A Theory for Multiresolution Signal Decomposition: The Wavelet Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
An improved least squares Laplacian pyramid for image compression
Signal Processing
Multirate systems and filter banks
Multirate systems and filter banks
Pyramid-based texture analysis/synthesis
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Multiresolution representation of data: a general framework
SIAM Journal on Numerical Analysis
Approximation properties of multivariate wavelets
Mathematics of Computation
Optimal Interpolatory Subdivision Schemes in Multidimensional Spaces
SIAM Journal on Numerical Analysis
Wavelets: tools for science & Technology
Wavelets: tools for science & Technology
Towards an Example-Based Image Compression Architecture for Video-Conferencing
Towards an Example-Based Image Compression Architecture for Video-Conferencing
Frame-theoretic analysis of oversampled filter banks
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
On the DPCM compression of Gaussian autoregressive sequences
IEEE Transactions on Information Theory
Lossless image compression by quantization feedback in a content-driven enhanced Laplacian pyramid
IEEE Transactions on Image Processing
The contourlet transform: an efficient directional multiresolution image representation
IEEE Transactions on Image Processing
| Hi-index | 35.68 |
The Laplacian pyramid (LP) is a multiresolution representation introduced originally for images, and it has been used in many applications. A major shortcoming of the LP representation is that it is oversampled. The dependency among the LP coefficients is studied in this paper. It is shown that whenever the LP compression filter is interpolatory, the redundancy in the LP coefficients can be removed effortlessly by merely discarding some of the LP coefficients. Furthermore, it turns out that the remaining, now critically sampled, LP coefficients are actually the coefficients of a wavelet filter bank. As a result, a new algorithm for designing a nonredundant wavelet filter bank from non-biorthogonal lowpass filters is obtained. Our methodology presented in this paper does not depend on the spatial dimension of the data or the dilation matrix for sampling.