scholarly journals Conjugate Phase Retrieval in Paley–Wiener Space

2021 ◽  
Vol 27 (6) ◽  
Author(s):  
Chun-Kit Lai ◽  
Friedrich Littmann ◽  
Eric S. Weber
Keyword(s):  
Phase Retrieval ◽  
Wiener Space

Quantitative analysis by reconstruction of HREM focal series

1994 ◽  
Vol 52 ◽  
pp. 740-741
Author(s):  
W. Coene ◽  
A. Thust ◽  
M. Op de Beeck ◽  
D. Van Dyck
Keyword(s):  
Phase Retrieval ◽  
Image Plane ◽  
Initial Guess ◽  
Recursive Least Squares ◽  
Objective Lens ◽  
Electron Wave ◽  
Electron Sources ◽  
Original Algorithm ◽  
Coherent Field ◽  
Direct Interpretation

Compared to conventional electron sources, the use of a highly coherent field-emission gun (FEG) in TEM improves the information resolution considerably. A direct interpretation of this extra information, however, is hampered since amplitude and phase of the electron wave are scrambled in a complicated way upon transfer from the specimen exit plane through the objective lens towards the image plane. In order to make the additional high-resolution information interpretable, a phase retrieval procedure is applied, which yields the aberration-corrected electron wave from a focal series of HRTEM images (Coene et al, 1992).Kirkland (1984) tackled non-linear image reconstruction using a recursive least-squares formalism in which the electron wave is modified stepwise towards the solution which optimally matches the contrast features in the experimental through-focus series. The original algorithm suffers from two major drawbacks : first, the result depends strongly on the quality of the initial guess of the first step, second, the processing time is impractically high.

Limitations to the Spacing Effect

2005 ◽  
Vol 52 (4) ◽  
pp. 257-263 ◽  
Author(s):  
Peter P. J. L. Verkoeijen ◽  
Remy M. J. P. Rikers ◽  
Henk G. Schmidt
Keyword(s):  
Free Recall ◽  
Phase Retrieval ◽  
Incidental Learning ◽  
Factor Model ◽  
Recall Performance ◽  
Spacing Effect ◽  
Word List ◽  
Intentional Learning ◽  
Study Phase ◽  
Learning Condition

Abstract. The spacing effect refers to the finding that memory for repeated items improves when the interrepetition interval increases. To explain the spacing effect in free-recall tasks, a two-factor model has been put forward that combines mechanisms of contextual variability and study-phase retrieval (e.g., Raaijmakers, 2003 ; Verkoeijen, Rikers, & Schmidt, 2004 ). An important, yet untested, implication of this model is that free recall of repetitions should follow an inverted u-shaped relationship with interrepetition spacing. To demonstrate the suggested relationship an experiment was conducted. Participants studied a word list, consisting of items repeated at different interrepetition intervals, either under incidental or under intentional learning instructions. Subsequently, participants received a free-recall test. The results revealed an inverted u-shaped relationship between free recall and interrepetition spacing in both the incidental-learning condition and the intentional-learning condition. Moreover, for intentionally learned repetitions, the maximum free-recall performance was located at a longer interrepetition interval than for incidentally learned repetitions. These findings are interpreted in terms of the two-factor model of spacing effects in free-recall tasks.

Study-Phase Retrieval: Suppressing False Recognition in a Repetition Paradigm

2007 ◽  
Author(s):  
Peter M. Wessels ◽  
Jonathan Schnader ◽  
Allison Smith ◽  
Christopher Thomas ◽  
Haley Titus
Keyword(s):  
False Recognition ◽  
Phase Retrieval ◽  
Study Phase

X-ray microscopy by phase-retrieval methods at the advanced light source

2003 ◽  
Vol 104 ◽  
pp. 557-561 ◽  
Author(s):  
M. R. Howells ◽  
H. Chapman ◽  
S. Hau-Riege ◽  
H. He ◽  
S. Marchesini ◽  
...  
Keyword(s):  
Light Source ◽  
Phase Retrieval ◽  
X Ray ◽  
Advanced Light Source

On the phase retrieval problem in optics

1988 ◽  
Vol 154 (4) ◽  
pp. 677 ◽  
Author(s):  
T.I. Kuznetsova
Keyword(s):  
Phase Retrieval ◽  
Retrieval Problem

Stable Ptychographic Phase Retrieval via Lost Subspace Completion

2021 ◽  
Author(s):  
Oleh Melnyk ◽  
Anton Forstner ◽  
Felix Krahmer ◽  
Nada Sissouno
Keyword(s):  
Phase Retrieval

scholarly journals Almost everywhere generalized phase retrieval

2021 ◽  
Vol 50 ◽  
pp. 16-33
Author(s):  
Meng Huang ◽  
Yi Rong ◽  
Yang Wang ◽  
Zhiqiang Xu
Keyword(s):  
Phase Retrieval ◽  
Almost Everywhere

scholarly journals The Hilbert Space of Double Fourier Coefficients for an Abstract Wiener Space

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 389
Author(s):  
Jeong-Gyoo Kim
Keyword(s):  
Hilbert Space ◽  
Fourier Series ◽  
Fourier Coefficients ◽  
Double Sequence ◽  
Intermediate Stage ◽  
Wiener Space ◽  
Abstract Wiener Space ◽  
Abstract Space ◽  
Double Sequences ◽  
Two Parameter

Fourier series is a well-established subject and widely applied in various fields. However, there is much less work on double Fourier coefficients in relation to spaces of general double sequences. We understand the space of double Fourier coefficients as an abstract space of sequences and examine relationships to spaces of general double sequences: p-power summable sequences for p = 1, 2, and the Hilbert space of double sequences. Using uniform convergence in the sense of a Cesàro mean, we verify the inclusion relationships between the four spaces of double sequences; they are nested as proper subsets. The completions of two spaces of them are found to be identical and equal to the largest one. We prove that the two-parameter Wiener space is isomorphic to the space of Cesàro means associated with double Fourier coefficients. Furthermore, we establish that the Hilbert space of double sequence is an abstract Wiener space. We think that the relationships of sequence spaces verified at an intermediate stage in this paper will provide a basis for the structures of those spaces and expect to be developed further as in the spaces of single-indexed sequences.

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.

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