Orthonormal wavelets with balanced uncertainty

This paper addresses the question: `what makes a good wavelet for image compression?´, by considering objective and subjective measurements of quality. A new metric is proposed for the design of the finite impulse response (FIR) filters used in the discrete wavelet transform (DWT). The metric is the diagonal of the Heisenberg uncertainty rectangle, with time weighted by a factor k relative to frequency. Minimization of the metric balances the time and frequency spreads of the filter response. The metric can be computed directly from the filter coefficients, so it can be used to optimize wavelets for image compression without the cost of repeatedly compressing and decompressing images. A psychovisual evaluation carried out with 24 subjects demonstrates that orthonormal FIR filters designed this way give good subjective results with zerotree image compression. With suitably chosen k, both better subjective quality and lower RMS error are achieved than with wavelets chosen for maximum regularity