Related papers: Synchrosqueezing-based Recovery of Instantaneous F…
We provide a statistical analysis of a tool in nonlinear-type time-frequency analysis, the synchrosqueezing transform (SST), for both the null and non-null cases. The intricate nonlinear interaction of different quantities in SST is…
Non-stationary signals are ubiquitous in real life. Many techniques have been proposed in the last decades which allow decomposing multi-component signals into simple oscillatory mono-components, like the groundbreaking Empirical Mode…
Spatial resolution of most imaging devices is fundamentally restricted by diffraction. This limitation is manifested in the loss of high spatial frequency information contained in evanescent waves. As a result, conventional far-field optics…
Recently it has been shown that the intensity time-bandwidth product of optical signals can be engineered to match that of the data acquisition instrument. In particular, it is possible to slow down an ultrafast signal, resulting in…
Many phenomena are described by bivariate signals or bidimensional vectors in applications ranging from radar to EEG, optics and oceanography. The time-frequency analysis of bivariate signals is usually carried out by analyzing two separate…
The theoretical basis for conventional acquisition of bandlimited signals typically relies on uniform time sampling and assumes infinite-precision amplitude values. In this paper, we explore signal representation and recovery based on…
We present a discrete-time algorithm for nonuniform sampling rate conversion that presents low computational complexity and memory requirements. It generalizes arbitrary sampling rate conversion by accommodating time-varying conversion…
Detrend fluctuation analysis (DFA) has become a choice method for effective analysis of a broad variety of nonstationary signals. We show in the present article that, provided the nonstationary fluctuations occur at a large enough time…
The ability of a radar to discriminate in both range and Doppler velocity is completely characterized by the ambiguity function (AF) of its transmit waveform. Mathematically, it is obtained by correlating the waveform with its…
We propose a Bayesian approach to the problem of multi-reference alignment -- the recovery of signals from noisy, randomly shifted observations. While existing frequentist methods accurately recover the signal at arbitrarily low…
In a variety of fields, in particular those involving imaging and optics, we often measure signals whose phase is missing or has been irremediably distorted. Phase retrieval attempts to recover the phase information of a signal from the…
We present a spectrogram separation method tailored for mixtures comprising two nonstationary components. By exploiting the unique characteristics of their time-frequency representations, we propose an inverse problem formulation to…
We study the problem of recovering an unknown compactly-supported multivariate function from samples of its Fourier transform that are acquired nonuniformly, i.e. not necessarily on a uniform Cartesian grid. Reconstruction problems of this…
We study the problem of interpolating a noisy Fourier-sparse signal in the time duration $[0, T]$ from noisy samples in the same range, where the ground truth signal can be any $k$-Fourier-sparse signal with band-limit $[-F, F]$. Our main…
This summary of the doctoral thesis provides a comprehensive formulation of the Extended Discrete Fourier Transform (EDFT), derived directly from the Fourier integral and its orthogonality properties. The method is obtained by solving…
We consider the problem of recovering a compactly-supported function from a finite collection of pointwise samples of its Fourier transform taking nonuniformly. First, we show that under suitable conditions on the sampling frequencies -…
The problem of signal recovery from the autocorrelation, or equivalently, the magnitudes of the Fourier transform, is of paramount importance in various fields of engineering. In this work, for one-dimensional signals, we give conditions,…
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…
Conventional sub-Nyquist sampling methods for analog signals exploit prior information about the spectral support. In this paper, we consider the challenging problem of blind sub-Nyquist sampling of multiband signals, whose unknown…
This paper introduces an innovative approach for signal reconstruction using data acquired through multi-input-multi-output (MIMO) sampling. First, we show that it is possible to perfectly reconstruct a set of periodic band-limited signals…