Dyadic Lifting Wavelet Based Signal Detection Theory and Simulation for Performance Evaluation

Local regularities of a signal contain important information such as edges in an image and QRS complexes in an Electrocardiogram (ECG). In order to detect such local regularities in the signal, wavelet transform has been focused on as a powerful tool for signal processing applications. Wavelet maxima at the time in which the signal abruptly changes are usually large in amplitude. However, with only the magnitude of the wavelet maxima the features of the signal cannot be known in detail. Mallat et al. proposed the Lipchitz regularity for observing signal cross scales in multiresolution signal analysis, but its computational cost was relatively expensive. This paper presents a novel method for signal detection using lifting dyadic wavelet transform, which has the time-invariant property. The lifting wavelet parameters contained in Swelden's formula were tuned, adapting them to the signals to be detected. The method for tuning these parameters was to learn the features of the target signals in the multiresolution analysis. To evaluate our methods we applied them to detect the QRS complexes contained in an ECG. The results showed that our methods were useful to detect target signals accurately.