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${b_{1_{new}}$ and $b_{k_{new}}\}$ in the equations 4.5 and 4.6 are integers.Their fractional part is ignored.Apply ${s_{i_{new}}$ and ${o_{i_{new}}}$ to \${{a_{k+1} ,a_{k+2} ,a_{k+3} ,...,a_{n}\}}$ producing \${b_{(k+1)_{new}},b_{(k+2)_{new}},b_{(k+3)_{new}},...,b_{n_{new}}\}$. Now,we write only \${b_{1_{new}},b_{(k+1)_{new}},b_{(k+2)_{new}},...,b_{n_{new}}\}$ over the corresponding pixels of $R_i$.