hardthres

PURPOSE ^

HARDTHRES image denoising by hard thresholding in the wavelet domain.

SYNOPSIS ^

function A=hardthres(Im,var,varargin)

DESCRIPTION ^

 HARDTHRES image denoising by hard thresholding in the wavelet domain.

 This routine uses 4 scales QMF orthogonal wavelets (see MatlabPyrTools).
 By default it uses the 3*sigma_n rule to set the threshold.
 The user may specify a different threshold factor, i.e.
 thres=thres_factor*sigma_n.

 Hard thresholding [Donoho95] can be derived in a Bayesian framework using
 a very specific combination of noise and image models (MAP estimation of
 Generalized Laplacian PDF signal with particular kurtosis (k=0.5) assuming
 Gaussian noise [Simoncelli99]).

 SYNTAX:

       im_r = hardthres(im_n,variance,thres_factor);

  Input
  -----
    * im_n         = noisy image
    * variance     = noise variance
    * thres_factor = factor on the noise deviation to set the threshold (optional!)
                     If no factor is provided the 3*sigma_n rule is applied.
  Output
  ------
    * im_r         = denoised image

 REFERENCES:

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

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 % HARDTHRES image denoising by hard thresholding in the wavelet domain.
0002 %
0003 % This routine uses 4 scales QMF orthogonal wavelets (see MatlabPyrTools).
0004 % By default it uses the 3*sigma_n rule to set the threshold.
0005 % The user may specify a different threshold factor, i.e.
0006 % thres=thres_factor*sigma_n.
0007 %
0008 % Hard thresholding [Donoho95] can be derived in a Bayesian framework using
0009 % a very specific combination of noise and image models (MAP estimation of
0010 % Generalized Laplacian PDF signal with particular kurtosis (k=0.5) assuming
0011 % Gaussian noise [Simoncelli99]).
0012 %
0013 % SYNTAX:
0014 %
0015 %       im_r = hardthres(im_n,variance,thres_factor);
0016 %
0017 %  Input
0018 %  -----
0019 %    * im_n         = noisy image
0020 %    * variance     = noise variance
0021 %    * thres_factor = factor on the noise deviation to set the threshold (optional!)
0022 %                     If no factor is provided the 3*sigma_n rule is applied.
0023 %  Output
0024 %  ------
0025 %    * im_r         = denoised image
0026 %
0027 % REFERENCES:
0028 %
0029 % [Donoho95]     David L. Donoho and Iain M. Johnstone. Adapting to unknown
0030 %                smoothness via wavelet shrinkage. J. Am. Stat. Assoc., 90:1200-1224, 1995.
0031 % [Simoncelli99] E. Simoncelli. Bayesian denoising of visual images in the wavelet
0032 %                domain. In Bayesian Inference in Wavelet Based Models, pages 291-308.
0033 %                Springer-Verlag, NY, 1999.
0034 % [Simoncelli97] E. Simoncelli. MatlabPyrTools. Matlab toolbox for wavelet transforms
0035 %                http://www.cns.nyu.edu/~lcv/software.php
0036 
0037 function A=hardthres(Im,var,varargin)
0038 
0039 NW=4;
0040 
0041 [pyr,ind]=buildWpyr(Im,NW);
0042 pyr2=abs(pyr);
0043 pyr_sg=sign(pyr);
0044 
0045 if nargin==2
0046    res=3*sqrt(var);
0047 else
0048    res=varargin{1}*sqrt(var);
0049 end
0050 
0051 PYR2=zeros(1,length(pyr2));
0052 PYR2(find(pyr2>res))=pyr2(find(pyr2>res));
0053 
0054 PYR2(65281:65536)=pyr(65281:65536);
0055 PYR3=PYR2.*pyr_sg';
0056 
0057 A=reconWpyr(PYR3',ind);

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