Multirate Filter Bank-based Conversion of Image Resolution Fumio Itami Faculty of Engineering, Saitama Institute of Technology, 1690, Fusaiji, Fukaya, Saitama, 369-0293, Japan E-mail:itami@sit.ac.jp Eiji Watanabe Faculty of Systems Engineering, Shibaura Institute of Technology, 307, Fukasaku, Saitama-shi, 330-8570, Japan Akinori Nishihara The Center for Research and Development of Educational Technology, Tokyo Institute of Technology, Tokyo, 152-8552, Japan Abstract— This paper proposes a multirate processing scheme for the conversion of image resolution by using filter banks. A resolution-converted signal is synthesized from decom- posed ones by the filter banks. A new design of filter banks for resolution conversion is proposed. The design strategy is that we make the output of synthesis filter banks nearly equal to the one of a direct resolution conversion approach. Simulation results are also given, in which we examine the performance of the proposed synthesis scheme. Keywords—filter banks, multirate signal processing I. I NTRODUCTION The conversion of image resolution is often required in many applications such as representing, editing and print- ing images. So far, several conversion schemes have been proposed[1]-[2]. Fundamentally up-sampling processing by interpolation is used to increase the image resolution, and down-sampling processing by decimation is used to decrease it. An approach referred to as direct rate conversion is accompanied by lowpass filters to suppress aliasing and imaging components caused by interpolation and decimation. Although this approach is simple, it gives good resolution- converted images. By the way, filter banks are used for many applications such as image compression, and numbers of their designs have been proposed[3]-[5]. The structure of a filter bank is similar to the one for the conversion of image resolution in the sense of including decimator, interpolator and filters. Therefore, it is possible that resolution-converted images can be synthesized from the decomposed components of original images, which are the output of analysis filter banks[6]. The structural advantages of such a filter bank- based approach are as follows. Sub-band processing can be directly carried out in the structure of resolution conversion without additional filter banks, whereas the direct conversion requires another filter bank for sub-band processing. In addition, resolution conversion and sub-band processing is implemented simultaneously, not sequentially. These lead to the reduction of processing complexity. However, it is not so easy to synthesize good resolution-converted images without experimental designs. In Ref.[6] the improvement of the quality of converted images remains to be studied. This paper treats the conversion of image resolution using filter banks. On the basis of the fundamental idea proposed in [6], we propose a new design of filter banks for resolution conversion. First, we briefly review the frequency characteristics of the decomposed signals, which are the output of analysis filter banks. We also review a scheme for the resolution conversion. Next, we propose a design method for filter banks for the scheme. The design strategy is that we make the output of synthesis filter banks nearly equal to the one of the direct conversion, whereas conventional filter banks are designed in order to be ’delay’ under so-called perfect reconstruction conditions. Finally, we examine the performance of the proposed synthesis scheme by simulation examples. II. THE FREQUENCY CHARACTERISTICS OF THE DECOMPOSED SIGNALS The analysis part given in Fig.1 shows a special structure of integer/fractional sampling filter banks[3], where the last analysis channel only contains down-sampling without up- sampling. We discuss resolution conversion by using this structure. The decomposed signals by the analysis part are described as Y c,i (z)= 1 L 2 L2-1  r=0 X(W L1r z L 1 L 2 )H i (W r z 1 L 2 ) (i =0, 1, ··· ,N − 2) (1) and Y c,N-1 (z)= 1 L 2 L2-1  r=0 X(W r z 1 L 2 )H N-1 (W r z 1 L 2 ) (2) where W = e -j 2π L 2 (3) holds. We illustrate the frequency characteristics of these signals in 2(a)-(e). Note that the bold lines represent π [rad] on the frequency axes. Fig.2(a) shows the one of the original 1232 1-4244-0387-1/06/$20.00 c 2006 IEEE