The LOT: transform coding without blocking effects

An exact derivation of an optimal lapped orthogonal transform (LOT) is presented. The optimal LOT is related to the discrete cosine transform (DCT) in such a way that a fast algorithm for a nearly optimal LOT is derived. Compared to the DCT, the fast LOT requires about 20-30% more computations, mostly additions. An image coding example demonstrates the effectiveness of the LOT in reducing blocking effects; the LOT actually leads to slightly smaller signal reconstruction errors than does the DCT. >

[1]  Jared Bernstein,et al.  Short-space Fourier transform image processing , 1984, ICASSP.

[2]  A. Cantoni,et al.  Eigenvalues and eigenvectors of symmetric centrosymmetric matrices , 1976 .

[3]  J. Makhoul.  On the eigenvectors of symmetric Toeplitz matrices , 1981 .

[4]  Jae S. Lim,et al.  Reduction of blocking effect in image coding , 1983, ICASSP.

[5]  C. Smith,et al.  Adaptive Coding of Monochrome and Color Images , 1977, IEEE Trans. Commun..

[6]  Henrique S. Malvar.  Fast computation of discrete cosine transform through fast Hartley transform , 1986 .

[7]  David H. Staelin,et al.  Encoding of images based on a lapped orthogonal transform , 1989, IEEE Trans. Commun..

[8]  Henrique S. Malvar.  Optimal pre- and post-filtering in noisy sampled-data systems , 1986 .

[9]  P. Pirsch,et al.  Advances in picture coding , 1985, Proceedings of the IEEE.

[10]  D. Pearson,et al.  Transform coding of images using interleaved blocks , 1984 .

[11]  Henrique S. Malvar,et al.  Reduction of blocking effects in image coding with a lapped orthogonal transform , 1988, ICASSP-88., International Conference on Acoustics, Speech, and Signal Processing.

[12]  Stefan Ericsson,et al.  Fixed and Adaptive Predictors for Hybrid Predictive/Transform Coding , 1985, IEEE Trans. Commun..

[13]  Martin Vetterli,et al.  A theory of multirate filter banks , 1987, IEEE Trans. Acoust. Speech Signal Process..

[14]  Henrique S. Malvar.  The LOT: a link between block transform coding and multirate filter banks , 1988, 1988., IEEE International Symposium on Circuits and Systems.

[15]  Henrique S. Malvar,et al.  A pre-and post-filtering technique for the reduction of blocking effects , 1987 .

[16]  Adrian Segall.  Bit allocation and encoding for vector sources , 1976, IEEE Trans. Inf. Theory.