Related papers: Sample Efficient Estimation and Recovery in Sparse…
We consider the problem of building numerically stable algorithms for computing Discrete Fourier Transform (DFT) of $N$- length signals with known frequency support of size $k$. A typical algorithm, in this case, would involve solving…
Discrete Fourier Transform (DFT) is widely used in signal processing to analyze the frequencies in a discrete signal. However, DFT fails to recover the exact Fourier spectrum, when the signal contains frequencies that do not correspond to…
Orthogonal time frequency space (OTFS) modulation is a two-dimensional modulation scheme designed in the delay-Doppler (DD) domain, exhibiting superior performance over orthogonal frequency division multiplexing (OFDM) modulation in…
We propose a simple and efficient time-series clustering framework particularly suited for low Signal-to-Noise Ratio (SNR), by simultaneous smoothing and dimensionality reduction aimed at preserving clustering information. We extend the…
The problem of recovering a one-dimensional signal from its Fourier transform magnitude, called Fourier phase retrieval, is ill-posed in most cases. We consider the closely-related problem of recovering a signal from its phaseless…
In this paper, we consider the sparse phase retrieval problem, recovering an $s$-sparse signal $\bm{x}^{\natural}\in\mathbb{R}^n$ from $m$ phaseless samples $y_i=|\langle\bm{x}^{\natural},\bm{a}_i\rangle|$ for $i=1,\ldots,m$. Existing…
Recent network traffic studies argue that network arrival processes are much more faithfully modeled using statistically self-similar processes instead of traditional Poisson processes [LTWW94,PF95]. One difficulty in dealing with…
We study convergence properties of sparse averages of partial sums of Fourier series of continuous functions. By sparse averages, we are considering an increasing sequences of integers $n_0 < n_1 < n_2 < ...$ and looking at…
This work deals with directional of arrival (DOA) estimation with a large antenna array. We first develop a novel signal model with a sparse system transfer matrix using an inverse discrete Fourier transform (DFT) operation, which leads to…
A new iterative low complexity algorithm has been presented for computing the Walsh-Hadamard transform (WHT) of an $N$ dimensional signal with a $K$-sparse WHT, where $N$ is a power of two and $K = O(N^\alpha)$, scales sub-linearly in $N$…
This paper introduces a novel method to separate noisy speech into low or high frequency frames, in order to improve fundamental frequency (F0) estimation accuracy. In this proposal, the target signal is analyzed by means of the ensemble…
In this work we propose a nonconvex two-stage \underline{s}tochastic \underline{a}lternating \underline{m}inimizing (SAM) method for sparse phase retrieval. The proposed algorithm is guaranteed to have an exact recovery from $O(s\log n)$…
The $N$-point discrete Fourier transform (DFT) is a cornerstone for several signal processing applications. Many of these applications operate in real-time, making the computational complexity of the DFT a critical performance indicator to…
Conventional sparse phase retrieval schemes can recover sparse signals from the magnitude of linear measurements only up to a global phase ambiguity. This work proposes a novel approach that instead utilizes the magnitude of affine…
We introduce a general purpose algorithm for rapidly computing certain types of oscillatory integrals which frequently arise in problems connected to wave propagation and general hyperbolic equations. The problem is to evaluate numerically…
Fourier transformation is an extensively studied problem in many research fields. It has many applications in machine learning, signal processing, compressed sensing, and so on. In many real-world applications, approximated Fourier…
We consider continuous-time sparse stochastic processes from which we have only a finite number of noisy/noiseless samples. Our goal is to estimate the noiseless samples (denoising) and the signal in-between (interpolation problem). By…
Compressed sensing of simultaneously sparse and low-rank matrices enables recovery of sparse signals from a few linear measurements of their bilinear form. One important question is how many measurements are needed for a stable…
Synchrosqueezing transform (SST) is a useful tool for vibration signal analysis due to its high time-frequency (TF) concentration and reconstruction properties. However, existing SST requires much processing time for large-scale data. In…
Analytic signals constitute a class of signals that are widely applied in time-frequency analysis such as extracting instantaneous frequency (IF) or phase derivative in the characterization of ultrashort laser pulse. The purpose of this…