Related papers: Local and Global Phaseless Sampling in Real Spline…
A linear and thus convex phase retrieval algorithm for the application in phaseless near-field far-field transformations is presented. The formulation exploits locally known phase relations among sets of measurement samples, which can in…
The problem of multiple sensors simultaneously acquiring measurements of a single object can be found in many applications. In this paper, we present the optimal recovery guarantees for the recovery of compressible signals from multi-sensor…
This paper presents some results on a well-known problem in Algebraic Signal Sampling and in other areas of applied mathematics: reconstruction of piecewise-smooth functions from their integral measurements (like moments, Fourier…
We study the recovery of multivariate functions from reproducing kernel Hilbert spaces in the uniform norm. Our main interest is to obtain preasymptotic estimates for the corresponding sampling numbers. We obtain results in terms of the…
Signal recovery is one of the key techniques of Compressive sensing (CS). It reconstructs the original signal from the linear sub-Nyquist measurements. Classical methods exploit the sparsity in one domain to formulate the L0 norm…
We study the problem of recovering the phase from magnitude measurements; specifically, we wish to reconstruct a complex-valued signal x of C^n about which we have phaseless samples of the form y_r = |< a_r,x >|^2, r = 1,2,...,m (knowledge…
Real-valued Phase retrieval is a non-convex continuous inference problem, where a high-dimensional signal is to be reconstructed from a dataset of signless linear measurements. Focusing on the noiseless case, we aim to disentangle the two…
In applications ranging from communications to genetics, signals can be modeled as lying in a union of subspaces. Under this model, signal coefficients that lie in certain subspaces are active or inactive together. The potential subspaces…
In this paper, we investigate the problem of source recovery in a dynamical system utilizing space-time samples. This is a specific issue within the broader field of dynamical sampling, which involves collecting samples from solutions to a…
We study the problem of sampling and reconstruction of bandlimited graph signals where the objective is to select a node subset of prescribed cardinality that ensures interpolation of the original signal with the lowest reconstruction…
In this paper we study the general reconstruction of a compactly supported function from its Fourier coefficients using compactly supported shearlet systems. We assume that only finitely many Fourier samples of the function are accessible…
We consider the recovery of square-integrable signals from discrete, equidistant samples of their Gabor transform magnitude and show that, in general, signals can not be recovered from such samples. In particular, we show that for any…
We introduce a framework for the recovery of points on a smooth surface in high-dimensional space, with application to dynamic imaging. We assume the surface to be the zero-level set of a bandlimited function. We show that the exponential…
We propose a new algorithm to learn a dictionary for reconstructing and sparsely encoding signals from measurements without phase. Specifically, we consider the task of estimating a two-dimensional image from squared-magnitude measurements…
Practically, for all real measuring devices the result of a measurement is a convolution of an input signal with a hardware function of a unit {\phi}. We call a spline to be {\phi}-interpolating if the convolution of an input signal with a…
Learning non-linear systems from noisy, limited, and/or dependent data is an important task across various scientific fields including statistics, engineering, computer science, mathematics, and many more. In general, this learning task is…
This paper studies several aspects of signal reconstruction of sampled data in spaces of bandlimited functions. In the first part, signal spaces are characterized in which the classical sampling series uniformly converge, and we investigate…
We tensorize the Faber spline system from [14] to prove sequence space isomorphisms for multivariate function spaces with higher mixed regularity. The respective basis coefficients are local linear combinations of discrete function values…
A signal recovery problem is considered, where the same binary testing problem is posed over multiple, independent data streams. The goal is to identify all signals, i.e., streams where the alternative hypothesis is correct, and noises,…
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 $O(s\log n)$…