function PSNR(A,B)
% PURPOSE: To find the PSNR (peak signal-to-noise ratio) between two
% intensity images A and B, each having values in the interval
% [0,1]. The answer is in decibels (dB).
%
% There is also a provision, in EXAMPLE 3 below, for images
% stored in the interval [0,255], i.e. 256 gray levels.
%
% SYNOPSIS: PSNR(A,B)
%
% DESCRIPTION: The following is quoted from "Fractal Image Compression",
% by Yuval Fisher et al.,(Springer Verlag, 1995),
% section 2.4, "Pixelized Data".
%
% "...PSNR is used to measure the difference between two
% images. It is defined as
%
% PSNR = 20 * log10(b/rms)
%
% where b is the largest possible value of the signal
% (typically 255 or 1), and rms is the root mean square
% difference between two images. The PSNR is given in
% decibel units (dB), which measure the ratio of the peak
% signal and the difference between two images. An increase
% of 20 dB corresponds to a ten-fold decrease in the rms
% difference between two images.
%
% There are many versions of signal-to-noise ratios, but
% the PSNR is very common in image processing, probably
% because it gives better-sounding numbers than other
% measures."
%
% EXAMPLE 1: load clown
% A = ind2gray(X,map); % Convert to an intensity image in [0,1].
% B = 0.95 * A; % Make B close to, but different from, A.
% PSNR(A,B) % ---> "PSNR = +33.49 dB"
%
% EXAMPLE 2: A = rand(256); % A is a random 256 X 256 matrix in [0,1].
% B = 0.9 * A; % Make B close to, but different from, A.
% PSNR(A,B) % ---> "PSNR = +24.76 dB (approx)"
%
% EXAMPLE 3: For images with 256 gray levels: this function PSNR was
% originally written for matrix-values between 0 and 1,
% because of MATLAB's preference for that interval.
%
% However, suppose the matrix has values in [0,255]. Taking
% Example 1 above, we could change the image to 256 gray levels.
%
% load clown
% A = ind2gray(X,map); % Convert to intensity image in [0,1]
% AA = uint8(255*A); % Change to integers in [0,255]
% BB = 0.95*AA; % Make BB close to AA.
%
% Now we must alter the code for this new case. Comment out the
% existing program (using %) and uncomment the alternative
% underneath it.
%
% PSNR(AA,BB) % ---> "PSNR = +33.56 dB"
%
% Note the slightly different result from Example 1, because
% decimal values were rounded into integers.
if A == B
error('Images are identical: PSNR has infinite value')
end
max2_A = max(max(A));
max2_B = max(max(B));
min2_A = min(min(A));
min2_B = min(min(B));
if max2_A > 1 || max2_B > 1 || min2_A < 0 || min2_B < 0
error('input matrices must have values in the interval [0,1]')
end
error_diff = A - B;
decibels = 20*log10(1/(sqrt(mean(mean(error_diff.^2)))));
disp(sprintf('PSNR = +%5.2f dB',decibels))
% if A == B
% error('Images are identical: PSNR has infinite value')
% end
% max2_A = max(max(A));
% max2_B = max(max(B));
% min2_A = min(min(A));
% min2_B = min(min(B));
%
% if max2_A > 255 || max2_B > 255 || min2_A < 0 || min2_B < 0
% error('input matrices must have values in the interval [0,255]')
% end
% error_diff = A - B;
% decibels = 20*log10(255/(sqrt(mean(mean(error_diff.^2)))));
% disp(sprintf('PSNR = +%5.2f dB',decibels))