Fourier and wavelet techniques in denoising and deconvolving sperm whale data from the northern Gulf of Mexico

The Fourier wavelet based regularized deconvolution (ForWaRD) algorithm combines Fourier deconvolution with wavelet denoising, originally proposed by Neelamani et al. (2004) and modified by Herrera et al. (2006). Our research uses the ForWaRD algorithm to process underwater acoustic data emitted by sperm whales in the northern Gulf of Mexico. To yield the best results, we modified the algorithm by applying a) wavelet denoising to smooth the recorded data and b) Fourier deconvolution to separate the signal from the impulse response. Results indicate that changing from Weiner deconvolution, a standard feature of ForWaRD, to least squares deconvolution improves the percent error in data reconstruction with underwater acoustic data. Additional modifications to the type of wavelet thresholding, as well as the wavelet choice for wavelet decomposition, drastically improve the error in the reconstructed signal. The ultimate goal of the work is to better identify individual sperm whales in the northern Gulf of Mexico to create an acoustic catalog of each individual sperm whale’s signal.