  The deconvolution, or cleaning, of radio interferometric images often
involves computing model visibilities from a list of clean components, in order
that the contribution from the model can be subtracted from the observed
visibilities. This step is normally performed using a forward fast Fourier
transform (FFT), followed by a 'degridding' step that interpolates over the uv
plane to construct the model visibilities. An alternative approach is to
calculate the model visibilities directly by summing over all the members of
the clean component list, which is a more accurate method that can also be much
slower. However, if the clean components are used to construct a model image on
the surface of the celestial sphere then the model visibilities can be
generated directly from the wavelet coefficients, and the sparsity of the model
means that most of these coefficients are zero, and can be ignored. We have
constructed a prototype imager that uses a spherical-wavelet representation of
the model image to generate model visibilities during each major cycle, and
find empirically that the execution time scales with the wavelet resolution
level, J, as O(1.07 J), and with the number of distinct clean components, N_C,
as O(N_C). The prototype organises the wavelet coefficients into a tree
structure, and does not store or process the zero wavelet coefficients.
