We consider minimax signal detection in the sequence model. Working with certain ellipsoids in the space of square-summable sequences of real numbers, with a ball of positive radius removed, we obtain upper and lower bounds for the minimax…
Quantum fluctuations yield inevitable noises in quantum detection. We derive an upper bound of signal to noise ratio for arbitrary quantum detection described by trace-class operators with discrete spectra. The bound is independent of…