On the role of differential geometry in signal processing

@article{Manton2005OnTR,
  title={On the role of differential geometry in signal processing},
  author={J. Manton},
  journal={Proceedings. (ICASSP '05). IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005.},
  year={2005},
  volume={5},
  pages={v/1021-v/1024 Vol. 5}
}
  • J. Manton
  • Published 2005
  • Mathematics, Computer Science
  • Proceedings. (ICASSP '05). IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005.
  • Traditionally, the majority of non-linear signal processing problems were tackled either by appropriate linearisations or by some ad hoc technique. By contrast, linear signal processing problems are routinely solved systematically by astute application of results from linear algebra. This paper shows by example how differential geometry provides the necessary tools and mindset for systematically solving certain non-linear problems commonly encountered in signal processing. 
    21 Citations

    Topics from this paper

    A differential geometric approach to discrete-coefficient filter design
    • 1
    • PDF
    Differential Geometry of Manifolds , Surfaces and Curves .
    • PDF
    Optimal Estimation and Detection in Homogeneous Spaces
    • 9
    • PDF
    Optimisation Geometry
    • 5
    • PDF
    Optimal Nonlinear Estimation in Statistical Manifolds with Application to Sensor Network Localization
    • 5
    • PDF
    Optimization under Unitary Matrix Constraint using Approximate Matrix Exponential
    • 6
    Conjugate gradient algorithm for optimization under unitary matrix constraint
    • 77
    • PDF
    Steepest Descent Algorithms for Optimization Under Unitary Matrix Constraint
    • 147
    • PDF
    Efficient Line Search Methods for Riemannian Optimization Under Unitary Matrix Constraint
    • 2
    • PDF

    References

    SHOWING 1-10 OF 30 REFERENCES
    On the algebraic identifiability of finite impulse response channels driven by linearly precoded signals
    • 5
    • PDF
    An improved least squares blind channel identification algorithm for linearly and affinely precoded communication systems
    • J. H. Manton
    • Computer Science, Mathematics
    • IEEE Signal Processing Letters
    • 2002
    • 11
    • PDF
    The role of differential geometry in statistical theory
    • 69
    • PDF
    Communication on the Grassmann manifold: A geometric approach to the noncoherent multiple-antenna channel
    • L. Zheng, D. Tse
    • Mathematics, Computer Science
    • IEEE Trans. Inf. Theory
    • 2002
    • 936
    • PDF
    Quantization on the Grassmann manifold: applications to precoded MIMO wireless systems
    • Bishwarup Mondal, R. Heath, L. Hanlen
    • Mathematics, Computer Science
    • Proceedings. (ICASSP '05). IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005.
    • 2005
    • 26
    The geometry of weighted low-rank approximations
    • J. Manton, R. Mahony, Yingbo Hua
    • Mathematics, Computer Science
    • IEEE Trans. Signal Process.
    • 2003
    • 106
    • PDF
    The Geometry of the Newton Method on Non-Compact Lie Groups
    • 73
    • PDF
    Design and analysis of linear precoders under a mean square error criterion, Part II: MMSE designs and conclusions
    • J. Manton
    • Mathematics, Computer Science
    • Syst. Control. Lett.
    • 2003
    • 12
    • PDF
    Optimization algorithms exploiting unitary constraints
    • J. Manton
    • Mathematics, Computer Science
    • IEEE Trans. Signal Process.
    • 2002
    • 384
    • PDF