Mean Squared Error (MSE), Peak Signal to Noise Ratio and compression ratios are estimated from the input image and output image

(A) Mean Squared Error (MSE)

MSE is computed by adding the squared differences of individual pixels without considering the spatial interaction among adjacent pixels. Where MSE is the Mean Squred Error is defined by

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Where I is original image, Id is approximation of compressed

Image and X, Y are dimensions of the image.

(B) Peak Signal to Noise Ratio (PSNR)

PSNR is the ratio between the maximum possible power of a signal and the power of corrupting noise. PSNR is usually expressed in terms of logarithmic decibel scale. The PSNR for gray scale image (8 bits/pixel) is defined by
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Here, MAXI is the maximum pixel value of the image. When the pixels are represented using 8 bits per sample, this is 256. For colour images with three red-green-blue (RGB) values per pixel, the definition of PSNR is the same except the MSE is the sum over all squared value differences divided by image size and by three. Typical values for the PSNR in lossy image and video compression are between 30 and 50 dB, where higher is better.

(C) Compression Ratio (CR)

To get the uncompressed size and the compressed size. Compression ratio (CR) as the ratio of the number of nonzero elements in original matrix to the number of nonzero elements in updated transformed matrix.