# Why PSNR decreases for Ultrasound Images?

I am working different types of filters to remove speckle noise in ultrasound image. I have taken the below paper as my base paper and trying to reproduce the results of this paper:

My Base Paper

I designed all the filters and tested with the default matlab images. I was happy with the results. The Mean Square Error (MSE) of filtered image is less than that of Noisy image and the Signal to Noise Ratio (SNR) and Peak Signal to Noise Ratio (PSNR) of the filtered image is greater than that of Noisy image.

But Sadly, When I tried it for ultrasound images the results are opposite. That is the MSE of filtered image is greater than that of Noisy Image and the SNR & PSNR of the filtered image is lesser than that of Noisy Image.

I tried for many other ultrasound images but unable to get it right.

Results for Lena.jpg

*******Quality Measurements***********

*******Noisy Image***********

Mean Square Error = 0.0080186

Signal to Noise Ratio (SNR) = 69.4875

Peak Signal-to-Noise Ratio(PSNR) = 69.0898

*******3 x 3 Median filter***********

Mean Square Error = 0.00257916

Signal to Noise Ratio (SNR) = 74.4137

Peak Signal-to-Noise Ratio(PSNR) = 74.016

*******5 x 5 Median filter***********

Mean Square Error = 0.00188434

Signal to Noise Ratio (SNR) = 75.7769

Peak Signal-to-Noise Ratio(PSNR) = 75.3792

*******7 x 7 Median filter***********

Mean Square Error = 0.00208378

Signal to Noise Ratio (SNR) = 75.34

Peak Signal-to-Noise Ratio(PSNR) = 74.9423

Results for ultrasound.jpg

*******Quality Measurements***********

*******Noisy Image***********

Mean Square Error = 0.00153502

Signal to Noise Ratio (SNR) = 64.8881

Peak Signal-to-Noise Ratio(PSNR) = 76.2697

*******3 x 3 Median filter***********

Mean Square Error = 0.00770785

Signal to Noise Ratio (SNR) = 57.8799

Peak Signal-to-Noise Ratio(PSNR) = 69.2615

*******5 x 5 Median filter***********

Mean Square Error = 0.00810142

Signal to Noise Ratio (SNR) = 57.6637

Peak Signal-to-Noise Ratio(PSNR) = 69.0452

*******7 x 7 Median filter***********

Mean Square Error = 0.00853159

Signal to Noise Ratio (SNR) = 57.439

Peak Signal-to-Noise Ratio(PSNR) = 68.8205

I am unsure why I am getting results like this. I have added code that I have used for quality measures. Please correct me If I have done anything wrong.

function metrics = Metrics1(Orig_Image,Esti_Image)

%---Mean-Square Error(MSE) Calculation
Orig_Image = im2double(Orig_Image);%---Convert image to double class
Esti_Image = im2double(Esti_Image);%---Convert image to double class
[M N] = size(Orig_Image);%---Size of Original Image
err = Orig_Image - Esti_Image;%---Difference between two images
metrics.M_SE = (sum(sum(err .* err)))/(M * N);

%---Signal-to-Noise Ratio(SNR) Calculation
metrics.SNR = 10*log10((1/M*N)*sum(sum(Orig_Image.*Orig_Image))/(metrics.M_SE));

%---Peak Signal-to-Noise Ratio(PSNR) Calculation
if(metrics.M_SE > 0)
metrics.PSNR = 10*log10(255*255/metrics.M_SE);
else
metrics.PSNR = 99;
end

%---Mean and Standard Deviation

%---Beta Calculation
h = fspecial('laplacian');
I1 = imfilter(Orig_Image,h);
I2 = imfilter(Esti_Image,h);
I_1 = mean2(I1);
I_2 = mean2(I2);
metrics.Beta = sum(sum((I1 - I_1).*(I2 - I_2)))./(sqrt(sum(((I1 - I_1).^2).*((I2 - I_2).^2))));
end

• Since the moving average filter is just some kind of low-pass, can it be that the ultrasound images contain lots of energy in the high frequencies? If so, low-pass filtering might do more harm than good. – jan Nov 18 '13 at 12:53
• @jan you may be right but in my base paper that I have mentioned in my post , they were able to get a proper output. See the tables in that paper – Premnath D Nov 18 '13 at 14:53
• Maybe there's a subtle error somewhere. Can you test your code with the image data used in the paper? – jan Nov 19 '13 at 2:22
• I couldn't get the same image for testing.. But I have tested many ultrasound images.. but it is not working.. today, somehow it worked properly for two ultrasound images.. – Premnath D Nov 19 '13 at 14:15