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BM3D_CFA.m
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BM3D_CFA.m
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function [varargout] = BM3D_CFA(z, sigma)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% BM3D_CFA is the modification of the BM3D algorithm for attenuation of additive white Gaussian noise from
% Bayer CFA images. This algorithm reproduces the results from the article:
%
% [1] A. Danielyan, M. Vehviläinen, A. Foi, V. Katkovnik, and K. Egiazarian,
% “Cross-color BM3D filtering of noisy raw data”,
% Proc. Int. Workshop on Local and Non-Local Approx. in Image Process.,
% LNLA 2009, Tuusula, Finland, pp. 125-129, August 2009.
%
% FUNCTION INTERFACE:
%
% [y_wiener, y_ht] = BM3D(z, sigma)
%
% ! The function can work without any of the input arguments,
% in which case, the internal default ones are used !
% INPUT ARGUMENTS (OPTIONAL):
%
% 2) z (matrix M x N): Noisy image (intensities in range [0,1] or [0,255])
% 3) sigma (double) : Std. dev. of the noise (corresponding to intensities
% in range [0,255] even if the range of z is [0,1])
% OUTPUTS:
% 1) y_wiener (matrix M x N): Final(wiener) estimate (in the range [0,1])
% 2) y_ht (matrix M x N): Basic (hard-thresholding) estimate (in the range [0,1])
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% Copyright (c) 2009-2014 Tampere University of Technology.
% All rights reserved.
% This work should only be used for nonprofit purposes.
%
% AUTHORS:
% Aram Danielyan, email: aram dot danielyan _at_ .tut.fi
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% In case, a noisy image z is not provided, then use the filename
%%%% below to read an original image (might contain path also). Later,
%%%% artificial AWGN noise is added and this noisy image is processed
%%%% by the BM3D.
%%%%
image_name = [
'kodim07.png'
% 'kodim08.png'
% 'kodim19.png'
% 'kodim23.png'
];
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% Quality/complexity trade-off profile selection
%%%%
%%%% 'np' --> Normal Profile (balanced quality)
if ~exist('profile','var')
profile = 'np'; %% default profile
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% Specify the std. dev. of the corrupting noise
%%%%
if ~exist('sigma','var')
sigma = 25; %% default standard deviation of the AWGN
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% Following are the parameters for the Normal Profile.
%%%%
%%%% Select transforms ('dct', 'dst', 'hadamard', or anything that is listed by 'help wfilters'):
transform_2D_HT_name = 'dct'; %% transform used for the HT filt. of size N1 x N1
transform_2D_Wiener_name = 'dct';
transform_3rd_dim_name = 'haar'; %% transform used in the 3-rd dim, the same for HT and Wiener filt.
%%%% Hard-thresholding (HT) parameters:
N1 = 5; %% N1 x N1 is the block size used for the hard-thresholding (HT) filtering
Nstep = 3; %% sliding step to process every next reference block
N2 = 16; %% maximum number of similar blocks (maximum size of the 3rd dimension of a 3D array)
Ns = 39; %% length of the side of the search neighborhood for full-search block-matching (BM), must be odd
lambda_thr2D = 0;
tau_match = 3000;%% threshold for the block-distance (d-distance)
lambda_thr3D = 2.7; %% threshold parameter for the hard-thresholding in 3D transform domain
beta = 2.0; %% parameter of the 2D Kaiser window used in the reconstruction
%%%% Step 2: Wiener filtering parameters:
N1_wiener = 6;
Nstep_wiener = 3;
N2_wiener = 32;
Ns_wiener = 39;
tau_match_wiener = 400;
beta_wiener = 2.0;
%%%% Block-matching parameters:
stepFS = 1; %% step that forces to switch to full-search BM, "1" implies always full-search
smallLN = 'not used in np'; %% if stepFS > 1, then this specifies the size of the small local search neighb.
stepFSW = 1;
smallLNW = 'not used in np';
thrToIncStep = 8; % if the number of non-zero coefficients after HT is less than thrToIncStep,
% than the sliding step to the next reference block is incresed to (nm1-1)
decLevel = 0; %% dec. levels of the dyadic wavelet 2D transform for blocks (0 means full decomposition, higher values decrease the dec. number)
thr_mask = ones(N1); %% N1xN1 mask of threshold scaling coeff. --- by default there is no scaling, however the use of different thresholds for different wavelet decompoistion subbands can be done with this matrix
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% Note: touch below this point only if you know what you are doing!
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% Create transform matrices, etc.
%%%%
[Tfor, Tinv] = getTransfMatrix(N1, transform_2D_HT_name, decLevel); %% get (normalized) forward and inverse transform matrices
[TforW, TinvW] = getTransfMatrix(N1_wiener, transform_2D_Wiener_name, 0); %% get (normalized) forward and inverse transform matrices
if (strcmp(transform_3rd_dim_name, 'haar') == 1) | (strcmp(transform_3rd_dim_name(end-2:end), '1.1') == 1),
%%% If Haar is used in the 3-rd dimension, then a fast internal transform is used, thus no need to generate transform
%%% matrices.
hadper_trans_single_den = {};
inverse_hadper_trans_single_den = {};
else
%%% Create transform matrices. The transforms are later applied by
%%% matrix-vector multiplication for the 1D case.
for hpow = 0:ceil(log2(max(N2,N2_wiener))),
h = 2^hpow;
[Tfor3rd, Tinv3rd] = getTransfMatrix(h, transform_3rd_dim_name, 0);
hadper_trans_single_den{h} = single(Tfor3rd);
inverse_hadper_trans_single_den{h} = single(Tinv3rd');
end
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% 2D Kaiser windows used in the aggregation of block-wise estimates
%%%%
if beta_wiener==2 & beta==2 & N1_wiener==8 & N1==8 % hardcode the window function so that the signal processing toolbox is not needed by default
Wwin2D = [ 0.1924 0.2989 0.3846 0.4325 0.4325 0.3846 0.2989 0.1924;
0.2989 0.4642 0.5974 0.6717 0.6717 0.5974 0.4642 0.2989;
0.3846 0.5974 0.7688 0.8644 0.8644 0.7688 0.5974 0.3846;
0.4325 0.6717 0.8644 0.9718 0.9718 0.8644 0.6717 0.4325;
0.4325 0.6717 0.8644 0.9718 0.9718 0.8644 0.6717 0.4325;
0.3846 0.5974 0.7688 0.8644 0.8644 0.7688 0.5974 0.3846;
0.2989 0.4642 0.5974 0.6717 0.6717 0.5974 0.4642 0.2989;
0.1924 0.2989 0.3846 0.4325 0.4325 0.3846 0.2989 0.1924];
Wwin2D_wiener = Wwin2D;
else
Wwin2D = kaiser(N1, beta) * kaiser(N1, beta)'; % Kaiser window used in the aggregation of the HT part
Wwin2D_wiener = kaiser(N1_wiener, beta_wiener) * kaiser(N1_wiener, beta_wiener)'; % Kaiser window used in the aggregation of the Wiener filt. part
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% If needed, read images, generate noise, or scale the images to the
%%%% [0,1] interval
%%%%
if ~exist('z','var')
yRGB = im2double(imread(image_name)); %% read a noise-free image and put in intensity range [0,1]
y = zeros(size(yRGB,1), size(yRGB,2));
y(1:2:end,1:2:end) = yRGB(1:2:end,1:2:end,2);
y(2:2:end,2:2:end) = yRGB(2:2:end,2:2:end,2);
y(1:2:end,2:2:end) = yRGB(1:2:end,2:2:end,1);
y(2:2:end,1:2:end) = yRGB(2:2:end,1:2:end,3);
randn('seed', 0); %% generate seed
z = y + (sigma/255)*randn(size(y)); %% create a noisy image
else % external images
image_name = 'External image';
% convert z to double precision if needed
z = double(z);
y= [];
end
if (size(z,3) ~= 1)
error('BM3D accepts only grayscale 2D images.');
end
%%% Check whether to dump information to the screen or remain silent
if isempty(y)
dump_output_information = false;
else
dump_output_information = true;
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% Print image information to the screen
%%%%
if dump_output_information
fprintf('Image: %s (%dx%d), sigma: %.1f\n', image_name, size(z,1), size(z,2), sigma);
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% Step 1. Produce the basic estimate by HT filtering
%%%%
tic;
y_ht = bm3d_CFA_thr(z, hadper_trans_single_den, Nstep, N1, N2, lambda_thr2D,...
lambda_thr3D, tau_match*N1*N1/(255*255), (Ns-1)/2, (sigma/255), thrToIncStep, single(Tfor), single(Tinv)', inverse_hadper_trans_single_den, single(thr_mask), Wwin2D, smallLN, stepFS );
estimate_elapsed_time = toc;
if dump_output_information
PSNR_INITIAL_ESTIMATE = 10*log10(1/mean((y(:)-double(y_ht(:))).^2));
fprintf('BASIC ESTIMATE, PSNR: %.2f dB\n', PSNR_INITIAL_ESTIMATE);
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% Step 2. Produce the final estimate by Wiener filtering (using the
%%%% hard-thresholding initial estimate)
%%%%
tic;
y_wiener = bm3d_CFA_wiener(z, y_ht, hadper_trans_single_den, Nstep_wiener, N1_wiener, N2_wiener, ...
'unused arg', tau_match_wiener*N1_wiener*N1_wiener/(255*255), (Ns_wiener-1)/2, (sigma/255), 'unused arg', single(TforW), single(TinvW)', inverse_hadper_trans_single_den, Wwin2D_wiener, smallLNW, stepFSW, single(ones(N1_wiener)) );
wiener_elapsed_time = toc;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% Calculate the final estimate's PSNR, print it, and show the
%%%% denoised image next to the noisy one
%%%%
y_wiener = double(y_wiener);
if dump_output_information
PSNR = 10*log10(1/mean((y(:)-y_wiener(:)).^2)); % y is valid
fprintf('FINAL ESTIMATE (total time: %.1f sec), PSNR: %.2f dB\n', ...
wiener_elapsed_time + estimate_elapsed_time, PSNR);
figure, imshow(z); title(sprintf('Noisy %s, PSNR: %.3f dB (sigma: %d)', ...
image_name(1:end-4), 10*log10(1/mean((y(:)-z(:)).^2)), sigma));
figure, imshow(y_wiener); title(sprintf('Denoised %s, PSNR: %.3f dB', ...
image_name(1:end-4), PSNR));
end
if nargout==0
varargout={};
else
varargout{1}=y_wiener;
varargout{2}=y_ht;
end
return;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Some auxiliary functions
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [Tforward, Tinverse] = getTransfMatrix (N, transform_type, dec_levels)
%
% Create forward and inverse transform matrices, which allow for perfect
% reconstruction. The forward transform matrix is normalized so that the
% l2-norm of each basis element is 1.
%
% [Tforward, Tinverse] = getTransfMatrix (N, transform_type, dec_levels)
%
% INPUTS:
%
% N --> Size of the transform (for wavelets, must be 2^K)
%
% transform_type --> 'dct', 'dst', 'hadamard', or anything that is
% listed by 'help wfilters' (bi-orthogonal wavelets)
% 'DCrand' -- an orthonormal transform with a DC and all
% the other basis elements of random nature
%
% dec_levels --> If a wavelet transform is generated, this is the
% desired decomposition level. Must be in the
% range [0, log2(N)-1], where "0" implies
% full decomposition.
%
% OUTPUTS:
%
% Tforward --> (N x N) Forward transform matrix
%
% Tinverse --> (N x N) Inverse transform matrix
%
if exist('dec_levels') ~= 1,
dec_levels = 0;
end
if N == 1,
Tforward = 1;
elseif strcmp(transform_type, 'hadamard') == 1,
Tforward = hadamard(N);
elseif (N == 8) & strcmp(transform_type, 'bior1.5')==1 % hardcoded transform so that the wavelet toolbox is not needed to generate it
Tforward = [ 0.353553390593274 0.353553390593274 0.353553390593274 0.353553390593274 0.353553390593274 0.353553390593274 0.353553390593274 0.353553390593274;
0.219417649252501 0.449283757993216 0.449283757993216 0.219417649252501 -0.219417649252501 -0.449283757993216 -0.449283757993216 -0.219417649252501;
0.569359398342846 0.402347308162278 -0.402347308162278 -0.569359398342846 -0.083506045090284 0.083506045090284 -0.083506045090284 0.083506045090284;
-0.083506045090284 0.083506045090284 -0.083506045090284 0.083506045090284 0.569359398342846 0.402347308162278 -0.402347308162278 -0.569359398342846;
0.707106781186547 -0.707106781186547 0 0 0 0 0 0;
0 0 0.707106781186547 -0.707106781186547 0 0 0 0;
0 0 0 0 0.707106781186547 -0.707106781186547 0 0;
0 0 0 0 0 0 0.707106781186547 -0.707106781186547];
elseif (N == 8) & strcmp(transform_type, 'dct')==1 % hardcoded transform so that the signal processing toolbox is not needed to generate it
Tforward = [ 0.353553390593274 0.353553390593274 0.353553390593274 0.353553390593274 0.353553390593274 0.353553390593274 0.353553390593274 0.353553390593274;
0.490392640201615 0.415734806151273 0.277785116509801 0.097545161008064 -0.097545161008064 -0.277785116509801 -0.415734806151273 -0.490392640201615;
0.461939766255643 0.191341716182545 -0.191341716182545 -0.461939766255643 -0.461939766255643 -0.191341716182545 0.191341716182545 0.461939766255643;
0.415734806151273 -0.097545161008064 -0.490392640201615 -0.277785116509801 0.277785116509801 0.490392640201615 0.097545161008064 -0.415734806151273;
0.353553390593274 -0.353553390593274 -0.353553390593274 0.353553390593274 0.353553390593274 -0.353553390593274 -0.353553390593274 0.353553390593274;
0.277785116509801 -0.490392640201615 0.097545161008064 0.415734806151273 -0.415734806151273 -0.097545161008064 0.490392640201615 -0.277785116509801;
0.191341716182545 -0.461939766255643 0.461939766255643 -0.191341716182545 -0.191341716182545 0.461939766255643 -0.461939766255643 0.191341716182545;
0.097545161008064 -0.277785116509801 0.415734806151273 -0.490392640201615 0.490392640201615 -0.415734806151273 0.277785116509801 -0.097545161008064];
elseif (N == 8) & strcmp(transform_type, 'dst')==1 % hardcoded transform so that the PDE toolbox is not needed to generate it
Tforward = [ 0.161229841765317 0.303012985114696 0.408248290463863 0.464242826880013 0.464242826880013 0.408248290463863 0.303012985114696 0.161229841765317;
0.303012985114696 0.464242826880013 0.408248290463863 0.161229841765317 -0.161229841765317 -0.408248290463863 -0.464242826880013 -0.303012985114696;
0.408248290463863 0.408248290463863 0 -0.408248290463863 -0.408248290463863 0 0.408248290463863 0.408248290463863;
0.464242826880013 0.161229841765317 -0.408248290463863 -0.303012985114696 0.303012985114696 0.408248290463863 -0.161229841765317 -0.464242826880013;
0.464242826880013 -0.161229841765317 -0.408248290463863 0.303012985114696 0.303012985114696 -0.408248290463863 -0.161229841765317 0.464242826880013;
0.408248290463863 -0.408248290463863 0 0.408248290463863 -0.408248290463863 0 0.408248290463863 -0.408248290463863;
0.303012985114696 -0.464242826880013 0.408248290463863 -0.161229841765317 -0.161229841765317 0.408248290463863 -0.464242826880013 0.303012985114696;
0.161229841765317 -0.303012985114696 0.408248290463863 -0.464242826880013 0.464242826880013 -0.408248290463863 0.303012985114696 -0.161229841765317];
elseif strcmp(transform_type, 'dct') == 1,
Tforward = dct(eye(N));
elseif strcmp(transform_type, 'dst') == 1,
Tforward = dst(eye(N));
elseif strcmp(transform_type, 'DCrand') == 1,
x = randn(N); x(1:end,1) = 1; [Q,R] = qr(x);
if (Q(1) < 0),
Q = -Q;
end;
Tforward = Q';
else %% a wavelet decomposition supported by 'wavedec'
%%% Set periodic boundary conditions, to preserve bi-orthogonality
dwtmode('per','nodisp');
Tforward = zeros(N,N);
for i = 1:N
Tforward(:,i)=wavedec(circshift([1 zeros(1,N-1)],[dec_levels i-1]), log2(N), transform_type); %% construct transform matrix
end
end
%%% Normalize the basis elements
Tforward = (Tforward' * diag(sqrt(1./sum(Tforward.^2,2))))';
%%% Compute the inverse transform matrix
Tinverse = inv(Tforward);
return;