Optimal Filtering of Wavelet-based Multiple Description Image Coding Using Correlating Transforms K. Khelil, T. Bouadjila, F. Berrezzek Univ. Souk Ahras, Fac. Sci & Tec., LEER Lab., Souk Ahras (41000), Algeria. k_khelil@yahoo.fr, khaled.khelil@univ-soukahras.dz Abstract— The objective of multiple description coding (MDC) is to encode a single information source into multiple bitstreams, in a manner that the reconstructed source can be produced at different qualities according to the amount of bitstreams received at the decoder. In this paper, we propose to employ an optimal filtering strategy as a post processing method for a multiple description transform coding (MDTC) approach which utilizes discrete wavelet transform (DWT). Experimental results show that the proposed approach provides better results compared to existing approaches in the literature. Keywords— Multiple description transform coding, optimal filtering, discrete wavelet transform, post-processing. I. INTRODUCTION Nowadays the sharing of multimedia information such as image or video over packet switched networks like the Internet is growing fast. Therefore, when transmitting data over such unreliable networks, packet losses and sometimes complete channel failures are practically inevitable. Moreover, packet loss and time delay may cause serious problems in applications that require real time data transmission, and may lead to a severe degradation of the received signal [1]. To alleviate these problems, multiple description coding (MDC) aim at splitting a data source into multiple bitstreams, called descriptions [2, 3]. The MDC coder is designed so that each description can be independently decoded, and the quality of the recovered signal increases smoothly with the number of received descriptions. In the literature, there are several different MDC approaches that have different redundancy adding schemes and complexity. The multiple description scalar quantization (MDSQ) approach proposed by Vaishampayan [4], creates descriptions using index assignment. The method in [5], which is referred to as polyphase downsampling (PD), performs encoding by adding redundancy to subsampled data to make the system robust in case of packet loss. These methods have also been applied to video coding [6-8]. PCT based MDC approaches, used in image coding, can be broadly classified into two main categories. The first class addresses MDTC for the case of two descriptions in the DCT domain [9]-[11]. A generalization of the scheme presented in [11], to more than two descriptions, is described in [12]. The approach falling into the second category uses a correlating transform in the discrete wavelet transform (DWT) domain instead of the DCT [13], [14]. In real applications, different network paths may have dissimilar channel capacities. Accordingly, Saitoh and Yakoha [15] suggested a scheme, referred to as ratio configurable multiple description correlating transform coding (RMDCTC), where the data size is adjusted among the descriptions to fit the inequality of channel bandwidth. Based on compressive sensing (CS), the authors in [16] proposed a rather new MDC approach for the case of two descriptions. In this technique, the input image is divided into two sub-images using quincunx downsampling and then DWT is applied to generate the two descriptions. In [17], the issue of designing near optimal down-sampling filter and interpolation filters, to improve block-based coders such as JPEG, is explored. It has been shown that using such a scheme may results in significant improvement over existing approaches. In this paper, it is proposed to use an optimal filtering approach with the wavelet based MDTC technique reported in [13] to improve the reconstruction quality of the source image. In this method, least-squares estimation is utilized to obtain the filter coefficients [17] minimizing the difference between encoded and original data, for each description. In other words, packets that are lost, due to channel failures, are generated using the received descriptions and the quality of the image, obtained by combining all the descriptions, is enhanced further through optimal filtering.