Quasi-analytic multidimensional signals

Open access

Abstract

In a recent paper, the authors have presented the unified theory of n-dimensional (n-D) complex and hypercomplex analytic signals with single-orthant spectra. This paper describes a specific form of these signals called quasi-analytic. A quasi-analytic signal is a product of a n-D low-pass (base-band) real (in general non-separable) signal and a n-D complex or hypercomplex carrier. By a suitable choice of the carrier frequency, the spectrum of a low-pass signal is shifted into a single orthant of the Fourier frequency space with a negligible leakage into other orthants. A measure of this leakage is defined. Properties of quasi-analytic signals are studied. Problems of polar representation of quasi-analytic signals and of its lower rank representation are discussed.

[1] K.M. Snopek and S.L. Hahn, “The unified theory of ndimensional complex and hypercomplex analytic signals”, Bull. Polish Ac.: Tech. 59 (2), 167-181 (2011).

[2] S.J. Sangwine and N. Le Bihan, Hypercomplex Analytic Signals: Extension of the Analytic Signal Concept to Complex Signals, EUSIPCO, Poznań, 2007.

[3] C. Wachinger, T. Klein, and N. Navab, “The 2D analytic signal for envelope detection and feature extraction on ultrasound images”, Medical Image Analysis 16, 1073-1084 (2012).

[4] T. B¨ulow and G. Sommer, A Novel Approach to the 2D Analytic Signal, pp. 25-32, Springer Verlag Berlin, 1999.

[5] T. B¨ulow and G. Sommer, “The hypercomplex signal - a novel extension of the analytic signal to the multidimensional case”, IEEE Trans. Signal Processing 49 (11), 2844-2852 (2001).

[6] S.L. Hahn, “Multidimensional complex signals with singleorthant spectra”, Proc. IEEE 80 (8), 1287-1300 (1992).

[7] S.L. Hahn, Hilbert Transforms in Signal Processing, Artech House Inc., London, 1996.

[8] S. Hahn, “Hilbert Transforms” in The Transforms and Applications Handbook, CRC Press, Orlando, 2010.

[9] C. H¨ohne, R. Boehm, and J. Prager, “Application of 2- dimensional analytic signals with single-orthant spectra for processing of SAFT-reconstructed images”, in Multidim. Syst. Sign. Process., Springer Science+Business Media, New York, 2013.

[10] S.J. Sangwine, C.J. Evans, and T.A. Ell, “Colour-sensitive edge detection using hypercomplex filters”, Proc. 10thEur. Signal Processing Conf. EUSIPCO 1, 107-110 (2000).

[11] D S. Alexiadis and G.D. Sergiadis, “Estimation of motions in color image sequences using hypercomplex Fourier transforms”, IEEE Trans. Image Processing 18 (1), 168-187 (2009).

[12] T. Bulow, M. Felsberg, and G. Sommer, “Non-commutative hypercomplex Fourier transforms of multidimensional signals” in Geometric Computing with Clifford Algebras, ed. G. Sommer, pp. 187-207, Springer, Berlin, 2001.

[13] T.A. Ell and S.J. Sangwine, “Hypercomplex Fourier transforms of color images”, IEEE Trans. Image Process, 16 (1), 22-35, (2007).

[14] S.L. Hahn and K.M. Snopek, “Comparison of properties of analytic, quaternionic and monogenic 2-D signals”, WSEAS Transactions on Computers 3 (3), 602-611 (2004). 1024

Bulletin of the Polish Academy of Sciences Technical Sciences

The Journal of Polish Academy of Sciences

Journal Information


IMPACT FACTOR 2016: 1.156
5-year IMPACT FACTOR: 1.238

CiteScore 2016: 1.50

SCImago Journal Rank (SJR) 2016: 0.457
Source Normalized Impact per Paper (SNIP) 2016: 1.239

Metrics

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 94 93 7
PDF Downloads 29 28 4