Stable, linear spline wavelets on nonuniform knots with vanishing moments

In wavelet analysis on nonuniform grids it is desirable that the wavelet scheme is stable in some norm independently of the grid spacing (grid stability). It is known that this kind of stability is difficult to achieve for spline wavelets based on orthogonal complements, with stability measured in the L2-norm. On the other hand, a wavelet scheme based on piecewise linear interpolation (Faber decomposition) is known to be grid stable in the L∞ norm. In this paper we show that Faber decomposition can be extended with preservation of moments, without sacrificing grid stability in the L∞ norm.