UNIVERSITY OF CALIFORNIA
SANTA CRUZ
 
   
 

Automatic Parameter Selection for Denoising Algorithms Using a No-Reference Measure of Image Content

Presented by Xiang Zhu and Peyman Milanfar

  
 

Abstract

Across the field of inverse problems in image and video processing, nearly all algorithms have various parameters which need to be set in order to yield good results. In practice, usually the choice of such parameters is made empirically with trial and error if no "ground-truth" reference is available. Some analytical methods such as cross-validation and Stein's unbiased risk estimate (SURE) have been successfully used to set such parameters. However, these methods tend to be strongly reliant on restrictive assumptions on the noise, and also computationally heavy. In this paper, we propose a no-reference metric Q which is based on singular value decomposition of local image gradient matrix, and provides a quantitative measure of true image content (i.e. sharpness and contrast as manifested in visually salient geometric features such as edges,) in the presence of noise and other disturbances. This measure (1) is easy to compute, (2) reacts reasonably to both blur and random noise, (3) works well even when the noise is not Gaussian. In the standard Gaussian white noise scenario, the proposed measure produces comparable results to the optimization of MSE for automatic parameter selection, but we do not require a reference image. In addition, we illustrate that our approach is also useful in more general non-standard noise scenarios, where MSE based approaches such as SURE typically fail. To illustrate its use in selection of parameters, the proposed measure is used to automatically and effectively set the parameters of two leading image denoising algorithms. Ample simulated and real data experiments support our claims. Furthermore, tests using the TID2008 database show that this measure correlates well with subjective quality evaluations for both blur and noise distortions. For the sake of completeness, statistical properties of the proposed metric Q in some special cases are also provided.

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Experiment Results

1. The following experiments show an example of optimizing the iteration number of the SKR filter using Metric Q. The noisy images are generated by adding white Gaussian noise to the clean images. MSE is also calculated as comparison.

MSE versus the tuning parameter in SKR denoising experiments using image Barbara (PSNR=30dB). Metric Q versus the tuning parameter in SKR denoising experiments using image Barbara (PSNR=30dB).
MSE optimized output image Barbara (using SKR, 3rd iteration, input PSNR=30dB). Metric Q optimized output image Barbara (using SKR, 5th iteration, input PSNR=30dB).
  
 
MSE versus the tuning parameter in SKR denoising experiments using image Barbara (PSNR=23dB). Metric Q versus the tuning parameter in SKR denoising experiments using image Barbara (PSNR=23dB).
MSE optimized output image Barbara (using SKR, 13th iteration, input PSNR=23dB). Metric Q optimized output image Barbara (using SKR, 16th iteration, input PSNR=23dB).
  
 
MSE versus the tuning parameter in SKR denoising experiments using image Man (PSNR=30dB). Metric Q versus the tuning parameter in SKR denoising experiments using image Man (PSNR=30dB).
MSE optimized output image Man (using SKR, 3rd iteration, input PSNR=30dB). Metric Q optimized output image Man (using SKR, 5th iteration, input PSNR=30dB).
  
 
MSE versus the tuning parameter in SKR denoising experiments using image Man (PSNR=23dB). Metric Q versus the tuning parameter in SKR denoising experiments using image Man (PSNR=23dB).
MSE optimized output image Man (using SKR, 11th iteration, input PSNR=23dB). Metric Q optimized output image Man (using SKR, 13th iteration, input PSNR=23dB).
  
 

2. In the following experiments, the SKR filter is applied in images suffered from real noise. Monte-Carlo SURE is implemented as comparison.

SURE versus the tuning parameter in SKR denoising experiments using image JFK. Metric Q versus the tuning parameter in SKR denoising experiments using image JFK.
SURE optimized output image JFK (using SKR, 1st iteration). Metric Q optimized output image JFK (using SKR, 4th iteration).
  
 
SURE versus the tuning parameter in SKR denoising experiments using image Coinlaundry. Metric Q versus the tuning parameter in SKR denoising experiments using image Coinlaundry.
SURE optimized output image Coinlaundry (using SKR, 2nd iteration). Metric Q optimized output image Coinlaundry (using SKR, 7th iteration).
  
 

3. In the following part we show experiments using BM3D. The tuning parameter is the estimated standard deviation of the random noise, which is required by the algorithm. The noisy images are simulated by adding white Gaussian noise to the clean images. MSE is also calculated as comparison.

MSE versus the tuning parameter in BM3D denoising experiments using image Barbara (PSNR=30dB). Metric Q versus the tuning parameter in BM3D denoising experiments using image Barbara (PSNR=30dB).
MSE optimized output image Barbara (using BM3D, test σ=9, input PSNR=30dB). Metric Q optimized output image Barbara (using BM3D, test σ=12, input PSNR=30dB).
  
 
MSE versus the tuning parameter in BM3D denoising experiments using image Barbara (PSNR=23dB). Metric Q versus the tuning parameter in BM3D denoising experiments using image Barbara (PSNR=23dB).
MSE optimized output image Barbara (using BM3D, test σ=19, input PSNR=23dB). Metric Q optimized output image Barbara (using BM3D, test σ=19, input PSNR=23dB).
  
 
MSE versus the tuning parameter in BM3D denoising experiments using image Man (PSNR=30dB). Metric Q versus the tuning parameter in BM3D denoising experiments using image Man (PSNR=30dB).
MSE optimized output image Man (using BM3D, test σ=8, input PSNR=30dB). Metric Q optimized output image Man (using BM3D, test σ=12, input PSNR=30dB).
  
 
MSE versus the tuning parameter in BM3D denoising experiments using image Man (PSNR=23dB). Metric Q versus the tuning parameter in BM3D denoising experiments using image Man (PSNR=23dB).
MSE optimized output image Man (using BM3D, test σ=17, input PSNR=23dB). Metric Q optimized output image Man (using BM3D, test σ=21, input PSNR=23dB).
  
 

4. In the following experiments, the BM3D filter is applied in images suffered from real noise. Monte-Carlo SURE is implemented as comparison.

SURE versus the tuning parameter in BM3D denoising experiments using image JFK. Metric Q versus the tuning parameter in BM3D denoising experiments using image JFK.
SURE optimized output image JFK (using BM3D, test σ=4). Metric Q optimized output image JFK (using BM3D, test σ=11).
  
 
SURE versus the tuning parameter in BM3D denoising experiments using image Coinlaundry. Metric Q versus the tuning parameter in BM3D denoising experiments using image Coinlaundry.
SURE optimized output image Coinlaundry (using BM3D, test σ=6). Metric Q optimized output image Coinlaundry (using BM3D, test σ=25).