Ultrasonic self-normalized wavelet-based detection and estimation of unknown transient vibrations in colored Gaussian noise and strong, low frequency clutter

The detection and quantitation of transitory audio frequency sounds originating from within the body are useful diagnostic tools. Such sounds arising from arterial stenoses, aneurysms and arterio-venous shunts, which are often superimposed on ultrasound Doppler data, may have short durations and varying frequencies. Automated detection and estimation (characterization) of these vibrations may enhance diagnosis of these disorders. The noise may be both non-stationary and colored, but can be assumed Gaussian; the clutter due to arterial wall movement may be extremely large. This paper addresses this detection challenge by using a binary hypothesis test for noise only, based on the continuous Morlet wavelet power spectrum normalized by adaptive noise variance estimates. The algorithm yields rough estimates of the amplitude, frequency range, time location and duration of detected vibrations. Simulated receiver operating curves are presented for short duration transient vibrations in colored and slowly time varying Gaussian noise and in 60 dB clutter. These curves indicate that this method achieves expected detection rates in excess of 99.8% at false alarm rates of 0.1% for (signal-on) signal to noise ratios as small as 1. A comparison is included to a slight modification of Wang and Willett´s recently published self-normalizing extension of Nutall´s power law detector. Although the two detectors yield similar results in the absence of clutter, the new detector achieves the same high detection rates when clutter is present while also providing estimates of the detected vibrations´ parameters.