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For time series data observed at non-random and possibly non-equidistant time points, we estimate the trend function nonparametrically. Under the assumption of a bounded total variation of the function and low-order moment conditions on the…

Recovery of arbitrarily positioned samples that are missing in sparse signals recently attracted significant research interest. Sparse signals with heavily corrupted arbitrary positioned samples could be analyzed in the same way as…

Time-varying graph signal recovery has been widely used in many applications, including climate change, environmental hazard monitoring, and epidemic studies. It is crucial to choose appropriate regularizations to describe the…

Electrocardiogram (ECG) signals are often degraded by various noise sources such as baseline wander, motion artifacts, and electromyographic interference, posing a major challenge in clinical settings. This paper presents a lightweight deep…

Time-varying linear state-space models are powerful tools for obtaining mathematically interpretable representations of neural signals. For example, switching and decomposed models describe complex systems using latent variables that evolve…

In this paper, we introduce a new adaptive data analysis method to study trend and instantaneous frequency of nonlinear and non-stationary data. This method is inspired by the Empirical Mode Decomposition method (EMD) and the recently…

Mechanical vibration signal denoising is a pivotal task in various industrial applications, including system health monitoring and failure prediction. This paper introduces a novel deep learning transformer-based architecture specifically…

This article introduces a nonparametric approach to spectral analysis of a high-dimensional multivariate nonstationary time series. The procedure is based on a novel frequency-domain factor model that provides a flexible yet parsimonious…

Conventional wavelet-domain methods for room impulse response denoising rely on thresholding detail coefficients, which is unsuited for low frequencies. In this work, we introduce a wavelet-based post-processing algorithm that extends…

The synchrosqueezing transform, a kind of reassignment method, aims to sharpen the time-frequency representation and to separate the components of a multicomponent non-stationary signal. In this paper, we consider the short-time Fourier…

In this paper, we introduce a total variation based variational model for denoising wrapped phase images. Our model improves on former methods by preserving discontinuities of the phase map and enforcing the fundamental Pythagorean…

This study proposes a deep learning model that effectively suppresses the false alarms in the intensive care units (ICUs) without ignoring the true alarms using single- and multimodal biosignals. Most of the current work in the literature…

In this work, we present a method for learning interpretable music signal representations directly from waveform signals. Our method can be trained using unsupervised objectives and relies on the denoising auto-encoder model that uses a…

Neural signals are characterized by rich temporal and spatiotemporal dynamics that reflect the organization of cortical networks. Theoretical research has shown how neural networks can operate at different dynamic ranges that correspond to…

We consider time-reversal of electromagnetic waves in a closed, wave-chaotic system containing a discrete, passive, harmonic-generating nonlinearity. An experimental system is constructed as a time-reversal mirror, in which excitations…

This paper considers the problem of sampling and reconstruction of a continuous-time sparse signal without assuming the knowledge of the sampling instants or the sampling rate. This topic has its roots in the problem of recovering multiple…

Locally adapted parameterizations of a model (such as locally weighted regression) are expressive but often suffer from high variance. We describe an approach for reducing the variance, based on the idea of estimating simultaneously a…

In this paper, a novel decomposition method for non-stationary and nonlinear signals is proposed. This method is inspired by the adaptive wavelet filter bank of the empirical wavelet transform (EWT) and Fourier intrinsic band functions…

Estimating and quantifying uncertainty in unknown system parameters from limited data remains a challenging inverse problem in a variety of real-world applications. While many approaches focus on estimating constant parameters, a subset of…

In this paper, we study a nonlinear spiked random matrix model where a nonlinear function is applied element-wise to a noise matrix perturbed by a rank-one signal. We establish a signal-plus-noise decomposition for this model and identify…