In this paper a G-Let based authentication technique has been proposed to authenticate digital documents through Hough transform generated signature generated from original autograph. The cover image is transformed into G-Let domain to generate n number of G-Lets out of which (n/2)-1 numbers of G-Lets are embedded with secret Hough signature bits for the purpose of authentication or copyright protection. The special feature of AHSG is to optimize the distortion rate, by adjustment at the last stage of the technique, using back propagation. Experimental results are computed and compared with the existing authentication techniques like Li's method, SCDFT, Region-Based method based on Mean Square Error (MSE), Peak Signal to Noise Ratio (PSNR), Image Fidelity (IF), Universal Quality Image (UQI) and Structural Similarity Index Measurement (SSIM) which shows better performance in AHSG, in terms of low computational complexity and better fidelity.