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It was proposed recently that quantized representations of the input source (e.g., images, video) can be used for the computation of the two-dimensional discrete wavelet transform (2D DWT) incrementally. The coarsely quantized input source is used for the initial computation of the forward or inverse DWT, and the result is successively refined with each new refinement of the source description via an embedded quantizer. This computation is based on the direct two-dimensional factorization of the DWT using the generalized spatial combinative lifting algorithm. In this correspondence, we investigate the use of prediction for the computation of the results, i.e., exploiting the correlation of neighboring input samples (or transform coefficients) in order to reduce the dynamic range of the required computations, and thereby reduce the circuit activity required for the arithmetic operations of the forward or inverse transform. We focus on binomial factorizations of DWTs that include (amongst others) the popular 9/7 filter pair. Based on an FPGA arithmetic co-processor testbed, we present energy-consumption results for the arithmetic operations of incremental refinement and prediction-based incremental refinement in comparison to the conventional (nonrefinable) computation. Our tests with combinations of intra and error frames of video sequences show that the former can be 70% more energy efficient than the latter for computing to half precision and remains 15% more efficient for full-precision computation.