Related papers: Quickest Sequence Phase Detection
A $k$-modal sequence is a sequence of real numbers that can be partitioned into $k+1$ (possibly empty) monotone sections such that adjacent sections have opposite monotonicities. For every positive integer $k$, we prove that any sequence of…
A fundamental question for edge detection in noisy images is how faint can an edge be and still be detected. In this paper we offer a formalism to study this question and subsequently introduce computationally efficient multiscale edge…
Three variants of the statistical complexity function, which is used as a criterion in the problem of detection of a useful signal in the signal-noise mixture, are considered. The probability distributions maximizing the considered variants…
An identification of a spherically symmetric potential by its phase shifts is an important physical problem. Recent theoretical results assure that such a potential is uniquely defined by a sufficiently large subset of its phase shifts at…
We study the large deviations performance of consensus+innovations distributed detection over noisy networks, where sensors at a time step k cooperate with immediate neighbors (consensus) and assimilate their new observations (innovation.)…
Time-frequency analysis is often used to study non stationary multicomponent signals, which can be viewed as the surperimposition of modes, associated with ridges in the TF plane. To understand such signals, it is essential to identify…
A novel quickest detection setting is proposed which is a generalization of the well-known Bayesian change-point detection model. Suppose \{(X_i,Y_i)\}_{i\geq 1} is a sequence of pairs of random variables, and that S is a stopping time with…
Change-point analysis is thriving in this big data era to address problems arising in many fields where massive data sequences are collected to study complicated phenomena over time. It plays an important role in processing these data by…
A communicating system is $k$-synchronizable if all of the message sequence charts representing the executions can be divided into slices of $k$ sends followed by $k$ receptions. It was previously shown that, for a fixed given $k$, one…
This work takes the first steps towards solving the "phaseless subspace tracking" (PST) problem. PST involves recovering a time sequence of signals (or images) from phaseless linear projections of each signal under the following structural…
Given an inhomogeneous chain embedded in a noisy image, we consider the conditions under which such an embedded chain is detectable. Many applications, such as detecting moving objects, detecting ship wakes, can be abstracted as the…
A vertex subset of a graph is called a distance-$k$ independent set if the distance between any two of its distinct vertices is at least $k + 1$. For all $n,k \geq 1$, we determine the minimum possible number of inclusion-wise maximal…
Accurate phase extraction from sinusoidal signals is a crucial task in various signal processing applications. While prior research predominantly addresses the case of asynchronous sampling with unknown signal frequency, this study focuses…
Time series subsequence anomaly detection is an important task in a large variety of real-world applications ranging from health monitoring to AIOps, and is challenging due to the following reasons: 1) how to effectively learn complex…
We present a general framework to study the simultaneous estimation of multiple phases in the presence of noise as a discretized model for phase imaging. This approach can lead to nontrivial bounds of the precision for multiphase…
The sequence reconstruction problem involves a model where a sequence is transmitted over several identical channels. This model investigates the minimum number of channels required for the unique reconstruction of the transmitted sequence.…
A Markov process is registered. At random moment $\theta$ the distribution of observed sequence changes. Using probability maximizing approach the optimal stopping rule for detecting the change is identified. Some explicit solution is…
We consider detecting the evolutionary oscillatory pattern of a signal when it is contaminated by non-stationary noises with complexly time-varying data generating mechanism. A high-dimensional dense progressive periodogram test is proposed…
We investigate phase and frequency estimation with different measurement strategies under the effect of collective phase noise. First, we consider the standard linear estimation scheme and present an experimentally realisable optimization…
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…