scholarly journals A simple Fourier transform-based reconstruction formula for photoacoustic computed tomography with a circular or spherical measurement geometry

2013 ◽  
Author(s):  
Kun Wang ◽  
Mark A. Anastasio
Keyword(s):  
Computed Tomography ◽  
Fourier Transform ◽  
Reconstruction Formula ◽  
Measurement Geometry

scholarly journals Helgason–Gabor–Fourier transform and uncertainty principles

2020 ◽  
pp. 2050056
Author(s):  
Mustapha Boujeddaine ◽  
Mohammed El Kassimi ◽  
Saïd Fahlaoui
Keyword(s):  
Fourier Transform ◽  
Uncertainty Principle ◽  
Plancherel Formula ◽  
Riemannian Symmetric Space ◽  
Uncertainty Principles ◽  
Reconstruction Formula ◽  
Time Frequency ◽  
Local Uncertainty Principle ◽  
Local Uncertainty ◽  
Parseval Formula

Windowing a Fourier transform is a useful tool, which gives us the similarity between the signal and time frequency signal, and it allows to get sense when/where certain frequencies occur in the input signal, this method was introduced by Dennis Gabor. In this paper, we generalize the classical Gabor–Fourier transform (GFT) to the Riemannian symmetric space calling it the Helgason–Gabor–Fourier transform (HGFT). We prove several important properties of HGFT like the reconstruction formula, the Plancherel formula and Parseval formula. Finally, we establish some local uncertainty principle such as Benedicks-type uncertainty principle.

scholarly journals Radiomic analysis of lung cancer for the assessment of patient prognosis and intratumor heterogeneity

2021 ◽  
Vol 54 (2) ◽  
pp. 87-93 ◽  
Author(s):  
José Raniery Ferreira Junior ◽  
Marcel Koenigkam-Santos ◽  
Camila Vilas Boas Machado ◽  
Matheus Calil Faleiros ◽  
Natália Santana Chiari Correia ◽  
...  
Keyword(s):  
Computed Tomography ◽  
Lung Cancer ◽  
Overall Survival ◽  
Fourier Transform ◽  
Survival Time ◽  
Risk Group ◽  
Mean Survival Time ◽  
Kaplan Meier ◽  
The Mean ◽  
The Fourier Transform

Abstract Objective: To determine whether the radiomic features of lung lesions on computed tomography correlate with overall survival in lung cancer patients. Materials and Methods: This was a retrospective study involving 101 consecutive patients with malignant neoplasms confirmed by biopsy or surgery. On computed tomography images, the lesions were submitted to semi-automated segmentation and were characterized on the basis of 2,465 radiomic variables. The prognostic assessment was based on Kaplan-Meier analysis and log-rank tests, according to the median value of the radiomic variables. Results: Of the 101 patients evaluated, 28 died (16 dying from lung cancer), and 73 were censored, with a mean overall survival time of 1,819.4 days (95% confidence interval [95% CI]: 1,481.2-2,157.5). One radiomic feature (the mean of the Fourier transform) presented a difference on Kaplan-Meier curves (p < 0.05). A high-risk group of patients was identified on the basis of high values for the mean of the Fourier transform. In that group, the mean survival time was 1,465.4 days (95% CI: 985.2-1,945.6), with a hazard ratio of 2.12 (95% CI: 1.01-4.48). We also identified a low-risk group, in which the mean of the Fourier transform was low (mean survival time of 2,164.8 days; 95% CI: 1,745.4-2,584.1). Conclusion: A radiomic signature based on the Fourier transform correlates with overall survival, representing a prognostic biomarker for risk stratification in patients with lung cancer.

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