Compression of Laplacian Pyramids Through Orthogonal Transforms and Improved Prediction

Scalable representation of visual signals, such as image and video signals, has become a subject of active research since early 1980s. Scalability allows the adaptation of the bit rate and/or the resolution of the transmitted data to the network bandwidth and/or the rendering capability of the receiving device. For many years, spatial scalability has been achieved through wavelets, but recently the Laplacian pyramid (LP) has become an alternative choice because of reduced aliasing in the lower resolutions. In this paper, we focus on the coding efficiency of the LP with a view to transmitting it over a communication channel. In particular, we aim to improve the compression efficiency of the LP detail layers through improved interlayer prediction and orthogonal spatial transforms. First, we consider an LP in the open-loop configuration and propose to improve its rate-distortion performance by compressing it to a critically sampled representation. We derive four different orthogonal spatial transforms from the upsampling and downsampling filters that can achieve this representation, and apply them on the detail layers. The application of these transforms to the detail layers renders a fixed number of transform coefficients either zero or redundant, thus making their transmission unnecessary. Then we consider the compression of an LP in the closed-loop configuration through similar spatial transforms. Because of the introduction of quantization in the prediction loop, these spatial transforms applied on the detail layers do not produce the same number of zero or redundant transform coefficients as in the open-loop case. Nevertheless, the insight obtained from the open-loop coding leads us to enhance the interlayer prediction, and the subsequent application of the spatial transforms to the new detail layers aims to achieve better energy compaction.