Hyperanalytic Thresholding

A new thresholding criterion is introduced, and combined with a local function decomposition, to form an estimate of a deterministic image immersed in white noise. The purpose of the new threshold is to construct image estimates exhibiting continuity jointly across spatial location and spatial frequency. The new threshold criterion is based on the magnitudes of the local decomposition coefficients of the image and phase-shifted versions of the image. Two possible sets of phase-shifted versions are used, and suitable universal thresholds noted. The additional computational cost of the proposed procedure is minor, and thus it makes an attractive improvement to existing thresholding methodology. Examples are given where the reconstructed image, using the new threshold, has improved visual characteristics, as well as a reduced mean square error.