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BM3DDEB.m
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function [ISNR, y_hat_RWI] = BM3DDEB(experiment_number, test_image_name)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% Copyright (c) 2008-2014 Tampere University of Technology. All rights reserved.
% This work should only be used for nonprofit purposes.
%
% AUTHORS:
% Kostadin Dabov
% Alessandro Foi email: alessandro.foi _at_ tut.fi
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% This function implements the image deblurring method proposed in:
%
% [1] K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, "Image
% restoration by sparse 3D transform-domain collaborative filtering,"
% Proc SPIE Electronic Imaging, January 2008.
%
% FUNCTION INTERFACE:
%
% [PSNR, y_hat_RWI] = BM3DDEB(experiment_number, test_image_name)
%
% INPUT:
% 1) experiment_number: 1 -> PSF 1, sigma^2 = 2
% 2 -> PSF 1, sigma^2 = 8
% 3 -> PSF 2, sigma^2 = 0.308
% 4 -> PSF 3, sigma^2 = 49
% 5 -> PSF 4, sigma^2 = 4
% 6 -> PSF 5, sigma^2 = 64
%
% 2) test_image_name: a valid filename of a grayscale test image
%
% OUTPUT:
% 1) ISNR: the output improvement in SNR, dB
% 2) y_hat_RWI: the restored image
%
% ! The function can work without any of the input arguments,
% in which case, the internal default ones are used !
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% Fixed regularization parameters (obtained empirically after a rough optimization)
Regularization_alpha_RI = 4e-4;
Regularization_alpha_RWI = 5e-3;
%%%% Experiment number (see below for details, e.g. how the blur is generated, etc.)
if (exist('experiment_number') ~= 1)
experiment_number = 3; % 1 -- 6
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% Select a single image filename (might contain path)
%%%%
if (exist('test_image_name') ~= 1)
test_image_name = [
% 'Lena512.png'
'Cameraman256.png'
% 'barbara.png'
% 'house.png'
];
end
%%%% Select 2D transforms ('dct', 'dst', 'hadamard', or anything that is listed by 'help wfilters'):
transform_2D_HT_name = 'dst'; %% 2D transform (of size N1 x N1) used in Step 1
transform_2D_Wiener_name = 'dct'; %% 2D transform (of size N1_wiener x N1_wiener) used in Step 2
transform_3rd_dimage_name = 'haar'; %% 1D tranform used in the 3-rd dim, the same for both steps
%%%% Step 1 (BM3D with collaborative hard-thresholding) parameters:
N1 = 8; %% N1 x N1 is the block size
Nstep = 3; %% sliding step to process every next refernece block
N2 = 16; %% maximum number of similar blocks (maximum size of the 3rd dimensiona of a 3D array)
Ns = 39; %% length of the side of the search neighborhood for full-search block-matching (BM)
tau_match = 6000;%% threshold for the block distance (d-distance)
lambda_thr2D = 0; %% threshold for the coarse initial denoising used in the d-distance measure
lambda_thr3D = 2.9; %% threshold for the hard-thresholding
beta = 0; %% the beta parameter of the 2D Kaiser window used in the reconstruction
%%%% Step 2 (BM3D with collaborative Wiener filtering) parameters:
N1_wiener = 8;
Nstep_wiener = 2;
N2_wiener = 16;
Ns_wiener = 39;
tau_match_wiener = 800;
beta_wiener = 0;
%%%% Specify whether to print results and display images
print_to_screen = 1;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% Note: touch below this point only if you know what you are doing!
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% Make parameters compatible with the interface of the mex-functions
%%%%
[Tfor, Tinv] = getTransfMatrix(N1, transform_2D_HT_name, 0); %% 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_dimage_name, 'haar') == 1),
%%% Fast internal transform is used, 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
%%% vector-matrix multiplications
for hpow = 0:ceil(log2(max(N2,N2_wiener))),
h = 2^hpow;
[Tfor3rd, Tinv3rd] = getTransfMatrix(h, transform_3rd_dimage_name, 0);
hadper_trans_single_den{h} = single(Tfor3rd);
inverse_hadper_trans_single_den{h} = single(Tinv3rd');
end
end
if beta == 0 & beta_wiener == 0
Wwin2D = ones(N1,N1);
Wwin2D_wiener = ones(N1_wiener,N1_wiener);
else
Wwin2D = kaiser(N1, beta) * kaiser(N1, beta)'; % Kaiser window used in the hard-thresholding part
Wwin2D_wiener = kaiser(N1_wiener, beta_wiener) * kaiser(N1_wiener, beta_wiener)'; % Kaiser window used in the Wiener filtering part
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% Read an image and generate a blurred and noisy image
%%%%
y = im2double(imread(test_image_name));
if experiment_number==1
sigma=sqrt(2)/255;
for x1=-7:7; for x2=-7:7; v(x1+8,x2+8)=1/(x1^2+x2^2+1); end, end; v=v./sum(v(:));
end
if experiment_number==2
sigma=sqrt(8)/255;
s1=0; for a1=-7:7; s1=s1+1; s2=0; for a2=-7:7; s2=s2+1; v(s1,s2)=1/(a1^2+a2^2+1); end, end; v=v./sum(v(:));
end
if experiment_number==3
BSNR=40; sigma=-1; % if "sigma=-1", then the value of sigma depends on the BSNR
v=ones(9); v=v./sum(v(:));
end
if experiment_number==4
sigma=7/255;
v=[1 4 6 4 1]'*[1 4 6 4 1]; v=v./sum(v(:)); % PSF
end
if experiment_number==5
sigma=2/255;
v=fspecial('gaussian', 25, 1.6);
end
if experiment_number==6
sigma=8/255;
v=fspecial('gaussian', 25, .4);
end
[Xv, Xh] = size(y);
[ghy,ghx] = size(v);
big_v = zeros(Xv,Xh); big_v(1:ghy,1:ghx)=v; big_v=circshift(big_v,-round([(ghy-1)/2 (ghx-1)/2])); % pad PSF with zeros to whole image domain, and center it
V = fft2(big_v); % frequency response of the PSF
y_blur = imfilter(y, v(end:-1:1,end:-1:1), 'circular'); % performs blurring (by circular convolution)
randn('seed',0); %%% fix seed for the random number generator
if sigma == -1; %% check whether to use BSNR in order to define value of sigma
sigma=sqrt(norm(y_blur(:)-mean(y_blur(:)),2)^2 /(Xh*Xv*10^(BSNR/10))); % compute sigma from the desired BSNR
end
%%%% Create a blurred and noisy observation
z = y_blur + sigma*randn(Xv,Xh);
tic;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% Step 1: Final estimate by Regularized Inversion (RI) followed by
%%%% BM3D with collaborative hard-thresholding
%%%%
%%%% Step 1.1. Regularized Inversion
RI= conj(V)./( (abs(V).^2) + Regularization_alpha_RI * Xv*Xh*sigma^2); % Transfer Matrix for RI %% Standard Tikhonov Regularization
zRI=real(ifft2( fft2(z).* RI )); % Regularized Inverse Estimate (RI OBSERVATION)
stdRI = zeros(N1, N1);
for ii = 1:N1,
for jj = 1:N1,
UnitMatrix = zeros(N1,N1); UnitMatrix(ii,jj)=1;
BasisElementPadded = zeros(Xv, Xh); BasisElementPadded(1:N1,1:N1) = Tinv*UnitMatrix*Tinv';
TransfBasisElementPadded = fft2(BasisElementPadded);
stdRI(ii,jj) = sqrt( (1/(Xv*Xh)) * sum(sum(abs(TransfBasisElementPadded.*RI).^2)) )*sigma;
end,
end
%%%% Step 1.2. Colored noise suppression by BM3D with collaborative hard-
%%%% thresholding
y_hat_RI = bm3d_thr_colored_noise(zRI, hadper_trans_single_den, Nstep, N1, N2, lambda_thr2D,...
lambda_thr3D, tau_match*N1*N1/(255*255), (Ns-1)/2, sigma, 0, single(Tfor), single(Tinv)',...
inverse_hadper_trans_single_den, single(stdRI'), Wwin2D, 0, 1 );
PSNR_INITIAL_ESTIMATE = 10*log10(1/mean((y(:)-y_hat_RI(:)).^2));
ISNR_INITIAL_ESTIMATE = PSNR_INITIAL_ESTIMATE - 10*log10(1/mean((y(:)-z(:)).^2));
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% Step 2: Final estimate by Regularized Wiener Inversion (RWI) followed
%%%% by BM3D with collaborative Wiener filtering
%%%%
%%%% Step 2.1. Regularized Wiener Inversion
Wiener_Pilot = abs(fft2(double(y_hat_RI))); %%% Wiener reference estimate
RWI = conj(V).*Wiener_Pilot.^2./(Wiener_Pilot.^2.*(abs(V).^2) + Regularization_alpha_RWI*Xv*Xh*sigma^2); % Transfer Matrix for RWI (uses standard regularization 'a-la-Tikhonov')
zRWI = real(ifft2(fft2(z).*RWI)); % RWI OBSERVATION
stdRWI = zeros(N1_wiener, N1_wiener);
for ii = 1:N1_wiener,
for jj = 1:N1_wiener,
UnitMatrix = zeros(N1_wiener,N1_wiener); UnitMatrix(ii,jj)=1;
BasisElementPadded = zeros(Xv, Xh); BasisElementPadded(1:N1_wiener,1:N1_wiener) = TinvW*UnitMatrix*TinvW';
TransfBasisElementPadded = fft2(BasisElementPadded);
stdRWI(ii,jj) = sqrt( (1/(Xv*Xh)) * sum(sum(abs(TransfBasisElementPadded.*RWI).^2)) )*sigma;
end,
end
%%%% Step 2.2. Colored noise suppression by BM3D with collaborative Wiener
%%%% filtering
y_hat_RWI = bm3d_wiener_colored_noise(zRWI, y_hat_RI, hadper_trans_single_den, Nstep_wiener, N1_wiener, N2_wiener, ...
0, tau_match_wiener*N1_wiener*N1_wiener/(255*255), (Ns_wiener-1)/2, 0, single(stdRWI'), single(TforW), single(TinvW)',...
inverse_hadper_trans_single_den, Wwin2D_wiener, 0, 1, single(ones(N1_wiener)) );
elapsed_time = toc;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% Calculate the final estimate's PSNR and ISNR, print them, and show the
%%%% restored image
%%%%
PSNR = 10*log10(1/mean((y(:)-y_hat_RWI(:)).^2));
ISNR = PSNR - 10*log10(1/mean((y(:)-z(:)).^2));
if print_to_screen == 1
fprintf('Image: %s, Exp %d, Time: %.1f sec, PSNR-RI: %.2f dB, PSNR-RWI: %.2f, ISNR-RWI: %.2f dB\n', ...
test_image_name, experiment_number, elapsed_time, PSNR_INITIAL_ESTIMATE, PSNR, ISNR);
figure,imshow(z);
figure,imshow(double(y_hat_RWI));
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;