Watermarking is a valuable technique for verifying medical images obtained through the internet for diagnosis. There is a greater need for security in medical pictures with ever- increasing security risks. This research presented a Finite Ridgelet Transform (FRT)-Hessenberg based watermarking scheme in medical images. The suggested paradigm is divided into two stages. Before watermark insertion, FRT is applied to medical images. The coefficients are combined into blocks of 4 x 4 and each block is decomposed using Hessenberg decomposition. The second column of the Q matrix is used to insert the watermark using the additive quantization technique. The results obtained from our experiment have given good visual quality of the watermarked images. The high PSNR value 53.6121 and NC value 1.0 show that our scheme is performing better. Moreover, the performance of our scheme is robust against several attacks. The consequences of this result imply that the anticipated scheme is effective for medical image watermarking.