This document discusses using an adaptive discrete wavelet transform (ADWT) technique for image fusion of synthetic aperture radar (SAR) images. The ADWT technique adapts the filter coefficients in the discrete wavelet transform through a bat algorithm optimization to minimize mean squared error and improve peak signal to noise ratio compared to conventional DWT. SAR images of San Francisco Bay captured at different times are fused using DWT with Daubechies and Symlet wavelets as well as the proposed ADWT technique. The results show that ADWT achieves a slightly lower MSE than DWT with Symlet wavelets and a significantly higher PSNR, demonstrating the effectiveness of the proposed ADWT image fusion method.