Image separation using particle filters

In this work, we will analyze the problem of source separation in the case of superpositions of different source images, which need to be extracted from a set of noisy observations. This problem occurs, for example, in the field of astrophysics, where the contributions of various Galactic and extra-Galactic components need to be separated from a set of observed noisy mixtures. Most of the previous work on the problem performed blind source separation, assuming noiseless models, and in the few cases when noise is taken into account, it is assumed that it is Gaussian and space-invariant. In this paper we review the theoretical fundamentals of particle filtering, an advanced Bayesian estimation method which can deal with non-Gaussian non-linear models and additive space-varying noise, and we introduce a hierarchical model and a fusion of multiple particle filters for the solution of the image separation problem. Our simulations on realistic astrophysical data show that the particle filter approach provides significantly better results in comparison with one of the most widespread algorithms for source separation (FastICA), especially in the case of low SNR.

[1]  J. Cardoso,et al.  Multidetector multicomponent spectral matching and applications for cosmic microwave background data analysis , 2002, astro-ph/0211504.

[2]  Hichem Snoussi,et al.  Blind separation of noisy Gaussian stationary sources. Application to cosmic microwave background imaging , 2002, 2002 11th European Signal Processing Conference.

[3]  Moon Gi Kang,et al.  Super-resolution image reconstruction , 2010, 2010 International Conference on Computer Application and System Modeling (ICCASM 2010).

[4]  Erkki Oja,et al.  Independent Component Analysis , 2001 .

[5]  Andreas Ziehe,et al.  TDSEP { an e(cid:14)cient algorithm for blind separation using time structure , 1998 .

[6]  T. Başar,et al.  A New Approach to Linear Filtering and Prediction Problems , 2001 .

[7]  Stephen J. Roberts,et al.  Bayesian ICA with hidden Markov model sources , 2003 .

[8]  Gianluca Morgante,et al.  The Flexible Planck Scanning Strategy , 2007 .

[9]  D. Chakrabarti,et al.  A fast fixed - point algorithm for independent component analysis , 1997 .

[10]  Jeffrey K. Uhlmann,et al.  New extension of the Kalman filter to nonlinear systems , 1997, Defense, Security, and Sensing.

[11]  Eric Moulines,et al.  A blind source separation technique using second-order statistics , 1997, IEEE Trans. Signal Process..

[12]  Kevin H. Knuth,et al.  Bayesian source separation and localization , 1998, Optics & Photonics.

[13]  Richard M. Everson,et al.  Particle Filters for Non-Stationary ICA , 2000 .

[14]  Hichem Snoussi,et al.  Bayesian source separation with mixture of Gaussians prior for sources and Gaussian prior for mixture coefficients , 2001 .

[15]  H. Snoussi,et al.  Bayesian blind component separation for Cosmic Microwave Background observations , 2001 .

[16]  Kevin H. Knuth.  A Bayesian approach to source separation , 1999 .

[17]  D. Mayne,et al.  Monte Carlo techniques to estimate the conditional expectation in multi-stage non-linear filtering† , 1969 .

[18]  G. Zotti,et al.  All-sky astrophysical component separation with Fast Independent Component Analysis (FastICA) , 2001, astro-ph/0108362.

[19]  P. Djurić,et al.  Particle filtering , 2003, IEEE Signal Process. Mag..

[20]  G. Kitagawa.  Monte Carlo Filter and Smoother for Non-Gaussian Nonlinear State Space Models , 1996 .

[21]  Petros G. Voulgaris,et al.  On optimal ℓ∞ to ℓ∞ filtering , 1995, Autom..

[22]  Christophe Andrieu,et al.  On-line non-stationary ICA using mixture models , 2000, 2000 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.00CH37100).

[23]  C. Andrieu,et al.  A Particle Filter for Model Based Audio Source Separation , 2000 .

[24]  C. Baccigalupi,et al.  Neural networks and the separation of cosmic microwave background and astrophysical signals in sky maps , 2000, astro-ph/0002257.

[25]  Anna Tonazzini,et al.  Source separation in astrophysical maps using independent factor analysis , 2003, Neural Networks.

[26]  Timothy J. Robinson,et al.  Sequential Monte Carlo Methods in Practice , 2003 .

[27]  R. E. Kalman,et al.  New Results in Linear Filtering and Prediction Theory , 1961 .

[28]  C. G. T. Haslam,et al.  A 408 MHz all-sky continuum survey. II. The atlas of contour maps. , 1982 .

[29]  Christian P. Robert,et al.  Monte Carlo Statistical Methods , 2005, Springer Texts in Statistics.