Related papers: Phaseless Sampling and Reconstruction of Real-Valu…
The conjugate phase retrieval problem concerns the determination of a complex-valued function, up to a unimodular constant and conjugation, from its magnitude observations. It can also be considered as a conjugate phaseless sampling and…
We consider the phase retrieval problem of reconstructing a $n$-dimensional real or complex signal $\mathbf{X}^{\star}$ from $m$ (possibly noisy) observations $Y_\mu = | \sum_{i=1}^n \Phi_{\mu i} X^{\star}_i/\sqrt{n}|$, for a large class of…
We consider the signal reconstruction problem under the case of the signals sampled in the multichannel way and with the presence of noise. Observing that if the samples are inexact, the rigorous enforcement of multichannel interpolation is…
We construct new classes of Parseval frames for a Hilbert space which allow signal reconstruction from the absolute value of the frame coefficients. As a consequence, signal reconstruction can be done without using noisy phase or its…
We study the space spanned by the integer shifts of a bivariate Gaussian function and the problem of reconstructing any function in that space from samples scattered across the plane. We identify a large class of lattices, or more generally…
In this paper, we discuss to the nonuniform sampling problem in principal shift-invariant subspaces of mixed Lebesgue spaces. We proposed a fast reconstruction algorithm which allows to exactly reconstruct the functions in the principal…
We introduce a continuous domain framework for the recovery of points on a surface in high dimensional space, represented as the zero-level set of a bandlimited function. We show that the exponential maps of the points on the surface…
Suppose that a sequence of numbers $x_n$ (a `signal') is transmitted through a noisy channel. The receiver observes a noisy version of the signal with additive random fluctuations, $x_n + \xi_n$, where $\xi_n$ is a sequence of independent…
Common problem in signal processing is reconstruction of the missing signal samples. Missing samples can occur by intentionally omitting signal coefficients to reduce memory requirements, or to speed up the transmission process. Also, noisy…
In many applications, signals are measured according to a linear process, but the phases of these measurements are often unreliable or not available. To reconstruct the signal, one must perform a process known as phase retrieval. This paper…
In this paper we tackle the problem of recovering the phase of complex linear measurements when only magnitude information is available and we control the input. We are motivated by the recent development of dedicated optics-based hardware…
We present a scalable low dimensional manifold model for the reconstruction of noisy and incomplete hyperspectral images. The model is based on the observation that the spatial-spectral blocks of a hyperspectral image typically lie close to…
We study the recovery of square-integrable signals from the absolute values of their wavelet transforms, also called wavelet phase retrieval. We present a new uniqueness result for wavelet phase retrieval. To be precise, we show that any…
Multiscale transforms designed to process analog and discrete-time signals and images cannot be directly applied to analyze high-dimensional data residing on the vertices of a weighted graph, as they do not capture the intrinsic geometric…
Multi-segment reconstruction (MSR) problem consists of recovering a signal from noisy segments with unknown positions of the observation windows. One example arises in DNA sequence assembly, which is typically solved by matching short reads…
Suppose that we observe noisy linear measurements of an unknown signal that can be modeled as the sum of two component signals, each of which arises from a nonlinear sub-manifold of a high dimensional ambient space. We introduce SPIN, a…
The sparse representation of signals defined on Euclidean domains has been successfully applied in signal processing. Bringing the power of sparse representations to non-regular domains is still a challenge, but promising approaches have…
The problem of finding suitable point embedding or geometric configurations given only Euclidean distance information of point pairs arises both as a core task and as a sub-problem in a variety of machine learning applications. In this…
Phase retrieval in dynamical sampling is a novel research direction, where an unknown signal has to be recovered from the phaseless measurements with respect to a dynamical frame, i.e. a sequence of sampling vectors constructed by the…
We study the problem of selecting the best sampling set for bandlimited reconstruction of signals on graphs. A frequency domain representation for graph signals can be defined using the eigenvectors and eigenvalues of variation operators…