Mapped inverse discrete wavelet transform for data compression

The discrete wavelet transform (DWT) has been applied to data compression to decorrelate the data and concentrate the energy in a small portion of the coefficients. Compression can be achieved since most of the quantized wavelet coefficients are zeros. For the decoder, the traditional inverse discrete wavelet transform (IDWT) has a complexity proportional to the size of the data. In this paper, we propose a mapped inverse discrete wavelet transform algorithm (MIDWT) that takes advantage of the sparsity of the quantized wavelet coefficients, and significantly lowers the complexity of the IDWT to the level that is proportional to the number of non-zero coefficients. We further generalize the MIDWT to progressive decoding, and propose a realization of progressive IDWT without any run-time multiplication operations. Experiments show that our algorithms outperform the traditional IDWT for sparse coefficients, especially for progressive decompression.