---
_id: '18332'
abstract:
- lang: eng
  text: Presented here is a generalization of the modified relative Newton method,
    recently proposed in [1] for quasi-maximum likelihood blind source separation.
    Special structure of the Hessian matrix allows to perform block-coordinate Newton
    descent, which significantly reduces the algorithm computational complexity and
    boosts its performance. Simulations based on artificial and real data show that
    the separation quality using the proposed algorithm outperforms other accepted
    blind source separation methods.
alternative_title:
- LNCS
article_processing_charge: No
author:
- first_name: Alexander
  full_name: Bronstein, Alexander
  id: 58f3726e-7cba-11ef-ad8b-e6e8cb3904e6
  last_name: Bronstein
  orcid: 0000-0001-9699-8730
- first_name: Michael M.
  full_name: Bronstein, Michael M.
  last_name: Bronstein
- first_name: Michael
  full_name: Zibulevsky, Michael
  last_name: Zibulevsky
citation:
  ama: 'Bronstein AM, Bronstein MM, Zibulevsky M. Blind source separation using the
    block-coordinate relative Newton method. In: <i>5th International Conference on
    Independent Component Analysis and Blind Signal Separation</i>. Vol 3195. Springer
    Nature; 2004:406–413. doi:<a href="https://doi.org/10.1007/978-3-540-30110-3_52">10.1007/978-3-540-30110-3_52</a>'
  apa: 'Bronstein, A. M., Bronstein, M. M., &#38; Zibulevsky, M. (2004). Blind source
    separation using the block-coordinate relative Newton method. In <i>5th International
    Conference on Independent Component Analysis and Blind Signal Separation</i> (Vol.
    3195, pp. 406–413). Granada, Spain: Springer Nature. <a href="https://doi.org/10.1007/978-3-540-30110-3_52">https://doi.org/10.1007/978-3-540-30110-3_52</a>'
  chicago: Bronstein, Alex M., Michael M. Bronstein, and Michael Zibulevsky. “Blind
    Source Separation Using the Block-Coordinate Relative Newton Method.” In <i>5th
    International Conference on Independent Component Analysis and Blind Signal Separation</i>,
    3195:406–413. Springer Nature, 2004. <a href="https://doi.org/10.1007/978-3-540-30110-3_52">https://doi.org/10.1007/978-3-540-30110-3_52</a>.
  ieee: A. M. Bronstein, M. M. Bronstein, and M. Zibulevsky, “Blind source separation
    using the block-coordinate relative Newton method,” in <i>5th International Conference
    on Independent Component Analysis and Blind Signal Separation</i>, Granada, Spain,
    2004, vol. 3195, pp. 406–413.
  ista: 'Bronstein AM, Bronstein MM, Zibulevsky M. 2004. Blind source separation using
    the block-coordinate relative Newton method. 5th International Conference on Independent
    Component Analysis and Blind Signal Separation. ICA: Independent Component Analysis
    and Blind Signal Separation, LNCS, vol. 3195, 406–413.'
  mla: Bronstein, Alex M., et al. “Blind Source Separation Using the Block-Coordinate
    Relative Newton Method.” <i>5th International Conference on Independent Component
    Analysis and Blind Signal Separation</i>, vol. 3195, Springer Nature, 2004, pp.
    406–413, doi:<a href="https://doi.org/10.1007/978-3-540-30110-3_52">10.1007/978-3-540-30110-3_52</a>.
  short: A.M. Bronstein, M.M. Bronstein, M. Zibulevsky, in:, 5th International Conference
    on Independent Component Analysis and Blind Signal Separation, Springer Nature,
    2004, pp. 406–413.
conference:
  end_date: 2004-09-24
  location: Granada, Spain
  name: 'ICA: Independent Component Analysis and Blind Signal Separation'
  start_date: 2004-09-22
date_created: 2024-10-15T11:20:54Z
date_published: 2004-10-27T00:00:00Z
date_updated: 2024-12-02T14:30:47Z
day: '27'
doi: 10.1007/978-3-540-30110-3_52
extern: '1'
intvolume: '      3195'
language:
- iso: eng
month: '10'
oa_version: None
page: 406–413
publication: 5th International Conference on Independent Component Analysis and Blind
  Signal Separation
publication_identifier:
  eisbn:
  - '9783540301103'
  eissn:
  - 1611-3349
  isbn:
  - '9783540230564'
  issn:
  - 0302-9743
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Blind source separation using the block-coordinate relative Newton method
type: conference
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 3195
year: '2004'
...
---
_id: '18333'
abstract:
- lang: eng
  text: The relative Newton algorithm, previously proposed for quasi maximum likelihood
    blind source separation and blind deconvolution of one-dimensional signals is
    generalized for blind deconvolution of images. Smooth approximation of the absolute
    value is used in modelling the log probability density function, which is suitable
    for sparse sources. We propose a method of sparsification, which allows blind
    deconvolution of sources with arbitrary distribution, and show how to find optimal
    sparsifying transformations by training.
alternative_title:
- LNCS
article_processing_charge: No
author:
- first_name: Alexander
  full_name: Bronstein, Alexander
  id: 58f3726e-7cba-11ef-ad8b-e6e8cb3904e6
  last_name: Bronstein
  orcid: 0000-0001-9699-8730
- first_name: Michael M.
  full_name: Bronstein, Michael M.
  last_name: Bronstein
- first_name: Michael
  full_name: Zibulevsky, Michael
  last_name: Zibulevsky
- first_name: Yehoshua Y.
  full_name: Zeevi, Yehoshua Y.
  last_name: Zeevi
citation:
  ama: 'Bronstein AM, Bronstein MM, Zibulevsky M, Zeevi YY. Optimal sparse representations
    for blind deconvolution of images. In: <i>5th International Conference on Independent
    Component Analysis and Blind Signal Separation</i>. Vol 3195. Springer Nature;
    2004:500-507. doi:<a href="https://doi.org/10.1007/978-3-540-30110-3_64">10.1007/978-3-540-30110-3_64</a>'
  apa: 'Bronstein, A. M., Bronstein, M. M., Zibulevsky, M., &#38; Zeevi, Y. Y. (2004).
    Optimal sparse representations for blind deconvolution of images. In <i>5th International
    Conference on Independent Component Analysis and Blind Signal Separation</i> (Vol.
    3195, pp. 500–507). Granada, Spain: Springer Nature. <a href="https://doi.org/10.1007/978-3-540-30110-3_64">https://doi.org/10.1007/978-3-540-30110-3_64</a>'
  chicago: Bronstein, Alex M., Michael M. Bronstein, Michael Zibulevsky, and Yehoshua
    Y. Zeevi. “Optimal Sparse Representations for Blind Deconvolution of Images.”
    In <i>5th International Conference on Independent Component Analysis and Blind
    Signal Separation</i>, 3195:500–507. Springer Nature, 2004. <a href="https://doi.org/10.1007/978-3-540-30110-3_64">https://doi.org/10.1007/978-3-540-30110-3_64</a>.
  ieee: A. M. Bronstein, M. M. Bronstein, M. Zibulevsky, and Y. Y. Zeevi, “Optimal
    sparse representations for blind deconvolution of images,” in <i>5th International
    Conference on Independent Component Analysis and Blind Signal Separation</i>,
    Granada, Spain, 2004, vol. 3195, pp. 500–507.
  ista: 'Bronstein AM, Bronstein MM, Zibulevsky M, Zeevi YY. 2004. Optimal sparse
    representations for blind deconvolution of images. 5th International Conference
    on Independent Component Analysis and Blind Signal Separation. ICA: Independent
    Component Analysis and Blind Signal Separation, LNCS, vol. 3195, 500–507.'
  mla: Bronstein, Alex M., et al. “Optimal Sparse Representations for Blind Deconvolution
    of Images.” <i>5th International Conference on Independent Component Analysis
    and Blind Signal Separation</i>, vol. 3195, Springer Nature, 2004, pp. 500–07,
    doi:<a href="https://doi.org/10.1007/978-3-540-30110-3_64">10.1007/978-3-540-30110-3_64</a>.
  short: A.M. Bronstein, M.M. Bronstein, M. Zibulevsky, Y.Y. Zeevi, in:, 5th International
    Conference on Independent Component Analysis and Blind Signal Separation, Springer
    Nature, 2004, pp. 500–507.
conference:
  end_date: 2004-09-24
  location: Granada, Spain
  name: 'ICA: Independent Component Analysis and Blind Signal Separation'
  start_date: 2004-09-22
date_created: 2024-10-15T11:20:54Z
date_published: 2004-10-27T00:00:00Z
date_updated: 2024-11-19T14:12:31Z
day: '27'
doi: 10.1007/978-3-540-30110-3_64
extern: '1'
intvolume: '      3195'
language:
- iso: eng
month: '10'
oa_version: None
page: 500-507
publication: 5th International Conference on Independent Component Analysis and Blind
  Signal Separation
publication_identifier:
  eisbn:
  - '9783540301103'
  eissn:
  - 1611-3349
  isbn:
  - '9783540230564'
  issn:
  - 0302-9743
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Optimal sparse representations for blind deconvolution of images
type: conference
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 3195
year: '2004'
...
---
_id: '18334'
abstract:
- lang: eng
  text: We propose a relative optimization framework for quasi maximum likelihood
    blind deconvolution and the relative Newton method as its particular instance.
    Special Hessian structure allows its fast approximate construction and inversion
    with complexity comparable to that of gradient methods. The use of rational IIR
    restoration kernels provides a richer family of filters than the traditionally
    used FIR kernels. Smoothed absolute value and the smoothed deadzone functions
    allow accurate and robust deconvolution of super- and sub-Gaussian sources, respectively.
    Simulation results demonstrate the efficiency of the proposed methods.
alternative_title:
- LNCS
article_processing_charge: No
author:
- first_name: Alexander
  full_name: Bronstein, Alexander
  id: 58f3726e-7cba-11ef-ad8b-e6e8cb3904e6
  last_name: Bronstein
  orcid: 0000-0001-9699-8730
- first_name: Michael M.
  full_name: Bronstein, Michael M.
  last_name: Bronstein
- first_name: Michael
  full_name: Zibulevsky, Michael
  last_name: Zibulevsky
citation:
  ama: 'Bronstein AM, Bronstein MM, Zibulevsky M. Blind deconvolution using the relative
    Newton method. In: <i>5th International Conference on Independent Component Analysis
    and Blind Signal Separation</i>. Vol 3195. Berlin, Heidelberg: Springer Nature;
    2004:554–561. doi:<a href="https://doi.org/10.1007/978-3-540-30110-3_71">10.1007/978-3-540-30110-3_71</a>'
  apa: 'Bronstein, A. M., Bronstein, M. M., &#38; Zibulevsky, M. (2004). Blind deconvolution
    using the relative Newton method. In <i>5th International Conference on Independent
    Component Analysis and Blind Signal Separation</i> (Vol. 3195, pp. 554–561). Berlin,
    Heidelberg: Springer Nature. <a href="https://doi.org/10.1007/978-3-540-30110-3_71">https://doi.org/10.1007/978-3-540-30110-3_71</a>'
  chicago: 'Bronstein, Alex M., Michael M. Bronstein, and Michael Zibulevsky. “Blind
    Deconvolution Using the Relative Newton Method.” In <i>5th International Conference
    on Independent Component Analysis and Blind Signal Separation</i>, 3195:554–561.
    Berlin, Heidelberg: Springer Nature, 2004. <a href="https://doi.org/10.1007/978-3-540-30110-3_71">https://doi.org/10.1007/978-3-540-30110-3_71</a>.'
  ieee: A. M. Bronstein, M. M. Bronstein, and M. Zibulevsky, “Blind deconvolution
    using the relative Newton method,” in <i>5th International Conference on Independent
    Component Analysis and Blind Signal Separation</i>, Granada, Spain, 2004, vol.
    3195, pp. 554–561.
  ista: 'Bronstein AM, Bronstein MM, Zibulevsky M. 2004. Blind deconvolution using
    the relative Newton method. 5th International Conference on Independent Component
    Analysis and Blind Signal Separation. ICA: Independent Component Analysis and
    Blind Signal Separation, LNCS, vol. 3195, 554–561.'
  mla: Bronstein, Alex M., et al. “Blind Deconvolution Using the Relative Newton Method.”
    <i>5th International Conference on Independent Component Analysis and Blind Signal
    Separation</i>, vol. 3195, Springer Nature, 2004, pp. 554–561, doi:<a href="https://doi.org/10.1007/978-3-540-30110-3_71">10.1007/978-3-540-30110-3_71</a>.
  short: A.M. Bronstein, M.M. Bronstein, M. Zibulevsky, in:, 5th International Conference
    on Independent Component Analysis and Blind Signal Separation, Springer Nature,
    Berlin, Heidelberg, 2004, pp. 554–561.
conference:
  end_date: 2004-09-24
  location: Granada, Spain
  name: 'ICA: Independent Component Analysis and Blind Signal Separation'
  start_date: 2004-09-22
date_created: 2024-10-15T11:20:54Z
date_published: 2004-10-24T00:00:00Z
date_updated: 2024-12-02T14:15:23Z
day: '24'
doi: 10.1007/978-3-540-30110-3_71
extern: '1'
intvolume: '      3195'
language:
- iso: eng
month: '10'
oa_version: None
page: 554–561
place: Berlin, Heidelberg
publication: 5th International Conference on Independent Component Analysis and Blind
  Signal Separation
publication_identifier:
  eissn:
  - 1611-3349
  isbn:
  - '9783540230564'
  - '9783540301103'
  issn:
  - 0302-9743
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Blind deconvolution using the relative Newton method
type: conference
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 3195
year: '2004'
...
---
_id: '18335'
abstract:
- lang: eng
  text: Blind deconvolution is considered as a problem of quasi maximum likelihood
    (QML) estimation of the restoration kernel. Simple closed-form expressions for
    the asymptotic estimation error are derived. The asymptotic performance bounds
    coincide with the Cramér-Rao bounds, when the true ML estimator is used. Conditions
    for asymptotic stability of the QML estimator are derived. Special cases when
    the estimator is super-efficient are discussed.
alternative_title:
- LNCS
article_processing_charge: No
author:
- first_name: Alexander
  full_name: Bronstein, Alexander
  id: 58f3726e-7cba-11ef-ad8b-e6e8cb3904e6
  last_name: Bronstein
  orcid: 0000-0001-9699-8730
- first_name: Michael M.
  full_name: Bronstein, Michael M.
  last_name: Bronstein
- first_name: Michael
  full_name: Zibulevsky, Michael
  last_name: Zibulevsky
- first_name: Yehoshua Y.
  full_name: Zeevi, Yehoshua Y.
  last_name: Zeevi
citation:
  ama: 'Bronstein AM, Bronstein MM, Zibulevsky M, Zeevi YY. QML blind deconvolution:
    Asymptotic analysis. In: <i>Proceedings of the 5th International Conference on
    Independent Component Analysis and Blind Signal Separation</i>. Vol 3195. Springer
    Nature; 2004:677–684. doi:<a href="https://doi.org/10.1007/978-3-540-30110-3_86">10.1007/978-3-540-30110-3_86</a>'
  apa: 'Bronstein, A. M., Bronstein, M. M., Zibulevsky, M., &#38; Zeevi, Y. Y. (2004).
    QML blind deconvolution: Asymptotic analysis. In <i>Proceedings of the 5th International
    Conference on Independent Component Analysis and Blind Signal Separation</i> (Vol.
    3195, pp. 677–684). Granada, Spain: Springer Nature. <a href="https://doi.org/10.1007/978-3-540-30110-3_86">https://doi.org/10.1007/978-3-540-30110-3_86</a>'
  chicago: 'Bronstein, Alex M., Michael M. Bronstein, Michael Zibulevsky, and Yehoshua
    Y. Zeevi. “QML Blind Deconvolution: Asymptotic Analysis.” In <i>Proceedings of
    the 5th International Conference on Independent Component Analysis and Blind Signal
    Separation</i>, 3195:677–684. Springer Nature, 2004. <a href="https://doi.org/10.1007/978-3-540-30110-3_86">https://doi.org/10.1007/978-3-540-30110-3_86</a>.'
  ieee: 'A. M. Bronstein, M. M. Bronstein, M. Zibulevsky, and Y. Y. Zeevi, “QML blind
    deconvolution: Asymptotic analysis,” in <i>Proceedings of the 5th International
    Conference on Independent Component Analysis and Blind Signal Separation</i>,
    Granada, Spain, 2004, vol. 3195, pp. 677–684.'
  ista: 'Bronstein AM, Bronstein MM, Zibulevsky M, Zeevi YY. 2004. QML blind deconvolution:
    Asymptotic analysis. Proceedings of the 5th International Conference on Independent
    Component Analysis and Blind Signal Separation. ICA: Independent Component Analysis
    and Blind Signal Separation , LNCS, vol. 3195, 677–684.'
  mla: 'Bronstein, Alex M., et al. “QML Blind Deconvolution: Asymptotic Analysis.”
    <i>Proceedings of the 5th International Conference on Independent Component Analysis
    and Blind Signal Separation</i>, vol. 3195, Springer Nature, 2004, pp. 677–684,
    doi:<a href="https://doi.org/10.1007/978-3-540-30110-3_86">10.1007/978-3-540-30110-3_86</a>.'
  short: A.M. Bronstein, M.M. Bronstein, M. Zibulevsky, Y.Y. Zeevi, in:, Proceedings
    of the 5th International Conference on Independent Component Analysis and Blind
    Signal Separation, Springer Nature, 2004, pp. 677–684.
conference:
  end_date: 2004-09-24
  location: Granada, Spain
  name: 'ICA: Independent Component Analysis and Blind Signal Separation '
  start_date: 2004-09-22
date_created: 2024-10-15T11:20:54Z
date_published: 2004-10-27T00:00:00Z
date_updated: 2024-11-19T08:28:11Z
day: '27'
doi: 10.1007/978-3-540-30110-3_86
extern: '1'
intvolume: '      3195'
language:
- iso: eng
month: '10'
oa_version: None
page: 677–684
publication: Proceedings of the 5th International Conference on Independent Component
  Analysis and Blind Signal Separation
publication_identifier:
  isbn:
  - '9783540230564'
  - '9783540301103'
  issn:
  - 0302-9743
  - 1611-3349
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'QML blind deconvolution: Asymptotic analysis'
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 3195
year: '2004'
...