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A Comparison of Block Based Kalman Filter and H-Infinity Algorithms for Blind Image Separation

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Blind image separation is a method of recovering the original images from a set of image mixtures, with no information about the source images or about the mixing process. Blind source separation problem has been used to extract sources from one-dimensional mixture signals such as speech, whereas, application of source separation for images (two-dimensional signals) has been examined to a limited extent. The independent component analysis (ICA) method assumes statistical independence of the source signals and at least one of the source could be non-gaussian. These assumptions do not hold for image mixing conditions. An alternative approach is to use Kalman filter that operates on the noisy input data recursively to produce statistically optimal estimate of the underlying sources. In this paper, a robust filter on H-infinity norm is proposed and compared with for image separation of Kalman filter. The extension of the algorithms to a simple and block based approach wherein the image mixture is converted to a sparse representation is proposed. The image mixture is subdivided into blocks of known sizes and the sparseness of each block is measured using l_0 norm and the block with maximum sparseness is used for extraction of original sources. This reduces the computational complexity that exists with the large dimensions of images. The algorithms are validated for natural image data sets and also for window reflection images taken under different lighting conditions. The analysis results suggest that the proposed methods provide significantly good quality of separation as measured by the performance metrics.

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Authors and Affiliations

  1. Ramaiah Institute of Technology/Dept. of Electronics and Instrumentation Engineering, Bangalore, India

    M. Jyothirmayi & S. Sethu Selvi

  2. Ramaiah Institute of Technology/Dept. of Mathematics, Bangalore, India

    P. A. Dinesh

Authors
  1. M. Jyothirmayi
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  2. S. Sethu Selvi
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  3. P. A. Dinesh
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Correspondence to M. Jyothirmayi.

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Jyothirmayi, M., Selvi, S.S. & Dinesh, P.A. A Comparison of Block Based Kalman Filter and H-Infinity Algorithms for Blind Image Separation. Comput Math Model 32, 339–355 (2021). https://doi.org/10.1007/s10598-021-09535-w

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  • DOI: https://doi.org/10.1007/s10598-021-09535-w

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