The Gaussian phase distribution approximation enables analysis of restricted diffusion encoded by general gradient waveforms but fails to account for the diffraction-like features that may occur for simple pore geomet...The Gaussian phase distribution approximation enables analysis of restricted diffusion encoded by general gradient waveforms but fails to account for the diffraction-like features that may occur for simple pore geometries.We investigate the range of validity of the approximation by random walk simulations of restricted diffusion in a cylinder using isotropic diffusion encoding sequences as well as conventional single gradient pulse pairs and oscillating gradient waveforms.The results show that clear deviations from the approximation may be observed at relative signal attenuations below 0.1 for onedimensional sequences with few oscillation periods.Increasing the encoding dimensionality and/or number of oscillations while extending the total duration of the waveform diminishes the non-Gaussian effects while preserving the low apparent diffusivities characteristic of restriction.展开更多
This paper proposed a new normalized transform domain conjugate gradient algorithm (NT-CGA), which applies the data independent normalized orthogonal transform technique to approximately whiten the input signal and ut...This paper proposed a new normalized transform domain conjugate gradient algorithm (NT-CGA), which applies the data independent normalized orthogonal transform technique to approximately whiten the input signal and utilises the modified conjugate gradient method to perform sample-by-sample updating of the filter weights more efficiently. Simulation results illustrated that the proposed algorithm has the ability to provide a fast convergence speed and lower steady-error compared to that of traditional least mean square algorithm (LMSA), normalized transform domain least mean square algorithm (NT- LMSA), Quasi-Newton least mean square algorithm (Q-LMSA) and time domain conjugate gradient algorithm (TD-CGA) when the input signal is heavily coloured.展开更多
基金financially supported by the Swedish Research Council(2022-04422_VR)。
文摘The Gaussian phase distribution approximation enables analysis of restricted diffusion encoded by general gradient waveforms but fails to account for the diffraction-like features that may occur for simple pore geometries.We investigate the range of validity of the approximation by random walk simulations of restricted diffusion in a cylinder using isotropic diffusion encoding sequences as well as conventional single gradient pulse pairs and oscillating gradient waveforms.The results show that clear deviations from the approximation may be observed at relative signal attenuations below 0.1 for onedimensional sequences with few oscillation periods.Increasing the encoding dimensionality and/or number of oscillations while extending the total duration of the waveform diminishes the non-Gaussian effects while preserving the low apparent diffusivities characteristic of restriction.
文摘This paper proposed a new normalized transform domain conjugate gradient algorithm (NT-CGA), which applies the data independent normalized orthogonal transform technique to approximately whiten the input signal and utilises the modified conjugate gradient method to perform sample-by-sample updating of the filter weights more efficiently. Simulation results illustrated that the proposed algorithm has the ability to provide a fast convergence speed and lower steady-error compared to that of traditional least mean square algorithm (LMSA), normalized transform domain least mean square algorithm (NT- LMSA), Quasi-Newton least mean square algorithm (Q-LMSA) and time domain conjugate gradient algorithm (TD-CGA) when the input signal is heavily coloured.
