Rapid laser solver for the phase retrieval problem

Tailored physical systems were recently exploited to rapidly solve hard computational challenges, such as spin simulators, combinatorial optimization, and focusing through scattering media. Here, we address the phase retrieval problem where an object is reconstructed from its scattered intensity distribution. This is a key problem in many applications, ranging from x-ray imaging to astrophysics, and currently, it lacks efficient direct reconstruction methods: The widely used indirect iterative algorithms are inherently slow. We present an optical approach based on a digital degenerate cavity laser, whose most probable lasing mode rapidly and efficiently reconstructs the object. Our experimental results suggest that the gain competition between the many lasing modes acts as a highly parallel computer that could rapidly solve the phase retrieval problem. Our approach applies to most two-dimensional objects with known compact support, including complex-valued objects, and can be generalized to imaging through scattering media and other hard computational tasks.

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Iterative algorithms to solve the phase retrieval problem by noncoherent source image

10.1117/12.458433 ◽

2002 ◽

Author(s):

Gennadii Degtyarev ◽

Anatolii V. Makhan'ko ◽

Sergei Chernyavskii ◽

Alexandr Chernyavskii

Keyword(s):

Phase Retrieval ◽

Iterative Algorithms ◽

Source Image ◽

Retrieval Problem

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On the phase retrieval problem in optics

Uspekhi Fizicheskih Nauk ◽

10.3367/ufnr.0154.198804e.0677 ◽

1988 ◽

Vol 154 (4) ◽

pp. 677 ◽

Cited By ~ 27

Author(s):

T.I. Kuznetsova

Keyword(s):

Phase Retrieval ◽

Retrieval Problem

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Complex wavefront sensing based on coherent diffraction imaging using vortex modulation

Scientific Reports ◽

10.1038/s41598-021-88523-x ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Rujia Li ◽

Liangcai Cao

Keyword(s):

Phase Retrieval ◽

Dynamic Range ◽

A Priori ◽

Measured Intensity ◽

Physical Constraints ◽

Coherent Diffraction Imaging ◽

Effective Dynamic ◽

Ill Posed ◽

Retrieval Problem ◽

Diffraction Imaging

AbstractPhase retrieval seeks to reconstruct the phase from the measured intensity, which is an ill-posed problem. A phase retrieval problem can be solved with physical constraints by modulating the investigated complex wavefront. Orbital angular momentum has been recently employed as a type of reliable modulation. The topological charge l is robust during propagation when there is atmospheric turbulence. In this work, topological modulation is used to solve the phase retrieval problem. Topological modulation offers an effective dynamic range of intensity constraints for reconstruction. The maximum intensity value of the spectrum is reduced by a factor of 173 under topological modulation when l is 50. The phase is iteratively reconstructed without a priori knowledge. The stagnation problem during the iteration can be avoided using multiple topological modulations.

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

Journal of Applied Analysis ◽

10.1515/jaa-2021-2052 ◽

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.

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Evaluation of Algebraic Iterative Image Reconstruction Methods for Tetrahedron Beam Computed Tomography Systems

International Journal of Biomedical Imaging ◽

10.1155/2013/609704 ◽

2013 ◽

Vol 2013 ◽

pp. 1-14

Author(s):

Joshua Kim ◽

Huaiqun Guan ◽

David Gersten ◽

Tiezhi Zhang

Keyword(s):

Computed Tomography ◽

Iterative Reconstruction ◽

Cone Angle ◽

Iterative Algorithms ◽

Projection Data ◽

Reconstruction Algorithms ◽

Reconstruction Methods ◽

Large Cone Angle ◽

Using Data ◽

Dual Detector

Tetrahedron beam computed tomography (TBCT) performs volumetric imaging using a stack of fan beams generated by a multiple pixel X-ray source. While the TBCT system was designed to overcome the scatter and detector issues faced by cone beam computed tomography (CBCT), it still suffers the same large cone angle artifacts as CBCT due to the use of approximate reconstruction algorithms. It has been shown that iterative reconstruction algorithms are better able to model irregular system geometries and that algebraic iterative algorithms in particular have been able to reduce cone artifacts appearing at large cone angles. In this paper, the SART algorithm is modified for the use with the different TBCT geometries and is tested using both simulated projection data and data acquired using the TBCT benchtop system. The modified SART reconstruction algorithms were able to mitigate the effects of using data generated at large cone angles and were also able to reconstruct CT images without the introduction of artifacts due to either the longitudinal or transverse truncation in the data sets. Algebraic iterative reconstruction can be especially useful for dual-source dual-detector TBCT, wherein the cone angle is the largest in the center of the field of view.

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Sparse Signal Recovery from Modulo Observations

10.21203/rs.3.rs-42731/v1 ◽

2020 ◽

Author(s):

Viraj Shah ◽

Chinmay Hegde

Keyword(s):

Phase Retrieval ◽

Dynamic Range ◽

Signal Reconstruction ◽

Real Data ◽

Superior Performance ◽

Signal Recovery ◽

Reconstruction Methods ◽

Novel Approach ◽

Sparsity Constraints ◽

Improved Performance

Abstract We consider the problem of reconstructing a signal from under-determined modulo observations (or measurements). This observation model is inspired by a (relatively) less well-known imaging mechanism called modulo imaging, which can be used to extend the dynamic range of imaging systems; variations of this model have also been studied under the category of phase unwrapping. Signal reconstruction in the under-determined regime with modulo observations is a challenging ill-posed problem, and existing reconstruction methods cannot be used directly. In this paper, we propose a novel approach to solving the inverse problem limited to two modulo periods, inspired by recent advances in algorithms for phase retrieval under sparsity constraints. We show that given a sufficient number of measurements, our algorithm perfectly recovers the underlying signal and provides improved performance over other existing algorithms. We also provide experiments validating our approach on both synthetic and real data to depict its superior performance.

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