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In this paper, a learnable cellular nonlinear network (CNN) with space-variant templates, ratio memory (RM), and modified Hebbian learning algorithm is proposed and analyzed. By integrating both the modified Hebbian learning algorithm with the self-feedback function and a ratio memory into CNN architecture, the resultant ratio-memory (RMCNN) is called the self-feedback RMCNN (SRMCNN) which can serve as the associative memory. It can generate the absolute weights and then transform them into the ratioed A-template weights as the ratio memories for recognizing noisy input patterns. Simulation results have shown that with the stronger feature enhancement effect, the SRMCNN under constant leakage current can store and recognize more patterns than the RMCNN. For 18 /spl times/ 18 SRMCNN, 93 noisy patterns with a uniform distribution noise level of 0.8 and a variance of normal distribution noise of 0.3 can be learned, stored, and recognized with 100% success rate. The SRMCNN has greater learning and recognition capability when the learned patterns are simpler and the noise is lower. For the learning and recognition of complicated patterns, the allowable pattern number is decreased for a 100% success rate. Simulation results have successfully verified the correct functions and better performance of SRMCNN in the pattern recognition. With high integration capability and excellent pattern association performance, the proposed SRMCNN can be applied to nanoelectronic associative-memory systems for image processing applications.