Sparsity and Noise Removal - Sparse Image and Signal Processing - page 144

Figure 6.7. Poisson denoising of smooth ridges (image size, 256×256).
(top left) Intensity image (the peak intensities of the nine vertical ridges
vary progressively from 0 . 1to0 . 5; the inclined ridge has a maximum inten-
sity of 0 . 3; background = 0 . 05). (top right) Poisson noisy image. (bottom
left) Anscombe VST-based denoised image (UWT with 7/9 filter bank and
J = 4). (bottom right) MS-VST + ridgelet ( N max = 10 iterations).

6.7.1 Block Denoising

In this experiment, which can be reproduced by running the script

Scripts/

in the toolbox, term-by-term (hard and soft) thresholding
and block thresholding are applied with three different transforms: DWT, UDWT,
and DCTG2. The results on “Barbara” and “Peppers” are displayed in Fig. 6.9 and
Fig. 6.10, respectively. Block denoising is systematically better than individual
thresholding. Owing to block shrinkage, even the orthogonal DWT becomes com-
petitive with redundant transforms. As discussed at the end of Section 6.2.2.2, for the

blockgenfigvisual.m

DWT, soft thresholding with a threshold √ 3 .

This is not valid with redundant transforms such as the UDWT or the DCTG2. Note
that the additional computational burden of block shrinkage compared to individ-
ual thresholding is marginal: 0.1s, 1s, and 0.7s for the DWT, UDWT, and DCTG2,
respectively, with 512

σ is better than hard thresholding 3 σ

× 512 images and less than 0.03s, 0.2s, and 0.1, respectively,

for 256 256 images. The algorithms were run under MATLAB with an Intel Xeon

Core Duo 3 GHz CPU, 8 GB RAM.

×