Adaptive Image Denoising by Mixture Adaptation

Enming Luo, Stanley H. Chan, and Truong Q. Nguyen

Video Processing Lab

University of California, San Diego

Abstract

We propose an adaptive learning procedure to learn effective image priors. The new algorithm, called the Expectation-Maximization (EM) adaptation, takes a generic prior learned from a generic external database and adapts it to the image of interest to generate a specific prior. Different from existing methods which combine internal and external statistics in an ad-hoc way, the proposed algorithm learns a single unified prior through an adaptive process. There are two major contributions in this paper. First, we rigorously derive the EM adaptation algorithm from the Bayesian hyper-prior perspective and show that it can be further simplified to improve the computational complexity. Second, in the absence of the latent clean image, we show how EM adaptation can be modified and applied on pre-filtered images. We discuss how to estimate internal parameters and demonstrate how to improve the denoising performance by running EM adaptation iteratively. Experimental results show that the adapted prior is consistently better than the originally un-adapted prior, and is superior than some state-of-the-art algorithms.

 

Results

1. PSNR results for denoising standard testing images

 

2. PSNR results for denoising natural testing images

  2.1 The 6 randomly chosen images are

  2.2 The PSNR results are

 

3. Visual comparison for denoising standard and natural images

  3.1 Visual comparison for standard images (PSNR and SSIM in the parenthesis)

Noisy image
BM3D
EPLL
aGMM-EPLL
σ = 20
33.67 dB (0.8709)
33.03 dB (0.8618)
33.63 dB (0.8671)
σ = 20
31.60 dB (0.8960)
31.41 dB (0.8917)
31.82 dB (0.8998)
σ = 20
31.14 dB (0.8843)
31.12 dB (0.8859)
31.44 dB (0.8926)

  3.2 Visual comparison for natural images (PSNR and SSIM in the parenthesis)

Noisy image
BM3D
EPLL
aGMM-EPLL
σ = 40
28.78 dB (0.8196)
28.69 dB (0.8103)
28.90 dB (0.8270)
σ = 40
29.43 dB (0.7597)
29.45 dB (0.7555)
29.70 dB (0.7652)
σ = 40
29.80 dB (0.7687)
29.93 dB (0.7655)
30.21 dB (0.7751)

 

4. Visual comparison for external image denoising

noisy image
example image
EPLL
aGMM-example
aGMM-clean
σ = 50
 
26.90 dB (0.7918)
27.28 dB (0.8051)
27.84 dB (0.8181)
σ = 50
 
27.49 dB (0.7428)
27.68 dB (0.7507)
28.06 dB (0.7613)
σ = 50
 
29.79 dB (0.8414)
30.53 dB (0.8611)
30.68 dB (0.8630)
σ = 50
 
29.44 dB (0.8233)
30.26 dB (0.8513)
30.52 dB (0.8528)
σ = 50
 
20.29 dB (0.8524)
21.98 dB (0.9311)
22.49 dB (0.9373)
σ = 50
 
21.56 dB (0.8703)
23.02 dB (0.9302)
23.50 dB (0.9369)