Reduction of Blocking Effects in Image Coding with a Lapped Orthogonal Transform

The Lapped Orthogonal Transform (LOT) [1][3] is a new transform for block image coding. It has basis functions that overlap adjacent blocks and decay smoothly to zero, and so it can reduce the blocking effect to very low levels, without any data overhead. In t'his paper we show that a quasi-optimal LOT can be computed with an algorithm based on the discrete cosine transform (DCT), with only 30 percent more computations than the DCT. Unlike earlier approaches to the reduction of blocking effects, there is no penalty in coding gain for the LOT. In fact, the LOT actually increases the coding gain by 0.25dB for a first-order Markov process with p = 0.95. transforms based on the unidimensional profile, as it is usual in transform image coding [4]. Let us assume that the incoming discrete-time signal is a large segment of MN samples, where N is the block size. In traditional transform coding, M blocks of length N would be independently transformed and coded. In matrix notation, if we call Xo the original input vector of length MN, the vector Yo containing the transform coefficients of all blocks is Yo = Tixo, where Ti is the transpose of an MN x MN block-diagonal matrix T = diag(D, ..., D), where D is a matrix of order N whose columns are the basis functions that define the transform of each block. With the LOT, each block has L samples, with L > N, so that neighboring blocks overlap by LN samples. The basic operation of the LOT is thus similar to the overlapping method of [5]. A fundamental difference is that the LOT maps the L samples of each block into N transform coefficients. With the number of transform coefficients being equal to the block size, there is no increase in the data rate. The LOT is defined with Tin the form