$2.$ The discrete cosine transform $($DCT$)$ represents an image as a sum of sinusoids of varying

magnitudes and frequencies. The functions of DCT computes the two$-$dimensional DCT of an

image. The DCT has the property that, for a typical image, most of the visually significant

information about the image is concentrated in just a few coefficients of the DCT$.$ For this reason,

the DCT is often used in image compression applications

a$)$ Write a MATLAB Program to obtain low bit rate block and compressed image quality using

Discrete cosine transform $($DCT$)$ coding $(20$ Marks$)$

b$)$ Detail each step of compression and decompression and reduce the size to $8$x$8$ nonoverlapping blocks with DCT quantized coefficients for blocking artifacts by MATLAB program.

$(20$ Marks$)$

c$)$ Highlight the results of reduced artifacts and validate the quality using Peak Signal to Noise

Ratio $($PSNR$)$ value. Justify the result.