The discrete wavelet transform (DWT) provides an effective and efficient alternative to traditional Fourier and spatial-convolution processing techniques in the enhancement of aeromagnetic data. Standard operators such as horizontal and vertical derivatives, integrals of any order, and the Hilbert transform can be diagonalized in the wavelet domain, leading to an efficient algorithm. The DWT preserves the spatial localization of the components of the signal, allowing for intelligent discrimination between noise and signal in a given frequency range. This, for example, allows for more accurate calculation of higher order derivatives from noisy signals than is possible with conventional techniques. Additional accuracy can be gained by using a cycle-spinning algorithm to minimize local artifacts from the DWT denoising procedure.