READ_ME.md

READ ME file #################################################################

%%%% BCDM problem solution using CVX Library

1. Details can be found in paper: Aniket Roy, Rajat Subhra Chakraborty: "Optimal Distortion Estimation for Prediction Error Expansion Based Reversible Watermarking." IWDW 2016: 265-279.

2. run my_code_1.m for each image.

3. Need to setup CVX library as follows.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %steps for cvx setup % 1. cd C:\personal\cvx-w64\cvx %%% setup the path in which CVX exists % 2. cvx_setup % 3. then run this code % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % Steps: % 1. Read the image % 2. Create error histogram using DCT distribution % 3. Convex optimization based threshold finding % 4. Distortion calculation for given embedding capacity % 5. Plot bpp vs. PSNR.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % sample output %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

cvx_begin variable L minimize( -2b^2entr(L) - (2*b^2 + 0.5)*L ) CVX Warning: Models involving "entr" or other functions in the log, exp, and entropy family are solved using an experimental successive approximation method. This method is slower and less reliable than the method CVX employs for other models. Please see the section of the user's guide entitled The successive approximation method for more details about the approach, and for instructions on how to suppress this warning message in the future. subject to L <= (N - c)/N; cvx_end

Successive approximation method to be employed. For improved efficiency, SDPT3 is solving the dual problem. SDPT3 will be called several times to refine the solution. Original size: 4 variables, 2 equality constraints 1 exponentials add 8 variables, 5 equality constraints

Cones | Errors | Mov/Act | Centering Exp cone Poly cone | Status --------+---------------------------------+--------- 1/ 1 | 9.752e-01 5.825e-02 0.000e+00 | Solved 1/ 1 | 9.178e-02 5.280e-04 0.000e+00 | Solved 1/ 1 | 1.281e-02 1.026e-05 0.000e+00 | Solved 1/ 1 | 1.829e-03 2.092e-07 0.000e+00 | Solved 0/ 1 | 2.603e-04 4.050e-09 0.000e+00 | Solved

Status: Solved Optimal value (cvx_optval): -108.168

echo off

T =

 1

cvx_begin variable L minimize( -2b^2entr(L) - (2*b^2 + 0.5)*L ) subject to L <= (N - c)/N; cvx_end

Successive approximation method to be employed. For improved efficiency, SDPT3 is solving the dual problem. SDPT3 will be called several times to refine the solution. Original size: 4 variables, 2 equality constraints 1 exponentials add 8 variables, 5 equality constraints

Cones | Errors | Mov/Act | Centering Exp cone Poly cone | Status --------+---------------------------------+--------- 1/ 1 | 9.131e-01 5.114e-02 0.000e+00 | Solved 1/ 1 | 1.549e-01 1.506e-03 0.000e+00 | Solved 1/ 1 | 2.132e-02 2.842e-05 0.000e+00 | Solved 1/ 1 | 3.050e-03 5.814e-07 0.000e+00 | Solved 0/ 1 | 4.339e-04 1.176e-08 0.000e+00 | Solved

Status: Solved Optimal value (cvx_optval): -106.352

echo off

T =

 2

cvx_begin variable L minimize( -2b^2entr(L) - (2*b^2 + 0.5)*L ) subject to L <= (N - c)/N; cvx_end

Successive approximation method to be employed. For improved efficiency, SDPT3 is solving the dual problem. SDPT3 will be called several times to refine the solution. Original size: 4 variables, 2 equality constraints 1 exponentials add 8 variables, 5 equality constraints

Cones | Errors | Mov/Act | Centering Exp cone Poly cone | Status --------+---------------------------------+--------- 1/ 1 | 7.524e-01 3.484e-02 0.000e+00 | Solved 1/ 1 | 1.241e-01 9.663e-04 2.052e-11 | Solved 1/ 1 | 1.720e-02 1.849e-05 0.000e+00 | Solved 1/ 1 | 2.457e-03 3.777e-07 0.000e+00 | Solved 0/ 1 | 3.498e-04 7.658e-09 6.471e-12 | Solved

Status: Solved Optimal value (cvx_optval): -103.179

echo off

T =

 3

cvx_begin variable L minimize( -2b^2entr(L) - (2*b^2 + 0.5)*L ) subject to L <= (N - c)/N; cvx_end

Successive approximation method to be employed. For improved efficiency, SDPT3 is solving the dual problem. SDPT3 will be called several times to refine the solution. Original size: 4 variables, 2 equality constraints 1 exponentials add 8 variables, 5 equality constraints

Cones | Errors | Mov/Act | Centering Exp cone Poly cone | Status --------+---------------------------------+--------- 1/ 1 | 5.688e-01 2.000e-02 0.000e+00 | Solved 1/ 1 | 9.076e-02 5.162e-04 5.094e-13 | Solved 1/ 1 | 1.266e-02 1.003e-05 0.000e+00 | Solved 1/ 1 | 1.808e-03 2.044e-07 1.160e-11 | Solved 0/ 1 | 2.575e-04 4.146e-09 0.000e+00 | Solved

Status: Solved Optimal value (cvx_optval): -98.4543

echo off

T =

 4

cvx_begin variable L minimize( -2b^2entr(L) - (2*b^2 + 0.5)*L ) subject to L <= (N - c)/N; cvx_end

Successive approximation method to be employed. For improved efficiency, SDPT3 is solving the dual problem. SDPT3 will be called several times to refine the solution. Original size: 4 variables, 2 equality constraints 1 exponentials add 8 variables, 5 equality constraints

Cones | Errors | Mov/Act | Centering Exp cone Poly cone | Status --------+---------------------------------+--------- 1/ 1 | 3.544e-01 7.800e-03 0.000e+00 | Solved 1/ 1 | 5.427e-02 1.844e-04 0.000e+00 | Solved 1/ 1 | 7.632e-03 3.643e-06 0.000e+00 | Solved 1/ 1 | 1.088e-03 7.401e-08 0.000e+00 | Solved 0/ 1 | 1.548e-04 1.474e-09 0.000e+00 | Solved

Status: Solved Optimal value (cvx_optval): -91.916

echo off

T =

 6

cvx_begin variable L minimize( -2b^2entr(L) - (2*b^2 + 0.5)*L ) subject to L <= (N - c)/N; cvx_end

Successive approximation method to be employed. For improved efficiency, SDPT3 is solving the dual problem. SDPT3 will be called several times to refine the solution. Original size: 4 variables, 2 equality constraints 1 exponentials add 8 variables, 5 equality constraints

Cones | Errors | Mov/Act | Centering Exp cone Poly cone | Status --------+---------------------------------+--------- 1/ 1 | 9.591e-02 5.743e-04 0.000e+00 | Solved 1/ 1 | 1.393e-02 1.214e-05 0.000e+00 | Solved 1/ 1 | 1.975e-03 2.441e-07 0.000e+00 | Solved 0/ 1 | 2.812e-04 4.936e-09 0.000e+00 | Solved

Status: Solved Optimal value (cvx_optval): -83.1975

echo off

T =

 7

cvx_begin variable L minimize( -2b^2entr(L) - (2*b^2 + 0.5)*L ) subject to L <= (N - c)/N; cvx_end

Successive approximation method to be employed. For improved efficiency, SDPT3 is solving the dual problem. SDPT3 will be called several times to refine the solution. Original size: 4 variables, 2 equality constraints 1 exponentials add 8 variables, 5 equality constraints

Cones | Errors | Mov/Act | Centering Exp cone Poly cone | Status --------+---------------------------------+--------- 1/ 1 | 2.313e-01 3.364e-03 2.196e-12 | Solved 1/ 1 | 3.125e-02 6.105e-05 0.000e+00 | Solved 1/ 1 | 4.476e-03 1.253e-06 0.000e+00 | Solved 1/ 1 | 6.361e-04 2.530e-08 0.000e+00 | Solved 0/ 1 | 9.051e-05 4.916e-10 0.000e+00 | Solved

Status: Solved Optimal value (cvx_optval): -71.7431

echo off

T =

 9

cvx_begin variable L minimize( -2b^2entr(L) - (2*b^2 + 0.5)*L ) subject to L <= (N - c)/N; cvx_end

Successive approximation method to be employed. For improved efficiency, SDPT3 is solving the dual problem. SDPT3 will be called several times to refine the solution. Original size: 4 variables, 2 equality constraints 1 exponentials add 8 variables, 5 equality constraints

Cones | Errors | Mov/Act | Centering Exp cone Poly cone | Status --------+---------------------------------+--------- 1/ 1 | 6.814e-01 2.946e-02 0.000e+00 | Solved 1/ 1 | 8.243e-02 4.244e-04 0.000e+00 | Solved 1/ 1 | 1.194e-02 8.921e-06 0.000e+00 | Solved 1/ 1 | 1.695e-03 1.796e-07 0.000e+00 | Solved 0/ 1 | 2.413e-04 3.528e-09 0.000e+00 | Solved

Status: Solved Optimal value (cvx_optval): -56.6094

echo off

T =

12

cvx_begin variable L minimize( -2b^2entr(L) - (2*b^2 + 0.5)*L ) subject to L <= (N - c)/N; cvx_end

Successive approximation method to be employed. For improved efficiency, SDPT3 is solving the dual problem. SDPT3 will be called several times to refine the solution. Original size: 4 variables, 2 equality constraints 1 exponentials add 8 variables, 5 equality constraints

Cones | Errors | Mov/Act | Centering Exp cone Poly cone | Status --------+---------------------------------+--------- 1/ 1 | 1.423e+00 1.303e-01 0.000e+00 | Solved 1/ 1 | 1.381e-01 1.190e-03 0.000e+00 | Solved 1/ 1 | 2.026e-02 2.569e-05 0.000e+00 | Solved 1/ 1 | 2.873e-03 5.161e-07 0.000e+00 | Solved 0/ 1 | 4.097e-04 1.047e-08 0.000e+00 | Solved

Status: Solved Optimal value (cvx_optval): -35.81

echo off

T =

17

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