Related papers: Multi-frequency phase retrieval from noisy data

We consider the classical 1D phase retrieval problem. In order to overcome the difficulties associated with phase retrieval from measurements of the Fourier magnitude, we treat recovery from the magnitude of the short-time Fourier transform…

The availability of high-speed 3D video sensors has greatly facilitated 3D shape acquisition of dynamic and deformable objects, but high frame rate 3D reconstruction is always degraded by spatial noise and temporal fluctuations. This paper…

Deep neural networks have emerged as effective tools for computational imaging including quantitative phase microscopy of transparent samples. To reconstruct phase from intensity, current approaches rely on supervised learning with training…

We consider the robust phase retrieval problem of recovering the unknown signal from the magnitude-only measurements, where the measurements can be contaminated by both sparse arbitrary corruption and bounded random noise. We propose a new…

We describe and experimentally validate an algorithm to reconstruct an unknown extended object from through-focus measured image intensities blurred by unknown aberrations. It is shown that the method can recover diffraction-limited image…

Coherent X-ray diffraction imaging (CXDI) experiments are intrinsically limited by shot noise, a lack of prior knowledge about the sample's support, and missing measurements due to the experimental geometry. We propose a flexible, iterative…

Coherent diffraction imaging (CDI) for visualizing objects at atomic resolution has been realized as a promising tool for imaging single molecules. Drawbacks of CDI are associated with the difficulty of the numerical phase retrieval from…

The problem of phase retrieval is revisited and studied from a fresh perspective. In particular, we establish a connection between the phase retrieval problem and the sensor network localization problem, which allows us to utilize the vast…

In this paper, we aim to reconstruct an n-dimensional real vector from m phaseless measurements corrupted by an additive noise. We extend the noiseless framework developed in [15], based on mirror descent (or Bregman gradient descent), to…

Hypercomplex signal processing (HSP) offers powerful tools for analyzing and processing multidimensional signals by explicitly exploiting inter-dimensional correlations through Clifford algebra. In recent years, hypercomplex formulations of…

Block sparsity is an important parameter in many algorithms to successfully recover block sparse signals under the framework of compressive sensing. However, it is often unknown and needs to be estimated. Recently there emerges a few…

Imaging 3D nano-structures at very high resolution is crucial in a variety of scientific fields. However, due to fundamental limitations of light propagation we can only measure the object indirectly via 2D intensity measurements of the 3D…

The problem of reconstructing a sparse signal vector from magnitude-only measurements (a.k.a., compressive phase retrieval), emerges naturally in diverse applications, but it is NP-hard in general. Building on recent advances in nonconvex…

In this paper, we propose the SPR (sparse phase retrieval) method, which is a new phase retrieval method for coherent x-ray diffraction imaging (CXDI). Conventional phase retrieval methods effectively solve the problem for high…

We propose a multi-tone decomposition algorithm that can find the frequencies, amplitudes and phases of the fundamental sinusoids in a noisy observation sequence. Under independent identically distributed Gaussian noise, our method utilizes…

We propose and demonstrate a new phase retrieval method for imaging through random media. Although methods to recover the Fourier amplitude through random distortions are well established, recovery of the Fourier phase has been a more…

The problem of recovering signals of high complexity from low quality sensing devices is analyzed via a combination of tools from signal processing and harmonic analysis. By using the rich structure offered by the recent development in…

Phase retrieval, the problem of recovering lost phase information from measured intensity alone, is an inverse problem that is widely faced in various imaging modalities ranging from astronomy to nanoscale imaging. The current process of…

An estimation method is presented for polynomial phase signals, i.e., those adopting the form of a complex exponential whose phase is polynomial in its indices. Transcending the scope of existing techniques, the proposed estimator can…

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…