Global and local rate-distortion optimization for Lapped Biorthogonal Transform coding

It is a well-known fact that, in order to overcome annoying blocking artifacts, transforms with block-overlapping basis functions have been proposed for image coding. Typically in transform coding, the encoder determines the transform coefficient values by applying the forward transform followed by scalar quantization. In this paper we present an approach, how rate-distortion optimized Lapped Biorthogonal Transform (LBT) coefficient values can be determined by solving ℓ₁-regularized least squares problems. We compare a global version, where all the transform coefficients are obtained in one single optimization step, and a local version, where the optimization is done separately for each block, which results in losing optimality, but achieving highly reduced complexity. Our simulation results show gains of about 0.5 dB PSNR compared to ordinary forward transform and scalar quantization with only small losses (<; 0.1 dB) for the local variant.