Entropy-aware lightweight fault-tolerant median filtering
Mehrnaz Monajati · Microelectronics Reliability · 2026
This paper presents ATMED, an entropy-aware fault-tolerant median-filtering architecture that integrates Approximate Triple Modular Redundancy (ATMR) within the comparator hierarchy. Unlike conventional approaches that use approximation primarily for hardware reduction, ATMED exploits controlled approximation as an active fault-masking mechanism. The proposed design introduces 14 Redundant Eight-Bit Comparator (REBC) configurations that combine exact, approximate, and non-redundant Two-Bit Comparators (TBCs), enabling fine-grained trade-offs between reliability and hardware efficiency. To characterize fault behavior, this work introduces the Histogram-Weighted Undetected Fault Dispersion Profile (HUFDP), together with the Error Dispersion Score (EDS) and Entropy-Weighted EDS (EWEDS), which jointly capture fault distribution and image statistics. Experimental results show that several hybrid configurations (e.g., TAAA, TAAN, and TTAA) achieve reliability statistically comparable to full TMR (TTTT), with overlapping 95% confidence intervals and reliability differences on the order of 10 −6 –10 −5 . Comparator-level synthesis demonstrates up to 42.5% area reduction relative to TTTT, while system-level implementations achieve up to 72% area reduction and up to 85% reduction in power–delay product (PDP) compared with a conventional full-TMR median filter. Image-quality evaluation using PSNR and MSSIM confirms negligible perceptual degradation under combined noise and fault conditions. Entropy-aware redundancy enables scalable, energy-efficient, fault-resilient median filtering.