The established methods for today's clinical applications include the use of the diffusion Magnetic Resonance Imaging (dMRI). The proposed work concerns wavelet-based denoising of the Diffusion Spectrum Imaging (DSI) data. Both simulated data and real brain data are considered. Diffusion data are first reconstructed by inverse Fourier transform and then projected to the multiscale domain by 3D wavelet transform. The 3D extensions of both critically sampled (Discrete Wavelet Transformation, DWT) and overcomplete representations (Stationary Wavelet Transformation, SWT) have been considered and applied to the 3D reconstructed diffusion propagator. Then, denoising has been performed by (soft/hard) thresholding. The two-fiber crossing case has been considered for both the synthetic DSI data and real data. Simulation data for fiber crossings with different fiber-crossing angles (45, 60, 90 degree), Rician-noise SNR (10, 15, 20, 30, 50, 100 db) using 514-point grid sampling scheme and the maximum b-value of 6000 s/mm-square were generated. Simulations were repeated 100 times. The Kullback-LeiblerDivergence (KLD) has been used to evaluate the performance of the denoising algorithm after signal recovery. Real data were acquired on a healthy volunteer using a 3T scanner (TIM Trio, Siemens, Erlangen, Germany). The maximum b-value was 8000 s/mm-square with 514 diffusion directions. In this case, the KLD was used to quantify the difference between the two reconstruction strategies since the ground truth was not available. Visual inspection confirmed that SWT providesbetter ODF (Orientation Distribution Function) recovery with respect to DWT. Overall, results show that the SWT algorithm provides a more reliable reconstruction of the ODF with respect to the DWT and improves DSI data denoising in sparse domains. Ongoing work includes the assessment of the improvement in terms of angular resolution.
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