A lossless H.263 video codec using the reversible DCT

Unified lossless and lossy image coding system is useful for various applications, since we can reconstruct lossy and lossless images from a part and the whole of the encoded data, respectively. This coding system can be realized by using reversible transforms. Reversible wavelet transform (R WT), Lossless-DCT (LDCT) and reversible Walsh-Hadamard transform (R WHT) have been proposed as reversible transforms. In this paper, an N-point reversible discrete cosine transform (RDCT) based H.263 video codec is presented, then 8-point RDCT is obtained by substituting the 2 and 4-point reversible transforms for 2 and 4-point transforms which compose 8-point discrete cosine transform (DCT), respectively. Integer input signal can be losslessly recovered, although the transform coefficients are integer numbers. The RDCT is then implemented on the H.263 video codec. Simulations of the RDCT-based H.263 shows a petfect reconstruction of the original video sequence in lossless mode, and lossy compression efJiciencies comparable to those obtained with the conventional fast DCT-based H.263 in low bit rates. where L.1 corresponds to downward truncation, 80 and el are integer transform coefficients and ~0 and X I are integer inputs. If the real numbers CO and C I satisfy CO C I 5 0, this transform becomes reversible. If the floor functions are deleted, the determinant of the transform matrix becomes (1 CO cl). Therefore redundancy occurs in transform domain, when co cI < 0. This problem is avoided by using the following transform instead: It is obvious that this transform is reversible for any co and c1. If the floor functions are deleted, the coefficients of xo and X I of 81 become cI and ( I+ CO cl), respectively, that is, the determinant becomes 1. However, the problem that the dynamic range is nonuniform remains. The dynamic range can become uniform by using the following transform instead: I. THE REVERSIBLE DISCRETE COSINE TRANSFORM: RDCT In this section, a reversible discrete cosine transform (RDCT) is presented. When integer input signal is transformed by DCT, the transform Eoefficients become real. Therefore the quantization step must be reduced in order to reconstruct input losslessly. This results in low compession efficiency. where the transform coefficients are and Oz. a) 2-Point Reversible Transform: Let's consider the following 2-point transform: 0-7803-8575-6/04/$20.00 02004 IEEE 407 Figure 1 : 2-Point Reversible Transform Ladder Network. (3) Figure 1 shows the ladder network for the 2-point reversible transform, where quantizer, R, represents rounding to the nearest integer, xi are integer inputs, 0i are integer outputs and ci are real multipliers. If the floor functions are deleted, the coefficients of xo and XI of 81 become cl and (1+ CO cl), respectively, and those of 02 become (1+ C I CZ) and (CO+ c2f CO C I c2), respectively, Therefore, the determinant becomes 1 : [:]=[I CO +c, +CoCqC, I [ : ; ] (4) The inverse transform is as follows : b) N-Point Reversible Transform The 2-point reversible transform can be easily generalized into N-point reversible transform as follows: -1 N-1 where c = c = 0 and the transform coefficients are 01, 0 2 ,. . ., eN. The Inverse transform is as follows: j=O j=N e, = e,,, LZci,.ei + osJ J + O S , (7) c) 8-Point Reversible Discrete Cosine Transform : A normalized 8-point Reversible DCT (RDCT) is obtained by comparing Equation (6) with N =8 with the normalized 8-point DCT. However, we can obtain RDCT more easily, since the 8-point DCT can be decomposed into 2-point and 4-point transforms that could be replaced with the corresponding ladder networks. It is obvious that the whole transform is reversible, when reversible transforms are substituted for every transform in Figure 2. Figure 2 : 8-Point DCT Decomposition The DCT decomposition leads to three different transforms as shown in Figure 3. To obtain the coefficients CO, cI and cz of the 2-point reversible transform in Figure 3.a, we just need to compare it with Eq. (4). This leads to: