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Sensitivity limits are usually determined using the Cram\'er-Rao bound. Recently this approach has been used to obtain the ultimate resolution limit for the estimation of the separation between two incoherent point sources. However, methods…
We consider the problem of estimating the spatial separation between two mutually incoherent point light sources using the super-resolution imaging technique based on spatial mode demultiplexing with noisy detectors. We show that in the…
We present a method for audio denoising that combines processing done in both the time domain and the time-frequency domain. Given a noisy audio clip, the method trains a deep neural network to fit this signal. Since the fitting is only…
Noise reduction techniques based on deep learning have demonstrated impressive performance in enhancing the overall quality of recorded speech. While these approaches are highly performant, their application in audio engineering can be…
We consider the problem of reconstructing a discrete-time signal (sequence) with continuous-valued components corrupted by a known memoryless channel. When performance is measured using a per-symbol loss function satisfying mild regularity…
Recent advances in the field of data-driven dynamics allow for the discovery of ODE systems using state measurements. One approach, known as Sparse Identification of Nonlinear Dynamics (SINDy), assumes the dynamics are sparse within a…
We present an algorithm based on numerical techniques that have become standard for solving nonlinear integral equations: Newton's method, homotopy continuation, the multilevel method and random projection to solve the inversion problem…
Sampling a signal below the Shannon-Nyquist rate causes aliasing, meaning different frequencies to become indistinguishable. It is also well-known that recovering spectral information from a signal using a parametric method can be ill-posed…
Identification of nonlinear dynamical systems has been popularized by sparse identification of the nonlinear dynamics (SINDy) via the sequentially thresholded least squares (STLS) algorithm. Many extensions SINDy have emerged in the…
The problem of estimating the frequencies of an exponential sum has been studied extensively over the last years. It can be understood as a sparse estimation problem, as it strives to identify the sparse representation of a signal using…
Diffusion-based extreme image compression methods have achieved impressive performance at extremely low bitrates. However, constrained by the iterative denoising process that starts from pure noise, these methods are limited in both…
This paper focuses on stochastic proximal gradient methods for optimizing a smooth non-convex loss function with a non-smooth non-convex regularizer and convex constraints. To the best of our knowledge we present the first non-asymptotic…
We consider the inverse problem of recovering the locations and amplitudes of a collection of point sources represented as a discrete measure, given $M+1$ of its noisy low-frequency Fourier coefficients. Super-resolution refers to a stable…
The autoregressive time series model is a popular second-order stationary process, modeling a wide range of real phenomena. However, in applications, autoregressive signals are often corrupted by additive noise. Further, the autoregressive…
We investigate the sparse spikes deconvolution problem onto spaces of algebraic polynomials. Our framework encompasses the measure reconstruction problem from a combination of noiseless and noisy moment measurements. We study a TV-norm…
As technology grows, higher frequency signals are required to be processed in various applications. In order to digitize such signals, conventional analog to digital convertors are facing implementation challenges due to the higher sampling…
Reconstruction of undersampled periodic signals of unknown period is an important signal processing operation. It is especially difficult operation when the sequences of samples are short and no information on the inter-sequence time…
We determine the largest non-trivial rate of exponential decay at infinity for solutions to the Dirac equation \begin{equation*} \mathcal{D}_n \psi + \mathbb{V} \psi = 0 \quad \text{ in }\mathbb{R}^n, \end{equation*} being $\mathcal{D}_n$…
Decentralized optimization is a powerful paradigm that finds applications in engineering and learning design. This work studies decentralized composite optimization problems with non-smooth regularization terms. Most existing gradient-based…
Compressed sensing has shown that it is possible to reconstruct sparse high dimensional signals from few linear measurements. In many cases, the solution can be obtained by solving an L1-minimization problem, and this method is accurate…