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Many existing scene-adaptive nonuniformity correction (NUC) methods suffer from slow convergence rate together with ghosting effects. In this paper, an improved NUC algorithm based on total variation penalized neural network regression is presented. Our work mainly focuses on solving the overfitting problem in least mean square (LMS) regression of traditional neural network NUC methods, which is realized by employing a total variation penalty in the cost function and redesigning the processing architecture. Moreover, an adaptive gated learning rate is presented to further reduce the ghosting artifacts and guarantee fast convergence. The performance of the proposed algorithm is comprehensively investigated with artificially corrupted test sequences and real infrared image sequences, respectively. Experimental results show that the proposed algorithm can effectively accelerate the convergence speed, suppress ghosting artifacts, and promote correction precision.