Algorithm 3: Proposed Image Compression

1: Apply the improved embedding to the medical image.

2: Perform the extraction operation.

3: Apply the hard threshold using             $y_{hard}\left(t\right)=x\left(t\right) when abs\left(x\left(t\right)\right)>T$             $y_{hard}\left(t\right)=0, when abs\left(x\left(t\right)\right)\le T$

4: Perform the soft threshold using             $y_{soft}\left(t\right)=x\left(t\right)-T when abs\left(x\left(t\right)\right)>T$             $y_{soft}\left(t\right)=0, when abs\left(x\left(t\right)\right)\le T$

5: Find the entropy encoding h(s).             $h\left(s\right)=-{\displaystyle \sum _{j=1}^q}p\left(s_i\right)log p\left(s_i\right)$

6: Determine the Shannon entropy M(C(b))).

7: Apply the wavelets based multi resolution analysis.

8: Define the Haar transform $I_{k, n}=[k{2}^{-n}$, $\left(k+1\right)2^{-n}]$

9: Perform the dilation using             $\varnothing \left(x\right)=\sqrt{2}{\displaystyle \sum _{k\in z}}\varnothing \left(-k+2x\right)h\left(k\right)$

10: Apply the wavelet operation using             $\phi \left(x\right)=\sqrt{2}{\displaystyle \sum _{k\in z}}g\left(-k+2x\right)g\left(k\right)$

11: Perform filtering operations using orthogonal quadrature.             $h\left(i\right)={\displaystyle \sum _{j=-\infty }^{\infty }}u\left(j\right).h\left(-j+2i\right)$             $g\left(i\right)={\displaystyle \sum _{j=-\infty }^{\infty }}u\left(j\right).g\left(-j+2i\right)$

12: Apply the filters using bi-orthogonal quadrature.

13: Decompose the image using wavelets and apply the color conversion.             $\left[\begin{array}{c}Y\\ C_b\\ C_r\end{array}\right]=\left[\begin{array}{ccc}0.3& 0.6& 0.1\\ -0.2& -0.3& 0.5\\ 0.5& -0.4& -0.1\end{array}\right]\left[\begin{array}{c}R\\ G\\ B\end{array}\right]$

14: Find RGB using             $\left[\begin{array}{c}R\\ G\\ B\end{array}\right]=\left[\begin{array}{ccc}1& 0.1& 1.3\\ 1& 0.3& -0.5\\ 1& 1.8& -0.1\end{array}\right]\left[\begin{array}{c}Y\\ C_b\\ C_r\end{array}\right]$

15: Apply the lossless compression through             $\left[\begin{array}{c}{Y}_r\\ V_r\\ U_r\end{array}\right]=\left[\begin{array}{c}\left(2G+R+B\right)/4\\ R-G\\ B-G\end{array}\right]$             $\left[\begin{array}{c}G\\ R\\ B_r\end{array}\right]=\left[\begin{array}{c}{Y}_r-\left(V_r+U_r\right)/4\\ G+V_r\\ G+U_r\end{array}\right]$