Phaseless super-resolution in the continuous domain

Multiple Illumination Phaseless Super-Resolution (MIPS) with Applications To Phaseless DOA Estimation and Diffraction Imaging

Phaseless super-resolution is the problem of recovering an unknown signal from measurements of the magnitudes of the low frequency Fourier transform of the signal. This problem arises in applications where measuring the phase, and making high-frequency measurements, are either too costly or altogether infeasible. The problem is especially challenging because it combines the difficult problems of phase retrieval and classical super-resolution

基于结构调制的无限维空间无相位信号恢复

Phaseless Signal Recovery in Infinite Dimensional Spaces using Structured Modulations

本文研究了无限维空间中连续信号从其频率样本的幅值恢复的问题。它提出了一种采样方案，其中涉及过采样和调制与复指数相结合。充分条件给出，使得几乎每个信号与紧支持可以重建到一个幺模常数仅使用其幅度样本在频域中。最后，它表明，平均采样率的四倍的奈奎斯特速率是足够的重建几乎每一个时间有限的信号。

Phase Retrieval of Real-Valued Signals in a Shift-Invariant Space

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 in a shift-invariant space from its phaseless samples taken either on the whole line or on a set with finite sampling rate. We find the equivalence between nonseparability of signals in a linear space and its phase retrievability with phaseless samples taken on the whole line. For a spline signal of order $N$, we show that it can be well approximated, up to…

Non-Convex Recovery from Phaseless Low-Resolution Blind Deconvolution Measurements using Noisy Masked Patterns

This paper addresses recovery of a kernel $\boldsymbol{h}\in \mathbb{C}^{n}$ and a signal $\boldsymbol{x}\in \mathbb{C}^{n}$ from the low-resolution phaseless measurements of their noisy circular convolution $\boldsymbol{y} = \left \rvert \boldsymbol{F}_{lo}( \boldsymbol{x}\circledast \boldsymbol{h}) \right \rvert^{2} + \boldsymbolη$, where $\boldsymbol{F}_{lo}\in \mathbb{C}^{m\times n}$ stands for a partial discrete Fourier transform ($m<n$), $\boldsymbolη$ models the noise, and $\lvert \cdot \rvert$ is the element-wise absolute value function. This problem is severely ill-posed because both …

从仅PMI反馈在FDD系统中估计下行链路通道矩阵：最大似然与精确超额风险界

Non-Asymptotic Performance Guarantees for MLE under a Gumbel-Softmax Index Model with Phaseless Measurements

研究在FDD大规模MIMO系统中，基于仅PMI反馈的下行链路通道估计，提出受限反馈架构下的最大似然估计器，并建立全局超额风险界及局部速率。

Prony-Based Super-Resolution Phase Retrieval of Sparse, Multivariate Signals

Phase retrieval consists in the recovery of an unknown signal from phaseless measurements of its usually complex-valued Fourier transform. Without further assumptions, this problem is notorious to be severe ill posed such that the recovery of the true signal is nearly impossible. In certain applications like crystallography, speckle imaging in astronomy, or blind channel estimation in communications, the unknown signal has a specific, sparse structure. In this paper, we exploit these sparse structure to recover the unknown signal uniquely up to inevitable ambiguities as global phase shifts, tr…