New deblocking artifact, or blocking artifact reduction, algorithms based on nonlinear adaptive soft-threshold anisotropic filter in wavelet are proposed. Our deblocking algorithm uses soft-threshold, adaptive wavelet direction, adaptive anisotropic filter, and estimation. The novelties of this paper are an adaptive soft-threshold for deblocking artifact and an optimal intersection of confidence intervals (OICI) method in deblocking artifact estimation. The soft-threshold values are adaptable to different thresholds of flat area, texture area, and blocking artifact. The OICI is a reconstruction technique of estimated deblocking artifact which improves acceptable quality level of estimated deblocking artifact and reduces execution time of deblocking artifact estimation compared to the other methods. Our adaptive OICI method outperforms other adaptive deblocking artifact methods. Our estimated deblocking artifact algorithms have up to 98% of MSE improvement, up to 89% of RMSE improvement, and up to 99% of MAE improvement. We also got up to 77.98% reduction of computational time of deblocking artifact estimations, compared to other methods. We have estimated shift and add algorithms by using Euler++(E++) and Runge-Kutta of order 4++ (RK4++) algorithms which iterate one step an ordinary differential equation integration method. Experimental results showed that our E++ and RK4++ algorithms could reduce computational time in terms of shift and add, and RK4++ algorithm is superior to E++ algorithm.