Robust phase retrieval of complex-valued object in phase modulation by hybrid Wirtinger flow method

2017 ◽  
Vol 56 (09) ◽  
pp. 1
Author(s):  
Zhun Wei ◽  
Wen Chen ◽  
Tiantian Yin ◽  
Xudong Chen
Keyword(s):  
Phase Modulation ◽  
Phase Retrieval ◽  
Flow Method ◽  
Complex Valued

Translation uniqueness of phase retrieval and magnitude retrieval of band-limited signals

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Lung-Hui Chen
Keyword(s):  
Fourier Transform ◽  
Entire Function ◽  
Convex Hull ◽  
Scattering Theory ◽  
Phase Retrieval ◽  
Indicator Function ◽  
Band Limited ◽  
The Fourier Transform ◽  
Complex Valued ◽  
Spectral Invariant

Abstract In this paper, we discuss how to partially determine the Fourier transform F ⁢ ( z ) = ∫ - 1 1 f ⁢ ( t ) ⁢ e i ⁢ z ⁢ t ⁢ 𝑑 t , z ∈ ℂ , F(z)=\int_{-1}^{1}f(t)e^{izt}\,dt,\quad z\in\mathbb{C}, given the data | F ⁢ ( z ) | {\lvert F(z)\rvert} or arg ⁡ F ⁢ ( z ) {\arg F(z)} for z ∈ ℝ {z\in\mathbb{R}} . Initially, we assume [ - 1 , 1 ] {[-1,1]} to be the convex hull of the support of the signal f. We start with reviewing the computation of the indicator function and indicator diagram of a finite-typed complex-valued entire function, and then connect to the spectral invariant of F ⁢ ( z ) {F(z)} . Then we focus to derive the unimodular part of the entire function up to certain non-uniqueness. We elaborate on the translation of the signal including the non-uniqueness associates of the Fourier transform. We show that the phase retrieval and magnitude retrieval are conjugate problems in the scattering theory of waves.

Amplitude spaces of mono-components from Blaschke products and an intrinsic multiresolution analysis

2020 ◽  
Vol 18 (06) ◽  
pp. 2050051
Author(s):  
Qiuhui Chen ◽  
Luoqing Li ◽  
Weibin Wu
Keyword(s):  
Multiresolution Analysis ◽  
Phase Modulation ◽  
Real Variable ◽  
Finite Energy ◽  
Analytic Signal ◽  
Blaschke Products ◽  
Frequency Components ◽  
The Hilbert Transform ◽  
Complex Valued ◽  
Analytic Signals

A mono-component is a real-variable and complex-valued analytic signal with nonnegative frequency components. The amplitude of an analytic signal is determined by its phase in a canonical amplitude-phase modulation. This paper investigates the amplitude spaces of analytic signals in terms of the Blaschke products with zeros in [Formula: see text]. It is proved that these amplitude spaces are invariant under the Hilbert transform and form a multiresolution analysis in the Hilbert space of signals with finite energy.

scholarly journals Dictionary Learning Phase Retrieval from Noisy Diffraction Patterns

Sensors ◽  
2018 ◽  
Vol 18 (11) ◽  
pp. 4006 ◽  
Author(s):  
Joshin Krishnan ◽  
José Bioucas-Dias ◽  
Vladimir Katkovnik
Keyword(s):  
Dictionary Learning ◽  
High Performance ◽  
Phase Retrieval ◽  
Learning Phase ◽  
Complex Domain ◽  
Sparsity Constraints ◽  
Diffraction Patterns ◽  
The Fourier Transform ◽  
Complex Valued ◽  
Complex Images

This paper proposes a novel algorithm for image phase retrieval, i.e., for recovering complex-valued images from the amplitudes of noisy linear combinations (often the Fourier transform) of the sought complex images. The algorithm is developed using the alternating projection framework and is aimed to obtain high performance for heavily noisy (Poissonian or Gaussian) observations. The estimation of the target images is reformulated as a sparse regression, often termed sparse coding, in the complex domain. This is accomplished by learning a complex domain dictionary from the data it represents via matrix factorization with sparsity constraints on the code (i.e., the regression coefficients). Our algorithm, termed dictionary learning phase retrieval (DLPR), jointly learns the referred to dictionary and reconstructs the unknown target image. The effectiveness of DLPR is illustrated through experiments conducted on complex images, simulated and real, where it shows noticeable advantages over the state-of-the-art competitors.

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