On exploiting phase constraint with image wavelet coefficients

This paper investigates the potential of exploiting a phase-related constraint to improve the performance of wavelet-based image coders. The phase-related constraint originates from the fact that the FFT of the 1D intensity profile along an oblique edge is identical up to a fixed phase shift. However, due to the decimation operation of wavelet transform (WT), the linear phase shifting characteristic is destroyed in the wavelet domain. We propose to recover the odd-phase coefficients from the even-phase ones by a novel phase shifting filter and to interpolate the fractional-phase coefficients from the integer-phase ones by Lagrange filters. The fractional amount of phase shift can be estimated from the causal neighbors in the spatial and frequency domain. Our coding results have demonstrated the effectiveness of the proposed techniques for both synthetic and real images.