In signal approximation, classical wavelet synthesis are known to produce Gibbs-like phenomenon around discontinuities when wavelet coefficients in the cone of influence of the discontinuities are quantized. By analyzing a function in a piecewise manner, filtering across discontinuities can be avoided. Using this principle, the interval wavelet transform can generate sparser representations in the vicinity of discontinuities than classical wavelet transforms. This work introduces two new constructions of interval wavelets and shows how they can be used for image compression and upscaling.
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