Twofold of algebraic decomposition method used for a watermarking scheme with $LWT$ over medical images

Mathematics has always been of great importance in various sciences, especially computer science. The mechanism used to embed various types of information in a host medical images to safeguard the privacy of the patient including the patient's name, doctor's digital signature is called watermarking. There are a lot of improved watermark algorithms, however, this information is susceptible to attack when the data are transferred over universal internet channels. This paper proposed a robust watermark algorithm that uses a Lifting Wavelet Transform $(LWT)$ and two times of the Hessenberg Matrix Decomposition Method $(HMDM)$ to embed a watermark in a chosen channel of the host image after performing the transform. The experimental results demonstrate that the improvement appears (higher robustness against $JPEG$ compression attack) and good imperceptibility against some attacks, to evaluate the fineness of the original with watermarked images and the extracted watermark respectively.