Optimization of filter banks based on properties of the input signal

Filter banks and wavelets have found applications in signal compression, noise removal, and in many other signal processing contexts. In this tutorial we review a number of recent results on the optimization of filter banks based on the knowledge of the input. The main emphasis will be the minimization of error due to subband quantization, and its connection to principal component reconstruction. Both uniform and nonuniform filter banks are considered.

[1]  Henrique S. Malvar.  Biorthogonal and nonuniform lapped transforms for transform coding with reduced blocking and ringing artifacts , 1998, IEEE Trans. Signal Process..

[2]  Clifford T. Mullis,et al.  Minimum mean-squared error transform coding and subband coding , 1996, IEEE Trans. Inf. Theory.

[3]  Michel Barlaud,et al.  Image coding using wavelet transform , 1992, IEEE Trans. Image Process..

[4]  Tor A. Ramstad,et al.  On the optimality of nonunitary filter banks in subband coders , 1995, IEEE Transactions on Image Processing.

[5]  P. P. Vaidyanathan,et al.  Theory and design of optimum FIR compaction filters , 1998, IEEE Trans. Signal Process..

[6]  I. Johnstone,et al.  Ideal spatial adaptation by wavelet shrinkage , 1994 .

[7]  K Ramchandran,et al.  Best wavelet packet bases in a rate-distortion sense , 1993, IEEE Trans. Image Process..

[8]  Ali N. Akansu,et al.  A very efficient low-bit-rate subband image/video codec using shift-only PR-QMF and zero-zone linear quantizers , 1997, 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[9]  Jerome M. Shapiro,et al.  Embedded image coding using zerotrees of wavelet coefficients , 1993, IEEE Trans. Signal Process..

[10]  Anastasios Delopoulos,et al.  Optimal filterbanks for signal reconstruction from noisy subband components , 1994, Proceedings of 1994 28th Asilomar Conference on Signals, Systems and Computers.

[11]  P. P. Vaidyanathan,et al.  Statistically optimal synthesis banks for subband coders , 1994, Proceedings of 1994 28th Asilomar Conference on Signals, Systems and Computers.

[12]  P. P. Vaidyanathan,et al.  Theory of optimal orthonormal subband coders , 1998, IEEE Trans. Signal Process..

[13]  Michael G. Strintzis,et al.  Optimal construction of filter banks for subband coding of quantised signals , 1997, Signal Process..

[14]  P. P. Vaidyanathan,et al.  On optimal analysis/synthesis filters for coding gain maximization , 1996, IEEE Trans. Signal Process..

[15]  J. Tuqan,et al.  The role of the discrete-time Kalman-Yakubovitch-Popov lemma in designing statistically optimum FIR orthonormal filter banks , 1998, ISCAS '98. Proceedings of the 1998 IEEE International Symposium on Circuits and Systems (Cat. No.98CH36187).

[16]  Stefanos D. Kollias,et al.  Optimal filter banks for signal reconstruction from noisy subband components , 1996, IEEE Trans. Signal Process..

[17]  Pierre Moulin.  A new look at signal-adapted QMF bank design , 1995, 1995 International Conference on Acoustics, Speech, and Signal Processing.

[18]  P. P. Vaidyanathan,et al.  Optimum low cost two channel IIR orthonormal filter bank , 1997, 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[19]  Necdet Uzun,et al.  Cyclostationary modeling, analysis, and optimal compensation of quantization errors in subband codecs , 1995, IEEE Trans. Signal Process..

[20]  Yair Shoham,et al.  Efficient bit allocation for an arbitrary set of quantizers [speech coding] , 1988, IEEE Trans. Acoust. Speech Signal Process..

[21]  Deepen Sinha,et al.  On the optimal choice of a wavelet for signal representation , 1992, IEEE Trans. Inf. Theory.

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

[23]  Georgios B. Giannakis,et al.  Principal component filter banks for optimal multiresolution analysis , 1995, IEEE Trans. Signal Process..

[24]  P. P. Vaidyanathan,et al.  On existence of FIR principal component filter banks , 1998, Proceedings of the 1998 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '98 (Cat. No.98CH36181).

[25]  C. Burrus,et al.  Optimal wavelet representation of signals and the wavelet sampling theorem , 1994 .

[26]  Aria Nosratinia.  Post-processing of compressed images with side information , 1998, ISCAS '98. Proceedings of the 1998 IEEE International Symposium on Circuits and Systems (Cat. No.98CH36187).

[27]  Jelena Kovacevic,et al.  Wavelets and Subband Coding , 2013, Prentice Hall Signal Processing Series.

[28]  A. Kirac,et al.  Results on optimal biorthogonal subband coders , 1998, ISCAS '98. Proceedings of the 1998 IEEE International Symposium on Circuits and Systems (Cat. No.98CH36187).

[29]  Pierre Moulin,et al.  Theory and design of signal-adapted FIR paraunitary filter banks , 1998, IEEE Trans. Signal Process..

[30]  K. H. Barratt.  Digital Coding of Waveforms , 1985 .

[31]  Jelena Kovacevic,et al.  Subband coding systems incorporating quantizer models , 1995, IEEE Trans. Image Process..

[32]  Pierre Duhamel,et al.  Filter bank design for minimum distortion in presence of subband quantization , 1996, 1996 IEEE International Conference on Acoustics, Speech, and Signal Processing Conference Proceedings.

[33]  Peter H. Westerink,et al.  Scalar quantization error analysis for image subband coding using QMFs , 1992, IEEE Trans. Signal Process..

[34]  Ronald A. DeVore,et al.  Image compression through wavelet transform coding , 1992, IEEE Trans. Inf. Theory.

[35]  Ali N. Akansu,et al.  On-signal decomposition techniques , 1991 .

[36]  B. Xuan,et al.  Complete FIR principal component filter banks , 1996, 1996 IEEE International Symposium on Circuits and Systems. Circuits and Systems Connecting the World. ISCAS 96.

[37]  Peter No,et al.  Digital Coding of Waveforms , 1986 .

[38]  William A. Pearlman,et al.  A survey of the state of the art and utilization of embedded, tree-based coding , 1998, ISCAS '98. Proceedings of the 1998 IEEE International Symposium on Circuits and Systems (Cat. No.98CH36187).