相关论文: On signal reconstruction without noisy phase

An axiomatic approach to signal reconstruction is formulated, involving a sample consistent set and a guiding set, describing desired reconstructions. New frame-less reconstruction methods are proposed, based on a novel concept of a…

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…

Frame design for phaseless reconstruction is now part of the broader problem of nonlinear reconstruction and is an emerging topic in harmonic analysis. The problem of phaseless reconstruction can be simply stated as follows. Given the…

Frames allow all elements of a Hilbert space to be reconstructed by inner product data in a stable manner. Recently, there is interest in relaxing the definition of frames to understand the implications for stable signal recovery. In this…

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 propose a new method for reconstruction of sparse signals with and without noisy perturbations, termed the subspace pursuit algorithm. The algorithm has two important characteristics: low computational complexity, comparable to that of…

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…

Sampling in shift-invariant spaces is a realistic model for signals with smooth spectrum. In this paper, we consider phaseless sampling and reconstruction of real-valued signals in a shift-invariant space from their magnitude measurements…

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…

We address the problem of signal reconstruction from intensity measurements with respect to a measurement frame. This non-convex inverse problem is known as phase retrieval. The case considered in this paper concerns phaseless measurements…

Phase retrieval arises in various fields of science and engineering and it is well studied in a finite-dimensional setting. In this paper, we consider an infinite-dimensional phase retrieval problem to reconstruct real-valued signals living…

We propose an effective deep learning model for signal reconstruction, which requires no signal prior, no noise model calibration, and no clean samples. This model only assumes that the noise is independent of the measurement and that the…

We describe a new algorithm to solve a particular phase retrieval problem, that has wide applications in audio processing: the reconstruction of a function from its scalogram, that is from the modulus of its wavelet transform. It is a…

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 propose a new approach to the problem of recovering signal from frame coefficients with erasures. Such problems arise naturally from applications where some of the coefficients could be corrupted or erased during the data transmission.…

Contrary to the traditional pursuit of research on nonuniform sampling of bandlimited signals, the objective of the present paper is not to find sampling conditions that permit perfect reconstruction, but to perform the best possible signal…

Phaseless reconstruction from space-time samples is a nonlinear problem of recovering a function $x$ in a Hilbert space $\mathcal{H}$ from the modulus of linear measurements $\{\lvert \langle x, \phi_i\rangle \rvert$, $ \ldots$, $\lvert…

We derive a method to reconstruct Gaussian signals from linear measurements with Gaussian noise. This new algorithm is intended for applications in astrophysics and other sciences. The starting point of our considerations is the principle…

Let $I\subseteq \Bbb N$ be a finite or infinite set and let ${(x_n)_{n\in I}}$ be a frame for a separable Hilbert space $\mathcal{H}$. Consider transmission of a signal $h\in\mathcal{H}$ where a finite subset $(\langle h,x_n\rangle)_{n\in…

Quantum noise is currently limiting efficient quantum information processing and computation. In this work, we consider the tasks of reconstructing and classifying quantum states corrupted by the action of an unknown noisy channel using…