  Here we present a method of constructing steerable wavelet frames in
$L_2(\mathbb{R}^d)$ that generalizes and unifies previous approaches, including
Simoncelli's pyramid and Riesz wavelets. The motivation for steerable wavelets
is the need to more accurately account for the orientation of data. Such
wavelets can be constructed by decomposing an isotropic mother wavelet into a
finite collection of oriented mother wavelets. The key to this construction is
that the angular decomposition is an isometry, whereby the new collection of
wavelets maintains the frame bounds of the original one. The general method
that we propose here is based on partitions of unity involving spherical
harmonics. A fundamental aspect of this construction is that Fourier
multipliers composed of spherical harmonics correspond to singular integrals in
the spatial domain. Such transforms have been studied extensively in the field
of harmonic analysis, and we take advantage of this wealth of knowledge to make
the proposed construction practically feasible and computationally efficient.
