Nowadays, highly sensitive medical images are vulnerable to data threats and privacy attacks. They must be kept secure while transmitting them across insecure channels precisely for this purpose. The robust image steganography is focused on this work by exploiting Redundant Integer Wavelet Transform (RIWT), Laplacian Pyramid, Arnold scrambling and Histogram shifting algorithm to facilitate secure communication of secret images in the context. Stego images thus generated are subjected to a deep learning approach to assess if it can be classified as a cover or not. If not, the HS parameter is modified to generate stego images in such a way to classify it as a cover image. Thus it is difficult to suspect the existence of a secret image by the Human Visual System (HVS). The efficiency of our method is analyzed by comparing it with related methods present in the literature. Average NCC values between the original secret image and the extracted secret image are 0.8917 which is higher than the schemes in the literature. Average PSNR values of the stego image are 36.375 even when the embedding rate is increased to 4 bits per pixel. The analysis was done on security and robustness also reveals better results. From the experimental analysis, it is proved that the proposed method is superior to the related methods of the literature. © 2020, Springer-Verlag GmbH Germany, part of Springer Nature.