Wavelet denoising of coarsely quantized signals

This paper presents a practical wavelet-based approach to denoising coarsely quantized signals. Such signals can arise from the status data collected within large-scale engineering plants employing traditional limit checking fault detection and identification (FDI). Transitioning such plants to more advanced FDI techniques requires that the coarsely quantized data be accurately denoised. As FDI by its nature is concerned with the analysis of nonstationary signals, wavelets offer an appropriate denoising framework. Existing techniques for optimal wavelet denoising presuppose Gaussian noise contamination and, hence, are suboptimal for coarsely quantized signals. In this paper, a secondary correction stage is added to the standard wavelet-denoising process to improve its denoising performance on coarsely quantized signals. This correction stage exploits a priori knowledge of the known coarsely quantized signal dependencies to "tune" the wavelet thresholds. The effectiveness of the approach is demonstrated through the analysis of real-world data collected from an operational large-scale engineering plant