scholarly journals On global convergence of gradient descent algorithms for generalized phase retrieval problem

2018 ◽  
Vol 329 ◽  
pp. 202-222 ◽  
Author(s):  
Ji Li ◽  
Tie Zhou ◽  
Chao Wang
Keyword(s):  
Global Convergence ◽  
Gradient Descent ◽  
Phase Retrieval ◽  
Descent Algorithms ◽  
Retrieval Problem

scholarly journals Complex wavefront sensing based on coherent diffraction imaging using vortex modulation

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.

scholarly journals A Cortical-Inspired Sub-Riemannian Model for Poggendorff-Type Visual Illusions

2021 ◽  
Vol 7 (3) ◽  
pp. 41
Author(s):  
Emre Baspinar ◽  
Luca Calatroni ◽  
Valentina Franceschi ◽  
Dario Prandi
Keyword(s):  
Heat Kernel ◽  
Mathematical Description ◽  
Gradient Descent ◽  
Numerical Results ◽  
Visual Illusions ◽  
Efficient Computation ◽  
Functional Architecture ◽  
Descent Algorithms ◽  
Interaction Term

We consider Wilson-Cowan-type models for the mathematical description of orientation-dependent Poggendorff-like illusions. Our modelling improves two previously proposed cortical-inspired approaches, embedding the sub-Riemannian heat kernel into the neuronal interaction term, in agreement with the intrinsically anisotropic functional architecture of V1 based on both local and lateral connections. For the numerical realisation of both models, we consider standard gradient descent algorithms combined with Fourier-based approaches for the efficient computation of the sub-Laplacian evolution. Our numerical results show that the use of the sub-Riemannian kernel allows us to reproduce numerically visual misperceptions and inpainting-type biases in a stronger way in comparison with the previous approaches.

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