A comparative study of image compression based on directional wavelets Discrete wavelet transform is an effective tool to generate scalable stream, but it cannot efficiently represent edges which are not aligned in horizontal or vertical directions, while natural images often contain rich edges and textures of this kind. Hence, recently, intensive research has been focused particularly on the directional wavelets which can effectively represent directional attributes of images. Specifically, there are two categories of directional wavelets: redundant wavelets (RW) and adaptive directional wavelets (ADW). One representative redundant wavelet is the dualtree discrete wavelet transform (DDWT), while adaptive directional wavelets can be further categorized into two types: with or without side information. In this paper, we briefly introduce directional wavelets and compare their directional bases and image compression performances.

Scalable direction representation for image compression with directionadaptive discrete wavelet transform The directionadaptive discrete wavelet transform (DADWT) locally adapts the filtering direction to the geometric flow in the image. DADWT image coders have been shown to achieve a ratedistortion performance superior to nonadaptive wavelet coders. However, since the direction information must always be signalled regardless of total bitrate, performance at very low bitrates might be worse. In this paper, we propose two scalable direction representations: the layered scheme which is similar to the scalable motion vector representation in scalable video coding and the levelunit scheme which provides finer granularity upon the layered scheme. Experimental results indicate that we can achieve the desirable performance at both low and high bit rates with our proposed levelunit scheme. Significant improvement in image quality (about 35 dB) is observed at very low bit rate, relative to nonscalable coding of the direction information.