Decimated Wavelet Representation of Images – Application to Compression

A new way to improve the representation of images using a discrete wavelet transform for coding purposes is presented. The idea lies in combining all wavelet coefficients related to detail information at a same resolution level but along different orientations (horizontal, vertical, and diagonal), into a single image. Given that detail information is located for all subband images in the neighborhood of high frequency textures or edge locations, the pattern of significant coefficients remains unchanged after the combination process. This process allows one to further reduce the number of transformed coefficients by 2/3, while preserving the multiresolution structure. This information can thus be efficiently coded using a multiresolution embedded coding scheme, such as Shapiro's (see IEEE Trans. on Signal Proc., vol.SP-41, no.12, p.3445-62, 1993) zerotree coder. Overall, a higher coding efficiency can be reached while preserving the cross-scale prediction of significance among the coefficients. Ultimately, approximate detail information must be recovered from the combined and coded data for each subband of the original wavelet, so as to reconstruct a decoded image