Subset averaged median filters

Abstract

By analyzing the subset averaged median (SAM) filter based on threshold decomposition, we show that the class of SAM filters is identical to the class of extended threshold Boolean filters (ETBFs) with the extended self-dual property. This result indicates that the class of SAM filters encompasses a variety of digital filters such as linear FIR, weighted median, symmetric L-filters and any filter defined by a linear combination of these filters. A procedure for determining an optimum SAM filter in the mean square error (MSE) sense is developed. It is shown that the optimization of SAM filters may result in an FIR Wiener filter when the input is Gaussian and in a median-type filter for non-Gaussian inputs. The SAM predictor is applied to the differential pulse code modulation(DPCM) coding of images. It is observed that DPCM coders with SAM predictors tend to isolate, not propagate, transmission errors in reconstructing input signals at the receiver. The error isolation condition of DPCM employing SAM predictors is derived. We also observe the importance of the DPCM decoder stability and derive a condition which guarantees the stability of DPCM with SAM predictors. Based on these results, we consider the design of median-based predictors that guarantees both the decoder stability and the channel error isolation characteristic, while minimizing the prediction error variance. It is shown that the designed SAM predictors can cause smaller prediction error variance and at the same time are robust to transmission errors. Computer simulations and experiments with real images show that the DPCM system employing SAM predictors is a useful alternative to the conventional DPCM system.