Related papers: Phaseless Reconstruction from Space-Time Samples
We present an alternative numerical reconstruction algorithm for direct tomographic reconstruction of a sample refractive indices from the measured intensities of its far-field coherent diffraction patterns. We formulate the well-known…
Similar to the obstacle or medium scattering problems, an important property of the phaseless far field patterns for source scattering problems is the translation invariance. Thus it is impossible to reconstruct the location of the…
We construct oscillatory solutions of fully semilinear wave equations in Minkowski space satisfying a null condition of the form $$\square u:=(-\partial_{x_0}^2 +\sum_{j=1}^n \partial_{x_j}^2 )u=…
This paper proposes a novel method for learning highly nonlinear, multivariate functions from examples. Our method takes advantage of the property that continuous functions can be approximated by polynomials, which in turn are representable…
The paper deals with the necessary and sufficient conditions for obtaining reconstruction formulae and sampling theorems for every function belonging to the principal shift invariant subspace of $L^2(\mathbb{H}^n)$, both in the time domain…
We consider state reconstruction from the measurement statistics of phase space observables generated by photon number states. The results are obtained by inverting certain infinite matrices. In particular, we obtain reconstruction…
The inverse problem we consider is to reconstruct the location and shape of buried obstacles in the lower half-space of an unbounded two-layered medium in two dimensions from phaseless far-field data. A main difficulty of this problem is…
Motivation: High acceleration factors place a limit on MRI image reconstruction. This limit is extended to segmentation models when treating these as subsequent independent processes. Goal: Our goal is to produce segmentations directly from…
Digital holography is one of the most widely used label-free microscopy techniques in biomedical imaging. Recovery of the missing phase information of a hologram is an important step in holographic image reconstruction. Here we demonstrate…
High resolution reconstruction of complicated objects from incomplete and noisy data can be achieved by solving modulation equations iteratively under physical constraints. This direct demodulation method is a powerful technique for dealing…
We consider signal reconstruction from the norms of subspace components generalizing standard phase retrieval problems. In the deterministic setting, a closed reconstruction formula is derived when the subspaces satisfy certain cubature…
We introduce a method to reconstruct an element of a Hilbert space in terms of an arbitrary finite collection of linearly independent reconstruction vectors, given a finite number of its samples with respect to any Riesz basis. As we…
We propose a new problem of missing data reconstruction in the time-frequency plane. This problem called phase inpainting, consists in reconstructing a signal from time-frequency observations where all amplitudes and some phases are known…
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…
We study the classical problem of recovering a multidimensional source signal from observations of nonlinear mixtures of this signal. We show that this recovery is possible (up to a permutation and monotone scaling of the source's original…
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…
In many signal processing problems arising in practical applications, we wish to reconstruct an unknown signal from its phaseless measurements with respect to a frame. This inverse problem is known as the phase retrieval problem. For each…
We propose an adaptive form of frameless rendering with the potential to dramatically increase rendering speed over conventional interactive rendering approaches. Without the rigid sampling patterns of framed renderers, sampling and…
In this work, we investigate the sampling and reconstruction of spectrally $s$-sparse bandlimited graph signals governed by heat diffusion processes. We propose a random space-time sampling regime, referred to as {randomized} dynamical…
We study the problem of recovering an unknown compactly-supported multivariate function from samples of its Fourier transform that are acquired nonuniformly, i.e. not necessarily on a uniform Cartesian grid. Reconstruction problems of this…