Related papers: Reconstruction of Bandlimited Functions from Unsig…
The reconstruction of a function from its spectrogram (i.e., the absolute value of its short-time Fourier transform (STFT)) arises as a key problem in several important applications, including coherent diffraction imaging and audio…
We present an online algorithm for reconstructing a signal from a set of non-uniform samples. By representing the signal using compactly supported basis functions, we show how estimating the expansion coefficients using least-squares can be…
Following the Unlimited Sampling strategy to alleviate the omnipresent dynamic range barrier, we study the problem of recovering a bandlimited signal from point-wise modulo samples, aiming to connect theoretical guarantees with hardware…
Sparse signals can be recovered from a reduced set of samples by using compressive sensing algorithms. In common methods the signal is recovered in the sparse domain. A method for the reconstruction of sparse signal which reconstructs the…
We investigate the reconstruction of multivariate functions from samples using sparse recovery techniques. For Square Root Lasso, Orthogonal Matching Pursuit, and Compressive Sampling Matching Pursuit, we demonstrate both theoretically and…
We study the problem of recovering a signal from magnitudes of its wavelet frame coefficients when the analyzing wavelet is real-valued. We show that every real-valued signal can be uniquely recovered, up to global sign, from its…
In many applications, the observations can be represented as a signal defined over the vertices of a graph. The analysis of such signals requires the extension of standard signal processing tools. In this work, first, we provide a class of…
A generalized sampling theorem for frequency localized signals is presented. The generalization in the proposed model of sampling is twofold: (1) It applies to various prefilters effecting a "soft" bandlimitation, (2) an approximate…
Sampling and reconstruction of functions is a central tool in science. A key result is given by the sampling theorem for bandlimited functions attributed to Whittaker, Shannon, Nyquist, and Kotelnikov. We develop an analogous sampling…
This paper presents an innovative set of tools to support a methodology for the multichannel interpolation (MCI) of a discrete signal. It is shown that a bandlimited signal $f$ can be exactly reconstructed from finite samples of $g_k$…
This paper studies linear reconstruction of partially observed functional data which are recorded on a discrete grid. We propose a novel estimation approach based on approximate factor models with increasing rank taking into account…
We show that bandlimited signals can be uniquely recovered (up to a constant global phase factor) from Gabor transform magnitudes sampled at twice the Nyquist rate in two frequency bins.
From a sufficiently large point sample lying on a compact Riemannian submanifold of Euclidean space, one can construct a simplicial complex which is homotopy-equivalent to that manifold with high confidence. We describe a corresponding…
Sampling and interpolation have been extensively studied, in order to reconstruct or estimate the entire graph signal from the signal values on a subset of vertexes, of which most achievements are about continuous signals. While in a lot of…
In this paper, we address the problem of sampling from a set and reconstructing a set stored as a Bloom filter. To the best of our knowledge our work is the first to address this question. We introduce a novel hierarchical data structure…
We analyze signal recovery when samples are taken concomitantly from a signal and its Fourier transform. This two-sided sampling framework extends classical one-sided reconstruction and is particularly useful when measurements in either…
Periodic nonuniform sampling has been considered in literature as an effective approach to reduce the sampling rate far below the Nyquist rate for sparse spectrum multiband signals. In the presence of non-ideality the sampling parameters…
Signals sparse in a transformation domain can be recovered from a reduced set of randomly positioned samples by using compressive sensing algorithms. Simple re- construction algorithms are presented in the first part of the paper. The…
In this paper we study the compressive sensing effects on 2D signals exhibiting sparsity in 2D DFT domain. A simple algorithm for reconstruction of randomly under-sampled data is proposed. It is based on the analytically determined…
We consider recovering a function $f : D \rightarrow \mathbb{C}$ in an $n$-dimensional linear subspace $\mathcal{P}$ from i.i.d. pointwise samples via (weighted) least-squares estimators. Different from most works, we assume the cost of…