scholarly journals Phase Retrieval from Sampled Gabor Transform Magnitudes: Counterexamples

2021 ◽  
Vol 28 (1) ◽  
Author(s):  
Rima Alaifari ◽  
Matthias Wellershoff
Keyword(s):  
Phase Retrieval ◽  
Gabor Transform ◽  
Good Concentration ◽  
Rectangular Lattices

AbstractWe consider the recovery of square-integrable signals from discrete, equidistant samples of their Gabor transform magnitude and show that, in general, signals can not be recovered from such samples. In particular, we show that for any lattice, one can construct functions in $$L^2({\mathbb {R}})$$ L 2 ( R ) which do not agree up to global phase but whose Gabor transform magnitudes sampled on the lattice agree. These functions have good concentration in both time and frequency and can be constructed to be real-valued for rectangular lattices.

scholarly journals Stability Estimates for Phase Retrieval from Discrete Gabor Measurements

2021 ◽  
Vol 27 (2) ◽  
Author(s):  
Rima Alaifari ◽  
Matthias Wellershoff
Keyword(s):  
Hilbert Spaces ◽  
Phase Retrieval ◽  
Gabor Transform ◽  
Stability Estimates ◽  
Signal Process ◽  
Infinite Dimensional ◽  
Bandlimited Signals ◽  
Finite Dimensional ◽  
Order Polynomial ◽  
In Trans

AbstractPhase retrieval refers to the problem of recovering some signal (which is often modelled as an element of a Hilbert space) from phaseless measurements. It has been shown that in the deterministic setting phase retrieval from frame coefficients is always unstable in infinite-dimensional Hilbert spaces (Cahill et al. in Trans Am Math Soc Ser B 3(3):63–76, 2016) and possibly severely ill-conditioned in finite-dimensional Hilbert spaces (Cahill et al. in Trans Am Math Soc Ser B 3(3):63–76, 2016). Recently, it has also been shown that phase retrieval from measurements induced by the Gabor transform with Gaussian window function is stable under a more relaxed semi-global phase recovery regime based on atoll functions (Alaifari in Found Comput Math 19(4):869–900, 2019). In finite dimensions, we present first evidence that this semi-global reconstruction regime allows one to do phase retrieval from measurements of bandlimited signals induced by the discrete Gabor transform in such a way that the corresponding stability constant only scales like a low order polynomial in the space dimension. To this end, we utilise reconstruction formulae which have become common tools in recent years (Bojarovska and Flinth in J Fourier Anal Appl 22(3):542–567, 2016; Eldar et al. in IEEE Signal Process Lett 22(5):638–642, 2014; Li et al. in IEEE Signal Process Lett 24(4):372–376, 2017; Nawab et al. in IEEE Trans Acoust Speech Signal Process 31(4):986–998, 1983).

Phase retrieval of microscope objects using the Wavelet-Gabor transform method from holographic filters

2014 ◽  
Author(s):  
Martín Hernández-Romo ◽  
Alfonso Padilla-Vivanco ◽  
Myung K. Kim ◽  
Carina Toxqui-Quitl
Keyword(s):  
Phase Retrieval ◽  
Gabor Transform ◽  
Transform Method

Adaptive Parameters Selection Method for Time-Frequency Distribution Series Based on Normalized Entropy

2013 ◽  
Vol 631-632 ◽  
pp. 1373-1378
Author(s):  
Xiu Li Du ◽  
Ming Ying Liu
Keyword(s):  
Frequency Distribution ◽  
Selection Method ◽  
Gabor Transform ◽  
Adaptive Selection ◽  
Time Frequency ◽  
Window Width ◽  
Parameters Selection ◽  
Cross Terms ◽  
Good Concentration ◽  
Time Frequency Distribution

To resolve the problem of Gabor transform window width and order selection for Time-Frequency Distribution Series (TFDS), a parameters selection method for TFDS based on normalized entropy has been proposed, especially the adaptive selection method of order. The normalized entropy is used to measure the concentration and cross-terms of TFDS firstly, and then the relation between the order and width of Gabor transform window function and the concentration and cross-terms of TFDS is used to realize adaptive selection of window width and order parameter, which overcomes the subjective selection problem of the order. The simulation results show that the proposed method can effectively select optimal TFDS parameters for simulated and experimental ultrasonic tesing signal, and can get TFDS with good concentration and high resolution.

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
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