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This paper presents likelihood processing (LP) for designing robust and energy-efficient multimedia systems in the presence of nanoscale non-idealities. LP exploits error statistics of the underlying hardware to compute the probability of a particular bit being a one or a zero. Multiple output observations are generated via either: 1) modular redundancy (MR), 2) estimation, or 3) exploiting spatio-temporal correlation. Energy efficiency and robustness of a 2D discrete-cosine transform (DCT) image codec employing LP is studied. Simulations in a commercial 45-nm CMOS process show that LP can tolerate up to 100×, and 5× greater component error probability as compared to conventional and triple-MR (TMR)-based systems, respectively, while achieving a peak-signal-to-noise ratio (PSNR) of 30 dB at a pre-correction error rate of 20%. Furthermore, LP is able to achieve energy savings of 71% over TMR at a PSNR of 28 dB, while tolerating a pre-correction error rate of 4%.