Signal reconstruction from a periodic nonuniform set of samples using H(infinity) optimization

We study the problem of signal reconstruction from a periodical nonuniform set of samples. The considered system takes samples of delayed versions of a continuous signal at low sampling rate, with different fractional delays for different channels. We design IIR synthesis filters so that the overall system approximates a sampling system of high sampling rate using techniques from model-matching problem in control theory with available software (such as Matlab). Unlike traditional signal processing methods, our approach uses techniques from control theory which convert systems with fractional delays into H-norm-equivalent discrete-time systems. The synthesis filters are designed so that they minimize the H(infinity) norm of the error system. As a consequence, the induced error is uniformly small over all (band-limited and band-unlimited) input signals. The experiments are also run for synthesized images.

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

[2]  L. D. Philipp,et al.  An improved refinable rational approximation to the ideal time delay , 1999 .

[3]  R. Y. Chiang,et al.  MATHLAB - Robust Control Toolbox , 2000 .

[4]  C. Loan.  Computing integrals involving the matrix exponential , 1978 .

[5]  Ian F. Akyildiz,et al.  Sensor Networks , 2002, Encyclopedia of GIS.

[6]  Parham Aarabi,et al.  Theory and design of multirate sensor arrays , 2005, IEEE Transactions on Signal Processing.

[7]  Cormac Herley,et al.  Minimum rate sampling and reconstruction of signals with arbitrary frequency support , 1999, IEEE Trans. Inf. Theory.

[8]  James Lam,et al.  Model reduction of delay systems using Pade approximants , 1993 .

[9]  Chi-Tsong Chen,et al.  Linear System Theory and Design , 1995 .

[10]  B. Francis,et al.  Optimal Sampled-data Control , 1995 .

[11]  B. Francis,et al.  A Course in H Control Theory , 1987 .

[12]  Robert H. Walden,et al.  Analog-to-digital converter survey and analysis , 1999, IEEE J. Sel. Areas Commun..

[13]  P. Vaidyanathan.  Multirate Systems And Filter Banks , 1992 .

[14]  M. G. Yoon,et al.  A new approximation method for time-delay systems , 1997, IEEE Trans. Autom. Control..

[15]  Tongwen Chen,et al.  Minimax design of hybrid multirate filter banks , 1996, 1996 IEEE International Symposium on Circuits and Systems. Circuits and Systems Connecting the World. ISCAS 96.

[16]  Michael Elad,et al.  Advances and challenges in super‐resolution , 2004, Int. J. Imaging Syst. Technol..

[17]  Bruce A. Francis,et al.  Optimal Sampled-Data Control Systems , 1996, Communications and Control Engineering Series.

[18]  Michael Elad,et al.  Super-Resolution Reconstruction of Image Sequences , 1999, IEEE Trans. Pattern Anal. Mach. Intell..

[19]  Takeo Kanade,et al.  Limits on Super-Resolution and How to Break Them , 2002, IEEE Trans. Pattern Anal. Mach. Intell..

[20]  Moon Gi Kang,et al.  Super-resolution image reconstruction: a technical overview , 2003, IEEE Signal Process. Mag..

[21]  Takeo Kanade,et al.  Limits on super-resolution and how to break them , 2000, Proceedings IEEE Conference on Computer Vision and Pattern Recognition. CVPR 2000 (Cat. No.PR00662).