Related papers: Joint Linear Trend Recovery Using L1 Regularizatio…

In this article, we discuss various implementation of L1 filtering in order to detect some properties of noisy signals. This filter consists of using a L1 penalty condition in order to obtain the filtered signal composed by a set of…

In this paper we analyze the asymptotic properties of l1 penalized maximum likelihood estimation of signals with piece-wise constant mean values and/or variances. The focus is on segmentation of a non-stationary time series with respect to…

This paper investigates the theoretical guarantees of L1-analysis regularization when solving linear inverse problems. Most of previous works in the literature have mainly focused on the sparse synthesis prior where the sparsity is measured…

This paper addresses the problem of segmenting a time-series with respect to changes in the mean value or in the variance. The first case is when the time data is modeled as a sequence of independent and normal distributed random variables…

This paper is dedicated to the fused trend filtering on a general graph, which is a combination of fused estimator and 1-st order trend filtering on a graph. There are two cases of fusion regularisers studied in this work: anisotropic total…

We study the problem of recovering the underlining sparse signals from clean or noisy phaseless measurements. Due to the sparse prior of signals, we adopt an L0regularized variational model to ensure only a small number of nonzero elements…

This article presents novel results concerning the recovery of signals from undersampled data in the common situation where such signals are not sparse in an orthonormal basis or incoherent dictionary, but in a truly redundant dictionary.…

Phase retrieval refers to a classical nonconvex problem of recovering a signal from its Fourier magnitude measurements. Inspired by the compressed sensing technique, signal sparsity is exploited in recent studies of phase retrieval to…

The couplings in a sparse asymmetric, asynchronous Ising network are reconstructed using an exact learning algorithm. L$_1$ regularization is used to remove the spurious weak connections that would otherwise be found by simply minimizing…

We develop a fully Bayesian hierarchical model for trend filtering, itself a new development in nonparametric, univariate regression. The framework more broadly applies to the generalized lasso, but focus is on Bayesian trend filtering. We…

Extracting the underlying trend signal is a crucial step to facilitate time series analysis like forecasting and anomaly detection. Besides noise signal, time series can contain not only outliers but also abrupt trend changes in real-world…

We consider the inverse problem of recovering a continuous-domain function from a finite number of noisy linear measurements. The unknown signal is modeled as the sum of a slowly varying trend and a periodic or quasi-periodic seasonal…

Given a linear system in a real or complex domain, linear regression aims to recover the model parameters from a set of observations. Recent studies in compressive sensing have successfully shown that under certain conditions, a linear…

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…

Decomposing complex time series into trend, seasonality, and remainder components is an important task to facilitate time series anomaly detection and forecasting. Although numerous methods have been proposed, there are still many time…

By using subsets of the HATNet and K2 (Kepler two-wheel) Campaign 1 databases, we examine the effectiveness of filtering out systematics from photometric time series while simultaneously searching for periodic signals. We carry out tests to…

This paper develops a unified and computationally efficient method for change-point estimation along the time dimension in a non-stationary spatio-temporal process. By modeling a non-stationary spatio-temporal process as a piecewise…

This paper introduces a novel approach for recovering sparse signals using sorted L1/L2 minimization. The proposed method assigns higher weights to indices with smaller absolute values and lower weights to larger values, effectively…

We consider the problem of detecting a change point in a sequence of mean functions from a functional time series. We propose an $L^1$ norm based methodology and establish its theoretical validity both for classical and for relevant…

We introduce an efficient method for the reconstruction of the correlation between a compressively measured image and a phase-only filter. The proposed method is based on two properties of phase-only filtering: such filtering is a unitary…