The primary purpose of this work was to study the morphological change of river-bed sediment surfaces over time using wavelet transform analysis techniques. The wavelet transform is a rapidly developing area of applied mathematics in both science and engineering. As it allows for interrogation of the spectral made up of local signal features, it has superior performance compared to the traditionally used Fourier transform which provides only signal averaged spectral information. The main study of this thesis includes the analysis of both synthetically generated sediment surfaces and laboratory experimental sediment bed-surface data. This was undertaken using two-dimensional wavelet transform techniques based on both the discrete and the stationary wavelet transforms. A comprehensive data-base of surface scans from experimental river-bed sediment surfaces topographies were included in the study. A novel wavelet-based characterisation measure - the form size distribution ifsd) - was developed to quantify the global characteristics of the sediment data. The fsd is based on the distribution of wavelet-based scale-dependent energies. It is argued that this measure will potentially be more useful than the traditionally used particle size distribution (psd), as it is the morphology of the surface rather than the individual particle sizes that affects the near bed flow regime and hence bed friction characteristics. Amplitude and scale dependent thresholding techniques were then studied. It was found that these thresholding techniques could be used to: (1) extract the overall surface structure, and (2) enhance dominant grains and formations of dominant grains within the surfaces. It is shown that assessment of the surface data-sets post-thresholding may allow for the detection of structural changes over time.