Wavelet analysis in SAR ocean image profiles for internal wave detection and wavelength estimation

Oceanographers and remote sensing researchers have long recognized the potential of using satellite imagery for studying oceanic internal waves, Radars are able to image internal waves because they are particularly sensitive to changes in the small-scale surface roughness (i.e., the capillary and ultragravity waves) present on the ocean surface which are altered by the velocity field associated with the internal waves, If, as seems likely, the greytone patterns of these images can be confirmed to correspond to trough and crest patterns of internal waves, then a great deal can be learnt about internal waves from satellite data, In this paper, the utility of wavelet analysis as a tool for oceanic internal wave detection and wavelength estimation Is examined using both continuous and discrete versions of the wavelet transform, The theoretical background of each procedure is briefly described and applied using a specific ''wavelet'' for each case, In this first approach, we only consider supervised detection for the internal wave train detection problem, Normally, an unsupervised method using the two-dimensional (2-D) wavelet transform is required for internal wave detection and orientation, including land-sea separation to avoid false alarms, We first present the construction of an appropriate wavelet basis, based on an oceanographic soliton internal wave analytical model, to detect and localize nonlinear wave signatures from SAR ocean image profiles, The structure of arbitrary wavelet basis derived from the compactly supported orthonormal B-splines wavelets is studied so as to obtain more optimal discrete wavelet decompositions, Comparisons are made for wavelet decompositions based on several families of compactly supported wavelets, Finally, the continuous wavelet transform is applied to estimate energies and wavelengths within soliton peaks from the detected internal wave trains, The advantages and drawbacks of the continuous and discrete wavelet transforms for the internal wave detection problem from SAR ocean image profiles are also discussed, The results from this study show that wavelet analysis is an excellent tool to detect internal waves against background noise, and to estimate, with a good degree of precision, soliton wavelengths from SAR ocean image profiles.