The end users of the ADL are expected to retrieve images at various resolutions and quality levels. To support this, we have developed a multiresolution integer wavelet transform - the Balanced Rounding (BR) transform - with interband prediction that is more suitable for lossless image retrieval than traditional techniques.
Reversible wavelet transforms usually involve local averages which are successively computed by summation and truncation. Although this method has little impact on image coding, the resulting biased roundoff errors lead to successively smaller local means at different resolutions. Although this effect is small, it still is not very desirable from an image analysis point of view.
For this reason, the team has investigated an alternate approach that yields an unbiased roundoff error. Such a modification can indeed be found by realizing that traditional reversible wavelet transforms are closely related to rounding transforms, i.e. a mathematical framework exists that allows extensions and modifications. To balance the roundoff error, for example, one can apply a rounding up operation along the rows and truncate along the columns. The resulting balanced rounding (BR) transform alternates between opposite rounding operations and, thus, achieves an unbiased (``balanced'') roundoff error. In other words, the low pass coefficients can be modeled by a sum of local mean and additive, zero mean noise. Similar to other integer wavelet transforms, the BR--transform is reversible and computationally efficient.
Furthermore, the proposed BR--transform is idempotent which means that an image can be received in a lossy form and recompressed to the same codestream. Thus, successive compression/decompression steps can be performed without further degrading the initial image quality. In addition, it can be shown that the absolute value of the reconstruction error is bounded, if wavelet coefficients are appropriately quantized. Although not of immediate concern for lossless reconstruction, this BR--transform property can be useful in applications where progressive fidelity transmission is incorporated into a multiresolution framework or when lossy compression is desired. The BR--transform can be easily combined with interband predictive coding for better compression and progressive delivery.