UNIVERSITY OF CALIFORNIA,
SANTA CRUZ

 
 
 
 
Regularized Kernel Regression-Based Deblurring (AKTV)
 
 

Hiroyuki Takeda, Dr. Sina Farsiu, and Prof. Peyman Milanfar

 
 
Abstract
 
 

Kernel regression is an effective tool for a variety of image processing tasks such as denoising and interpolation. In this work, we extended the use of kernel regression for deblurring applications. In some earlier examples in the literature, such non-parametric deblurring was sub-optimally performed in two sequential steps, namely, denoising followed by deblurring. In contrast, our optimal solution jointly denoises and deblurs images. The proposed algorithm takes advantage of an effective and novel image prior (Adaptive Kernel Total Variation -- AKTV) that generalizes some of the most popular regularization techniques in the literature.

Full paper [PDF] (accepted for publication in IEEE Transactions on Image Processing)

 
 
 
 
Examples
 
  Case 1: Large blur with a high SNR  
 
The original Cameraman image
Size : 256 x 256

A blurrly and noisy image
PSF(*1) : 19 x 19 uniform
BNSR(*2) : 40 [dB]
RMSE(*3): 29.67

Wiener filter
RMSE : 17.17


ForWaRD
RMSE: 14.39

LPA-ICI
RMSE : 13.36
AKTV
RMSE: 14.03
*1: Point Spread Function.
*2: Blurred Signal to Noise Ratio = 10 log (Blurred signal variance / Noise variance) [dB].
*3: Root Mean Square Error.


 
  Case 2: Large blur with a medium SNR  
 
The original Cameraman image
Size : 256 x 256
A blurrly and noisy image
PSF : 19 x 19 uniform
BNSR : 25 [dB]
RMSE : 29.82
Wiener filter
RMSE : 21.62

ForWaRD
RMSE: 20.78

LPA-ICI
RMSE : 18.23

AKTV
RMSE: 17.64

 
  Case 3: Small blur with a low SNR  
 
The original Lena image
Size : 512 x 512
A blurrly and noisy image
PSF : 5 x 5 Gausian with standard deviation of 1.5
BNSR : 15 [dB]
RMSE : 10.78
Wiener filter
RMSE : 11.18

ForWaRD
RMSE: 8.09
LPA-ICI
RMSE : 6.76
AKTV
RMSE: 6.12

 
  Case 4: A fair amount of blur and noise  
 
The original Chemical Plant image

A blurry and noisy image
PSF : 11 x 11 Gaussian with standard deviation of 1.75
BSNR : 30 [dB]
RMSE : 15.09

Wiener filter
RMSE : 9.29

ForWaRD
RMSE: 8.98
LPA-ICI
RMSE : 8.98
AKTV
RMSE: 8.57
 
 
 
 
Software
 
 

We've prepared the image deblurring toolbox for MATLAB that provides the experimental examples showed above. The latest version of the package can be downloaded from here.

Instruction:

  1. Extract the zip file.
  2. Run MATLAB, and set path to all the directories.
  3. Go to "Examples" directory. All the restored images above by our kernel regression-based method are generated by the follwoing M files,
    • Case 1: Cameraman_19x19ave_BSNR40.m
    • Case 2: Cameraman_19x19ave_BSNR25.m
    • Case 3: Lena_5x5Ga15_BSNR15.m
    • Case 4: ChemicalPlant_11x11Ga175_BSNR30.m
 
 
 
 
Acknowledgement
 
 
This work was supported in part by the US Air Force Grant F49620-03-1-0387.
 
 
 
 
last update on February 1st, 2008