FFT-Based High Order Central Difference Schemes for Poisson’s Equation with Staggered Boundaries

Feng, Hongsong; Long, Guangqing; Zhao, Shan

doi:10.1007/s10915-020-01379-7

Cited by 5 publications

(1 citation statement)

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“…Solving this equation using FFT or DCT algorithms facilitates determining the LS solution. Poisson's equation [12] solved by fast fourier transform (FFT) [13] utilizes mirror reflection property or complex conjugate symmetry property. This mirroring property implies that 2D FFT comprises the computational complexity of order 2N 2 log 2 N , increasing more computations and memory storage.…”

Section: Introductionmentioning

confidence: 99%

MRI Phase Image Unwrapping using DCT Based Modified Weighted Least Square Algorithm

Verma,

GOEL,

Tanveer

et al. 2023

Preprint

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Background: Phase images of magnetic resonance imaging (MRI) have applications in many fields, including the medical domain. It is often employed to identify biomarkers of neurodegenerative diseases such as Alzheimer's, Parkinson's, and others. However, directly extracted phase images from MRI exhibit the wrapped phase values within the ±π radian range. Methods: To circumvent these phase jumps or discontinuity, phase unwrapping is required. Path-following and minimum norms algorithms are unwrapping methods to retrieve the original unwrapped phase image. The path-following algorithm extracts the original phase value by considering the adjacent pixels along the integral path. In contrast, the minimum norms algorithm aims to minimize the difference between the partial derivatives of the wrapped and the unwrapped phase data. This paper presents the DCT-based modified minimum norm-based weighted least square (LS) phase unwrapping to improve the visibility and noise immunity of the phase images. The proposed algorithm eradicates residual noise by imposing spectral truncation of the low-frequency coefficient. Results and Conclusions: For the experimental validation of the proposed algorithm, the wrapped and unwrapped image phase profiles are demonstrated to show the effectiveness of the proposed phase unwrapping algorithm. In addition, the performance metrics, peak signal-to-noise ratio (PSNR), structural similarity index metric (SSIM), and root mean squared error (RMSE) are calculated to show the comparison of the proposed phase unwrapping algorithm with the state-of-the-art techniques.

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Section: Introductionmentioning

confidence: 99%