A typical definition of the ISNR in digital image processing is

  ISNR = 10 * log10 ( sum( abs(original(:) - noisy(:)).^2 )

                                 / sum( abs(original(:) - restored(:)).^2 ) )

(taken e.g. from the book "Digital Image Processing" by S. Jayaraman et al. 2011, p.357 or from the book "Encyclopedia of Optical Engineering" by R.G. Driggers 2003, p.413); "original" is the original image (without noise), "noisy" the corrupted image with noise, and "restored" the de-noised image.

The provided matlab code does almost (but not quite) the correct calculation of the ISNR; what you could have done is:

  noisy_norm = norm(original - noisy, 'fro')^2

  restored_norm = norm(original - restored, 'fro')^2

  isnr = 10*log10( noisy_norm / restored_norm)

or (moving the square in front of the logarithm):

  noisy_norm = norm(original - noisy, 'fro')

  restored_norm = norm(original - restored, 'fro')

  isnr = 20*log10( noisy_norm / restored_norm)

or, more explicitly:

  noisy_norm = sum(abs(original(:) - noisy(:)).^2)

  restored_norm = sum(abs(original(:) - restored(:)).^2)

  isnr = 10*log10( noisy_norm / restored_norm)

If you want to keep the PSNRs (assuming that the maximum ("peak") intensity in your images is indeed 1.0), you could also do:

  noisy_psnr = 10 * log10(1 / (norm(original - noisy, 'fro') ^ 2 / H / W))

  restored_psnr = 10 * log10(1 / (norm(original - restored, 'fro') ^ 2 / H / W))

  isnr = restored_psnr - noisy_psnr

i.e. the improvement in SNR is simply the difference between the improved SNR and the original SNR (if calculated in dB).

All these matlab lines should give you the same answer for the ISNR.

Have a look in our website: http://www.medinfo.cs.ucy.ac.cy/

under the tab Downloads-->Toolboxes.

Download the image despeckle filtering toolbox. There is a GUI provided with which you can do many things as well as calculate the snr and many other metrics between oringinal and trnasmitted images.

There are also some matlab functions that can be downloaded together with my book

Despeckle Filtering Algorithms and Software for Ultrasound Imaging

A typical definition of the ISNR in digital image processing is

  ISNR = 10 * log10 ( sum( abs(original(:) - noisy(:)).^2 )

                                 / sum( abs(original(:) - restored(:)).^2 ) )

(taken e.g. from the book "Digital Image Processing" by S. Jayaraman et al. 2011, p.357 or from the book "Encyclopedia of Optical Engineering" by R.G. Driggers 2003, p.413); "original" is the original image (without noise), "noisy" the corrupted image with noise, and "restored" the de-noised image.

The provided matlab code does almost (but not quite) the correct calculation of the ISNR; what you could have done is:

  noisy_norm = norm(original - noisy, 'fro')^2

  restored_norm = norm(original - restored, 'fro')^2

  isnr = 10*log10( noisy_norm / restored_norm)

or (moving the square in front of the logarithm):

  noisy_norm = norm(original - noisy, 'fro')

  restored_norm = norm(original - restored, 'fro')

  isnr = 20*log10( noisy_norm / restored_norm)

or, more explicitly:

  noisy_norm = sum(abs(original(:) - noisy(:)).^2)

  restored_norm = sum(abs(original(:) - restored(:)).^2)

  isnr = 10*log10( noisy_norm / restored_norm)

If you want to keep the PSNRs (assuming that the maximum ("peak") intensity in your images is indeed 1.0), you could also do:

  noisy_psnr = 10 * log10(1 / (norm(original - noisy, 'fro') ^ 2 / H / W))

  restored_psnr = 10 * log10(1 / (norm(original - restored, 'fro') ^ 2 / H / W))

  isnr = restored_psnr - noisy_psnr

i.e. the improvement in SNR is simply the difference between the improved SNR and the original SNR (if calculated in dB).

All these matlab lines should give you the same answer for the ISNR.