Assumptions about image continuity lead to oversmoothed edges in common image interpolation algorithms. A wavelet-based interpolation method that imposes no continuity constraints is introduced. The algorithm estimates the regularity of edges by measuring the decay of wavelet transform coefficients across scales and preserves the underlying regularity by extrapolating a new subband to be used in image resynthesis. The algorithm produces visibly sharper edges than traditional techniques and exhibits an average peak signal-to-noise ratio (PSNR) improvement of 2.5 dB over bilinear and bicubic techniques.