Distributed video coding based on sampling of signals with nite rate of innovation

This paper proposes a new approach to distributed video coding. Distributed video coding is a new paradigm in video coding, which is based on the concept of decoding with side information at the decoder. Such a coding scheme employs a low-complexity encoder, making it well suited for low-power devices such as mobile video cameras. The uniqueness of our work lies in the combined use of discrete wavelet transform (DWT) and the concept of sampling of signals with nite rate of innovation (FRI). This enables the decoder to retrieve the motion parameters and reconstruct the video sequence from the low-resolution version of each transmitted frame. Unlike the currently existing practical coders, we do not employ traditional channel coding technique. For a simple video sequence with a xed background, our preliminary results show that the proposed coding scheme can achieve a better PSNR than JPEG2000-intraframe coding at low bit rates. Keywords distributed video compression, wavelet, FRI signals, sampling, moments. 1. INTRODUCTION The rapid growth in the area of "uplink" rich media applications in todays emerging era of mobile devices has sparked the interest in the development of practical distributed coding algorithms. The theoretical foundation, however, dates back to the information theoretic results of Slepian and Wolf and Wyner and Ziv of the 1970s. Slepian and Wolf gave the achievable rate region for the lossless encoding of correlated sources while some extensions to the lossy case were presented in. These results can be used to develop video coding schemes, which use a low-complexity encoder while achieve a better compression e¢ ciency than the "intraframe" coding. This is made possible by shifting the load of computational complexity to the decoder side and the "interframe" dependency of the video sequence is exploited at the receiver. This unconventional balance in complexity is, in fact, a part of the architectural requirements of the "uplink" rich media applications. Existing distributed video coders use sophisticated channel codes to reconstruct the video sequence at the decoder (see for a comprehensive review). In this paper, we investigate the use of discrete wavelet transform (DWT) together with the concept of sampling of signals with nite rate of innovation (FRI) to implement motion estimation at the decoder. We present three coding schemes for the following scenarios: (a) a polygon moving by translation in a uniform background; (b) the extension of (a) to the case where motion can be described by an a¢ ne transform; (c) a real video sequence with a xed background. The problem of bit allocation as well as quantization will also be discussed. In the next section, main results of sampling of FRI signals are discussed. Our proposed distributed coding schemes for the three scenarios are presented in Section 3. In Section 4, we discuss the issue of quantization in our proposed schemes. The preliminary results are given in Section 5. Finally, conclusions are drawn in Section 6. Further author information: (Send correspondence to V.Chaisinthop) V.Chaisinthop: E-mail: varit.chaisinthop02@imperial.ac. uk P.L. Dragotti: E-mail: p.dragotti@imperial.ac. uk 2. SAMPLING OF 2-D FRI SIGNALS Recent developments in sampling theory have focussed on classes of non-band limited signal, one of which is a class of signals with nite rate of innovation (FRI). The de nition and sampling schemes of FRI signals are given in details in. In this section, we will only discuss the main results that will be used in the sequel. The family of sampling kernel used in our setup includes functions that reproduce polynomials and thus satisfy the Strang-Fix conditions. Let a 2-D continuous signal be f(x; y) with x; y 2 R and let the 2-D sampling kernel be '(x; y). In a typical sampling setup, the samples obtained by sampling f(x; y) with '(x; y) are given by: Sm;n = hf(x; y); '(x=T m; y=T n)i ; (1) where h i denotes the inner product and m;n 2 Z. Assume that the sampling kernel satis es the polynomial reproduction property i.e.: X