Wavelet transform based detection of photon-limited and low contrast objects

This paper presents methods for detection and localization of photon-limited objects in noise. As opposed to the correlation based or Fourier transform based techniques which exhibit sensitivity to object scaling, we propose a method based on the continuous wavelet transform with its ability to reject noise and to localize objects in space and time as well as in scale. An advantageous twist presented here is the use of the wavelet transform on the complex envelope of the signal of interest. This has the advantage of reducing “rippling” effects seen in the transform of the original waveform. An example of further post-processing on the wavelet-transformed data is provided.