Fig 1.
Difference in the formation of wavelet coefficient matrix W in case of the DWT and the DT-CWT operation; (left) arrangement of the empirical wavelet coefficients in a 2D matrix W in case of the DWT operation; (right) arrangement of the complex wavelet coefficients in a 3D matrix W in case of the DT-CWT operation, where first two layers contain the real parts and the last two layers contain the imaginary parts of the complex wavelet coefficients.
Fig 2.
Block diagram of the GoFShrink based on DWT.
Fig 3.
Test for Gaussianity via GoF tests where the case (a) shows noise detection as τ is expected to small; and the case (b) shows signal detection as τ is expected to large.
Fig 4.
Threshold versus Pfa graph generated empirically for the first five scales of wavelet decomposed Gaussian noise along with its curve fitted version.
Fig 5.
Empirical selection of Pfa: Mean squared error (MSE) versus the Pfa relation obtained empirically for several test images.
Notice that the Pfa values closer to zero yield better results.
Fig 6.
Block diagram of the GoFShrink based on DT-CWT.
Fig 7.
Selected input images along with their noisy versions at noise level σ = 30 namely, (a) Multi-focus image; (b) View image.
Table 1.
Comparison of the proposed methods with the state-of-the-art image denoising methods in terms of output PSNR for a range of input noise levels σ = 10 to σ = 50.
Table 2.
Comparison of the proposed methods with the state-of-the-art image denoising methods in terms of structural similarity (SSIM) and feature similarity (FSIM) for a range of input noise levels σ = 10 to σ = 50.
Fig 8.
Visual results for several state-of-the-art image denoising methods on the Side MRI image of a brain corrupted with the noise level σ = 20.
This figure is composed of (a) noisy image; (b) denoised image from Bi-Shrink; (c) PaPCA; (d) Surelet; (e) NieghSure; (f) cSM-EB; (g) GoFShrink-TI; and (h) GoFShrink-DT.
Fig 9.
Results of several state of the art image denoising methods on Multi-focus image corrupted with noise with standard deviation σ = 30; (a) original image (b) noisy image (c) denoised image by iTVD and a zoomed in region (d) denoised image by Surelet and a zoomed in region (e) denoised image by NeighSure and a zoomed in region (f) denoised image by GoFShrink-TI and a zoomed in region (g) denoised image by GoFShrink-DT and a zoomed in region.
Fig 10.
Visual performance comparison of various denoising methods on the View image at higher noise level σ = 40.
This figure is composed of (a) original image; (b) noisy image and denoised images from (d) aTVD; (e) cSM-EB; (f) GoFShrink-TI; and (g) GoFShrink-DT.