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Results

The numerical results for the synthetic data, shown in Fig. 2, indicate that the proposed '0 framelet denoising method gives the best performance for all noise levels, showing improvements over ' framelet denoising and the non-local means (NLM) algorithm [17]. The DW images, shown in Fig. 3, indicate that both ' and '0 give sharper edges compared with NLM. Noise, however, is not totally removed for the case of ' denoising. Only '0 denoising is able to effectively remove noise and preserve edges. Note that, for both synthetic and real data, noncentral chi bias was removed using the method described in [16]. The best tuning parameters for both ' and '0 were selected based on grid search.

Performance comparison between NLM and our method using synthetic data

Fig. 2 Performance comparison between NLM and our method using synthetic data

Comparison of denoised DW images given by different methods (u = 5)

Fig. 3 Comparison of denoised DW images given by different methods (u = 5)

For the real data, we used the average image as the ground truth for PSNR computation. The results, shown in Fig. 4, are consistent with Fig. 2, indicating that '0 gives the best performance. The visual results in Fig. 5 indicate that the results given by '0 is closest to the ground truth. In contrast, NLM over-smooths the image and edge information is hence lost.

Performance comparison between NLM and our method using real data

Fig. 4 Performance comparison between NLM and our method using real data

Comparison of denoised DW images using the real data

Fig. 5 Comparison of denoised DW images using the real data

 
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