JPEG Algorithm $-$ DCT Transform SOLVE WITH MATLAB GIVE THE CODE AND EXPLAIN.

DCT $8$x$8$ coefficient matrix is given below

FIND COE $=$ DCT IMG DCT$^$T and reconstruct the image REC $=DC{T}^T$COEDCT

a$)$ by using only one coefficient

b$)$ by using ony four largest $($amplitude$)$ coefficients

c$)$ by using ony $16$ largest $($amplitude$)$ coefficients out of $64$ coefficients

$DCT(8x8)$ matrix is given below.

$\backslash$table$[[0\mathrm{.}3536,0\mathrm{.}3536,0\mathrm{.}3536,0\mathrm{.}3536,0\mathrm{.}3536,0\mathrm{.}3536,0\mathrm{.}3536,0\mathrm{.}3536],[0\mathrm{.}4904,0\mathrm{.}4157,0\mathrm{.}2778,0\mathrm{.}0975,-0\mathrm{.}0975,-0\mathrm{.}2778,-0\mathrm{.}4157,-0\mathrm{.}4904],[0\mathrm{.}4619,0\mathrm{.}1913,-0\mathrm{.}1913,-0\mathrm{.}4619,-0\mathrm{.}4619,-0\mathrm{.}1913,0\mathrm{.}1913,0\mathrm{.}4619],[0\mathrm{.}4157,-0\mathrm{.}0975,-0\mathrm{.}4904,-0\mathrm{.}2778,0\mathrm{.}2778,0\mathrm{.}4904,0\mathrm{.}0975,-0\mathrm{.}4157],[0\mathrm{.}3536,-0\mathrm{.}3536,-0\mathrm{.}3536,0\mathrm{.}3536,0\mathrm{.}3536,-0\mathrm{.}3536,-0\mathrm{.}3536,0\mathrm{.}3536],[0\mathrm{.}2778,-0\mathrm{.}4904,0\mathrm{.}0975,0\mathrm{.}4157,-0\mathrm{.}4157,-0\mathrm{.}0975,0\mathrm{.}4904,-0\mathrm{.}2778],[0\mathrm{.}1913,-0\mathrm{.}4619,0\mathrm{.}4619,-0\mathrm{.}1913,-0\mathrm{.}1913,0\mathrm{.}4619,-0\mathrm{.}4619,0\mathrm{.}1913],[0\mathrm{.}0975,-0\mathrm{.}2778,0\mathrm{.}4157,-0\mathrm{.}4904,0\mathrm{.}4904,-0\mathrm{.}4157,0\mathrm{.}2778,-0\mathrm{.}0975]]$