High-order wavelets for hierarchical refinement in inverse rendering

It is common to use factored representation of visibility, lighting and BRDF in inverse rendering. Current techniques use Haar wavelets to calculate these triple product integrals efficiently [Ng et al. 2004]. Haar wavelets are an ideal basis for the piecewise constant visibility function, but suboptimal for the smoother lighting and material functions. How can we leverage compact high-order wavelet bases to improve efficiency, memory consumption and accuracy of an inverse rendering algorithm? If triple product integrals can be efficiently calculated for higher-order wavelets, the reduction in coefficients will reduce the number of calculations, therefore improving performance and memory usage. Some BRDFs can be stored five times more compactly.