Incremental Refinement of Computation for the Discrete Wavelet Transform

Contrary to the conventional paradigm of transform decomposition followed by quantization, we investigate the computation of two-dimensional discrete wavelet transforms (DWT) under quantized representations of the input source. The proposed method builds upon previous research on approximate signal processing and revisits the concept of incremental refinement of computation: Under a refinement of the source description (with the use of an embedded quantizer), the computation of the forward and inverse transform refines the previously-computed result thereby leading to incremental computation of the output. We study for which input sources (and computational-model parameters) can the proposed framework derive identical reconstruction accuracy to the conventional approach without any incurring computational overhead. This is termed successive refinement of computation, since all representation accuracies are produced incrementally under a single (continuous) computation of the refined input source and with no overhead in comparison to the conventional calculation approach that specifically targets each accuracy level and is not refinable.