KeCoDe_denoising

PURPOSE ^

KeCoDe_denosing applies wavelet-based image denoising algorithms to the

SYNOPSIS ^

function Im_d = KeCoDe_denoising(Im_n,model,var)

DESCRIPTION ^

 KeCoDe_denosing applies wavelet-based image denoising algorithms to the
 input 256*256 gray scale image. This version is thought only for gaussian
 noise. Note that the kernel denoising colud be applied to different
 kinds of noise, however some parameters have to be precomputed (see
 model 4 or [Laparra10] for details).

 The available denoising algorithms and the corresponding Matlab functions are:

   * model 1 - Hard Thresholding [Donoho95,Simoncelli99].... hardthres.m
       Assumes the noise variance is known.
       Applies the threshold=3*sigma_n rule.

   * model 2 - Soft Thresholding [Donoho95,Simoncelli99].... softthres.m
       Assumes the noise variance is known.
       Applies the threshold=3*sigma_n rule.

   * model 3 - Bayesian denoising assuming (1) Gaussian noise of known variance
     and, (2) Gaussian marginals for the wavelet coefficients of natural
     images [Figueiredo01]........................ bayesian_gauss_margin.m

   * model 4 - Kernel regularization in the wavelet domain with kernels inspired in
     mutual information measures [Laparra10] ..... mi_kernel_denoising.m

     NOTE: The function 'mi_kernel_denoising.m' admits precomputed parameters
     in order to apply the algorithm in different kinds of noise. See the
     JPEG example below.

     In 'KeCoDe_denoising.m' the algorithm is prepared to work with
     Gaussian nosie. In order to use 'mi_kernel_denoising.m' on different
     kind noise it requires some knowledge on the signal and
     the noise:
     1- Average variance of the signal in the wavelet domain to set
        the SVM penalization profile, C_i. This variance profile is an
        intrinsic feature of natural images and can be estimated from
        a natural image database.
     2- Average standard deviation of the noise in the wavelet domain to
        set the insensitivity profile, epsilon_i. This deviation profile
        can be estimated from noise samples.
     3- 2D histogram of the noise in the spatial domain to look for the
        SVM parameters that better identify the noise. SVM parameter
        optimization can be done by minimizing the KL divergence between
        the known noise histogram and the histogram of the estimated
        noise.
     The code provided in KeCoDe skips all the off-line
     preprocessing steps:
     1- Average variance of natural images in the steerable domain was
        precomputed from the McGill natural image data base
        (http://tabby.vision.mcgill.ca/) and stored in the file:
                "C_profile.mat"
     2- Average standard deviation profile of Gaussian noise and
        JPEG noise was precomputed from (1) noise realizations and
        (2) JPEG compressed (at MATLAB quality compression Q=7) examples
        respectively, and stored in the files:
            "Epsilon_profile_Gaussian.mat"
            "Epsilon_profile_JPEG_Q7.mat"
        If the Q factor of the JPEG quantization is modified, or another noise
        source is present, the epsilon profile should be computed by looking at
        the average wavelet transform of noise samples.
        For signal independent noise sources, the unit variance profile
        scales as: epsilon_profile=sqrt(Var)*unit_variance_epsilon_profile..
        Therefore, for white noise Gaussian sources the code provided here
        is general assuming known variance (as the other algorithms).
      3- KLD-based SVR selection is not implemented in the code. Instead, fixed
        (near optimum) values are given in each case (Gaussian and JPEG), in the
        ranges described in [Laparra08].

 [Laparra10]    V. Laparra, J. Gutierrez, G. Camps and J. Malo
                Image Denoising with Kernels based on Natural Image Relations
                Journal of Machine Learning Research 11(Feb):873?903, 2010

 [Donoho95]     David L. Donoho and Iain M. Johnstone. Adapting to unknown
                smoothness via wavelet shrinkage. J. Am. Stat. Assoc., 90:1200-1224, 1995.

 [Simoncelli99] E. Simoncelli. Bayesian denoising of visual images in the wavelet
                domain. In Bayesian Inference in Wavelet Based Models, pages 291-308.
                Springer-Verlag, NY, 1999.

 [Figueiredo01] M. Figueiredo and R. Nowak. Wavelet-based image estimation:
                an empirical Bayes approach using Jeffrey's noninformative prior.
                IEEE Transactions on Image Processing, 10(9):1322-1331, 2001.

 [Simoncelli97] E. Simoncelli. MatlabPyrTools. Matlab toolbox for wavelet transforms
                http://www.cns.nyu.edu/~lcv/software.php

 [Foi06]        Alessandro Foi. Routine  'function_stdEst2D.m'  for automatic
                noise variance estimation. Tampere University of
                Technology - 2005-2006
                http://www.cs.tut.fi/~lasip/2D

 SYNTAX:
 Im_d = KeCoDe_denoising(Im,model,var)

 Input variables:
 ----------------
  * Im_n           :  256*256 noisy image matrix double precision numbers in the range [0 255]
  * MODEL          :  1-4 (see above models explanation)
  * Var            :  Variance of Gaussian noise. This parameter is optinal.
                      If it is not provided, the variance will be estimated using
                      'function_stdEst2D.m' [Foi06]

 Output:
 -------
  * Im_d           :  Denoised image

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 %
0002 % KeCoDe_denosing applies wavelet-based image denoising algorithms to the
0003 % input 256*256 gray scale image. This version is thought only for gaussian
0004 % noise. Note that the kernel denoising colud be applied to different
0005 % kinds of noise, however some parameters have to be precomputed (see
0006 % model 4 or [Laparra10] for details).
0007 %
0008 % The available denoising algorithms and the corresponding Matlab functions are:
0009 %
0010 %   * model 1 - Hard Thresholding [Donoho95,Simoncelli99].... hardthres.m
0011 %       Assumes the noise variance is known.
0012 %       Applies the threshold=3*sigma_n rule.
0013 %
0014 %   * model 2 - Soft Thresholding [Donoho95,Simoncelli99].... softthres.m
0015 %       Assumes the noise variance is known.
0016 %       Applies the threshold=3*sigma_n rule.
0017 %
0018 %   * model 3 - Bayesian denoising assuming (1) Gaussian noise of known variance
0019 %     and, (2) Gaussian marginals for the wavelet coefficients of natural
0020 %     images [Figueiredo01]........................ bayesian_gauss_margin.m
0021 %
0022 %   * model 4 - Kernel regularization in the wavelet domain with kernels inspired in
0023 %     mutual information measures [Laparra10] ..... mi_kernel_denoising.m
0024 %
0025 %     NOTE: The function 'mi_kernel_denoising.m' admits precomputed parameters
0026 %     in order to apply the algorithm in different kinds of noise. See the
0027 %     JPEG example below.
0028 %
0029 %     In 'KeCoDe_denoising.m' the algorithm is prepared to work with
0030 %     Gaussian nosie. In order to use 'mi_kernel_denoising.m' on different
0031 %     kind noise it requires some knowledge on the signal and
0032 %     the noise:
0033 %     1- Average variance of the signal in the wavelet domain to set
0034 %        the SVM penalization profile, C_i. This variance profile is an
0035 %        intrinsic feature of natural images and can be estimated from
0036 %        a natural image database.
0037 %     2- Average standard deviation of the noise in the wavelet domain to
0038 %        set the insensitivity profile, epsilon_i. This deviation profile
0039 %        can be estimated from noise samples.
0040 %     3- 2D histogram of the noise in the spatial domain to look for the
0041 %        SVM parameters that better identify the noise. SVM parameter
0042 %        optimization can be done by minimizing the KL divergence between
0043 %        the known noise histogram and the histogram of the estimated
0044 %        noise.
0045 %     The code provided in KeCoDe skips all the off-line
0046 %     preprocessing steps:
0047 %     1- Average variance of natural images in the steerable domain was
0048 %        precomputed from the McGill natural image data base
0049 %        (http://tabby.vision.mcgill.ca/) and stored in the file:
0050 %                "C_profile.mat"
0051 %     2- Average standard deviation profile of Gaussian noise and
0052 %        JPEG noise was precomputed from (1) noise realizations and
0053 %        (2) JPEG compressed (at MATLAB quality compression Q=7) examples
0054 %        respectively, and stored in the files:
0055 %            "Epsilon_profile_Gaussian.mat"
0056 %            "Epsilon_profile_JPEG_Q7.mat"
0057 %        If the Q factor of the JPEG quantization is modified, or another noise
0058 %        source is present, the epsilon profile should be computed by looking at
0059 %        the average wavelet transform of noise samples.
0060 %        For signal independent noise sources, the unit variance profile
0061 %        scales as: epsilon_profile=sqrt(Var)*unit_variance_epsilon_profile..
0062 %        Therefore, for white noise Gaussian sources the code provided here
0063 %        is general assuming known variance (as the other algorithms).
0064 %      3- KLD-based SVR selection is not implemented in the code. Instead, fixed
0065 %        (near optimum) values are given in each case (Gaussian and JPEG), in the
0066 %        ranges described in [Laparra08].
0067 %
0068 % [Laparra10]    V. Laparra, J. Gutierrez, G. Camps and J. Malo
0069 %                Image Denoising with Kernels based on Natural Image Relations
0070 %                Journal of Machine Learning Research 11(Feb):873?903, 2010
0071 %
0072 % [Donoho95]     David L. Donoho and Iain M. Johnstone. Adapting to unknown
0073 %                smoothness via wavelet shrinkage. J. Am. Stat. Assoc., 90:1200-1224, 1995.
0074 %
0075 % [Simoncelli99] E. Simoncelli. Bayesian denoising of visual images in the wavelet
0076 %                domain. In Bayesian Inference in Wavelet Based Models, pages 291-308.
0077 %                Springer-Verlag, NY, 1999.
0078 %
0079 % [Figueiredo01] M. Figueiredo and R. Nowak. Wavelet-based image estimation:
0080 %                an empirical Bayes approach using Jeffrey's noninformative prior.
0081 %                IEEE Transactions on Image Processing, 10(9):1322-1331, 2001.
0082 %
0083 % [Simoncelli97] E. Simoncelli. MatlabPyrTools. Matlab toolbox for wavelet transforms
0084 %                http://www.cns.nyu.edu/~lcv/software.php
0085 %
0086 % [Foi06]        Alessandro Foi. Routine  'function_stdEst2D.m'  for automatic
0087 %                noise variance estimation. Tampere University of
0088 %                Technology - 2005-2006
0089 %                http://www.cs.tut.fi/~lasip/2D
0090 %
0091 % SYNTAX:
0092 % Im_d = KeCoDe_denoising(Im,model,var)
0093 %
0094 % Input variables:
0095 % ----------------
0096 %  * Im_n           :  256*256 noisy image matrix double precision numbers in the range [0 255]
0097 %  * MODEL          :  1-4 (see above models explanation)
0098 %  * Var            :  Variance of Gaussian noise. This parameter is optinal.
0099 %                      If it is not provided, the variance will be estimated using
0100 %                      'function_stdEst2D.m' [Foi06]
0101 %
0102 % Output:
0103 % -------
0104 %  * Im_d           :  Denoised image
0105 %
0106 function Im_d = KeCoDe_denoising(Im_n,model,var)
0107 warning('off','MATLAB:dispatcher:InexactMatch')
0108 Im_n=double(Im_n);
0109 if exist('var')
0110 else
0111     dev = function_stdEst2D(Im_n);
0112     var = dev^2;
0113 end
0114 if model==1
0115     Im_d = hardthres(Im_n,var);
0116 elseif model==2
0117     Im_d = softthres(Im_n,var);
0118 elseif model==3
0119     Im_d = bayesian_gauss_margin(Im_n,var);
0120 elseif model==4
0121     C       = 3000;
0122     S       = 4;
0123     epsilon = 2;
0124     load Epsilon_profile_Gaussian.mat
0125     epsilon_profile  = perfil_eps*sqrt(var);
0126     Im_d = mi_kernel_denoising(Im_n,epsilon,C,S,epsilon_profile);
0127 end

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