softthres

PURPOSE ^

SOFTTHRES image denoising by soft thresholding in the wavelet domain.

SYNOPSIS ^

function A=softthres(Im2,var,varargin)

DESCRIPTION ^

 SOFTTHRES image denoising by soft thresholding in the wavelet domain.

 This routine uses 4 scales QMF orthogonal wavelets (see MatlabPyrTools).
 By default, threshold is derived from the standard deviation of the noise
 using values optimized to minimize MSE in a set of natural images.
 Precomputed threshold values are given for variances in the range
 [0,1600].
 The user may specify a different threshold factor, i.e.
 thres=thres_factor*sigma_n.

 Soft 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=1) assuming
 Gaussian noise [Simoncelli99]).

 SYNTAX:

       im_r = softthres(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, threshold is estimated
  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 
0002 % SOFTTHRES image denoising by soft thresholding in the wavelet domain.
0003 %
0004 % This routine uses 4 scales QMF orthogonal wavelets (see MatlabPyrTools).
0005 % By default, threshold is derived from the standard deviation of the noise
0006 % using values optimized to minimize MSE in a set of natural images.
0007 % Precomputed threshold values are given for variances in the range
0008 % [0,1600].
0009 % The user may specify a different threshold factor, i.e.
0010 % thres=thres_factor*sigma_n.
0011 %
0012 % Soft thresholding [Donoho95] can be derived in a Bayesian framework using
0013 % a very specific combination of noise and image models (MAP estimation of
0014 % Generalized Laplacian PDF signal with particular kurtosis (k=1) assuming
0015 % Gaussian noise [Simoncelli99]).
0016 %
0017 % SYNTAX:
0018 %
0019 %       im_r = softthres(im_n,variance,thres_factor);
0020 %
0021 %  Input
0022 %  -----
0023 %    * im_n         = noisy image
0024 %    * variance     = noise variance
0025 %    * thres_factor = factor on the noise deviation to set the threshold (optional!)
0026 %                     If no factor is provided, threshold is estimated
0027 %  Output
0028 %  ------
0029 %    * im_r         = denoised image
0030 %
0031 % REFERENCES:
0032 %
0033 % [Donoho95]     David L. Donoho and Iain M. Johnstone. Adapting to unknown
0034 %                smoothness via wavelet shrinkage. J. Am. Stat. Assoc., 90:1200�1224, 1995.
0035 % [Simoncelli99] E. Simoncelli. Bayesian denoising of visual images in the wavelet
0036 %                domain. In Bayesian Inference in Wavelet Based Models, pages 291�308.
0037 %                Springer-Verlag, NY, 1999.
0038 % [Simoncelli97] E. Simoncelli. MatlabPyrTools. Matlab toolbox for wavelet transforms
0039 %                http://www.cns.nyu.edu/~lcv/software.php
0040 function A=softthres(Im2,var,varargin)
0041 [pyr,ind]=buildWpyr(Im2,4);
0042 if nargin==2
0043    if var<=1600
0044       fun=[1,4,10,17,25,34,44,55,66;0,5,10,15,20,25,30,35,40];
0045       des=sqrt(var);
0046       t=interp1(fun(2,:),fun(1,:),des);
0047       s = abs(pyr) - t;
0048       s = (s + abs(s))/2;
0049       y = sign(pyr).*s;
0050       PYR2=y;
0051       PYR2(65281:65536)=pyr(65281:65536);
0052       A=reconWpyr(PYR2,ind);
0053    else
0054       disp('  Input variance exceeds the precomputed range for')
0055       disp('  optimal threshold estimation.')
0056       disp('  Please specify threshold factor on variance!')
0057       A=0;
0058    end
0059 else
0060    t=varargin{1}*sqrt(var);
0061    s = abs(pyr) - t;
0062    s = (s + abs(s))/2;
0063    y = sign(pyr).*s;
0064    PYR2=y;
0065    PYR2(65281:65536)=pyr(65281:65536);
0066    A=reconWpyr(PYR2,ind);
0067 end

Generated on Fri 07-Mar-2014 13:28:33 by m2html © 2005