Descripción de los principales hallazgos alineado a los objetivos

This profile may be defined as Mainstream BM3D since the authors of BM3D [1] recom- mended to use Wavelet transform in their proposed denoising method. Although we improved the performance of DC-Only profile, unless we achieve improvement in the main stream

BM3D, we cannot claim that we improved the performance of BM3D. This is because, the main stream BM3Dhas PSNR gain way better than DC-Only profile. Hence, the major con- cern of this thesis is to improve the performance of Wavelet profile of BM3D.

In this section, we will explore that how the idea of our proposed Wiener filter achieves better denoising performance of BM3D. Unlike DC-Only profile, since there is no DC and AC coefficients, we have only proposed improvement in this case- to use our improved Wiener filter in the second step ofBM3D.

4.6.1

Parameterized Setup for Wavelet Profile

For the wavelet profile, we used exactly same parameterized setup as inBM3D[1]. We present the basic parameterized setup from the original article [1] in table 4.13 for reader’s conve- nience. We use exactly the same parameters to ensure the same environment for the experi- ment. The wavelet profile uses two sub-profiles called Normal Profile andFast Profile. The only difference between them is that we compromise the denoising performance to reduce computational complexity in fast profile. Another difference between these two profiles is the fast profile uses predictive searching in order to decrease its searching time while the normal profile uses only exhaustive searching.

4.6.2

Normal Profile

In normal profile, we executed the same experiments as in DC-Only profiles. Since the wavelet profile itself exploits higher performance as compared to DC-Only profile, even a small in- crease in PSNR/SSIM indicates a reasonable improvement. The experimental results for this profile are given in table 4.14.

The performance comparison curves show that our proposed method is capable of achieving a maximum of 1dBPSNR for higher noise levels, while for the lower noise level the achieved PSNR is less. Fig. 4.33 and Fig. 4.34 respective show the PSNR and SSIM comparison of normal profile of BM3Dwith our proposed method. Fig. 4.35 presents a subjective measure for Lena image withσ =50.

It is clearly visible from Fig. 4.33 and Fig. 4.34 that there is a sharp PSNR drop atσ= 40. This is becauseBM3Dtreats all noise levels belowσ =40 different than the noise levels above

10 20 30 40 50 60 70 80 90 100 0 5 10 15 20 25 30 35 Noise Level

Peak Signal to Noise Ratio

Normal Profile of BM3D Normal Profile of Proposed Method

Figure 4.33: Average PSNR Comparison of Normal Profile of BM3D with Proposed Method

10 20 30 40 50 60 70 80 90 100 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Noise Level

Structural Similarity (SSIM)

Normal Profile of BM3D Normal Profile of Proposed Method

Chapter4. ExperimentalResults andAnalysis 58

Fast Profile Normal Profile

Notations Meaning σ640 σ >40

Parameters for Step 1 (ht)

τht

2D 2D Transform Used 2D-Bior1.5 2D-Bior1.5 2D-DCT

Nht

1 Patch Size 8 8 12

Nht

2 Maximum Number of Similar Patches Retained 16 16 16 Nht

step Step of Reference Patch 6 3 4

Nht

S Size of Search Window 25 39 39

Nht

FS Exhaustive Search Window Size 6 1 1

Nht

PR Predictive Search Window Size 3 - -

βht _{Parameters for Kaiser Window 2.0 2.0 2.0}

λ2D Pre-processing Threshold 0 0 2.0

λ3D Hard Threshold 2.7 2.7 2.8

τht

match Similarity Threshold for Patches 2500 2500 5000

Parameters for Step 2 (wie)

τwie

2D 2D Transform Used 2D-DCT 2D-DCT 2D-DCT

Nwie

1 Patch Size 8 8 11

Nwie

2 Maximum Number of Similar Patches Retained 16 32 32 Nwie

step Step of Reference Patch 5 3 6

Nwie

S Size of Search Window 25 39 39

Nwie

FS Exhaustive Search Window Size 5 1 1

Nwie

PR Predictive Search Window Size 2 - -

τwie

match Similarity Threshold for Patches 400 400 3500

βwie _{Parameters for Kaiser Window 2.0 2.0 2.0}

Common 1D-Haar 1D-Haar 1D-Haar

Table 4.13: Parameterized Setup for Wavelet Profile of BM3D

σ = 40. Since we are following the same algorithm of BM3D, except that we are using our proposed Wiener filter, we are having the same sharp PSNR drop atσ=40.

4.6.3

Fast Profile

The fast profile is similar to normal profile, except that this profile is faster and the searching is predictive and the performance is slightly lower than normal profile. Still, this profile is comparable with normal profile unlike DC-Only profile where we have huge PSNR drop as compared to normal profile. The experimental results obtained for fast profile is presented in table 4.15.

Noise Level BM3D PSNR Proposed PSNR BM3D SSIM Proposed SSIM 10 34.17 34.16 0.903426 0.902944 20 31.04 31.10 0.843516 0.843756 30 29.08 29.28 0.788699 0.795423 40 27.42 27.87 0.730636 0.750625 50 26.79 27.05 0.701603 0.719319 60 25.85 26.28 0.656344 0.689510 70 25.06 25.65 0.615045 0.663826 80 24.37 25.11 0.575113 0.640845 90 23.70 24.59 0.533586 0.617141 100 23.15 24.18 0.500376 0.599786

Table 4.14: Performance Comparison of Normal Profile with Proposed Method

Noise Level BM3D PSNR Proposed PSNR BM3D SSIM Proposed SSIM

10 34.18 34.17 0.903621 0.903149 20 31.04 31.09 0.843739 0.843953 30 29.07 29.27 0.788761 0.795254 40 27.45 27.91 0.731555 0.752113 50 26.81 27.06 0.702944 0.720458 60 25.89 26.30 0.657783 0.690009 70 25.07 25.63 0.614373 0.662845 80 24.38 25.11 0.575239 0.641276 90 23.76 24.64 0.538769 0.620653 100 23.14 24.17 0.499743 0.599324

Table 4.15: Performance Comparison of Fast Profile with Proposed Method

We plot the table 4.15 in Fig. 4.36 and Fig. 4.36. One can examine that these two figures are almost similar to Fig. 4.33 and Fig. 4.34. If we compare these with any of DC-Only profile, we realize why the usage of DC-Only profile is discouraged. However, since we improve the DC-Only profile of BM3D, they are now comparable to any of the wavelet profiles. Fig. 4.38 shows a subjective measure for the image Lena withσ=50.