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Efficient iterative implementation of regularized solutions for image and signal reconstruction problems

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Abstract

Regularized signal and image reconstruction is one of the powerful tools to acquire original signals or images from the versions degraded with convolution and noise effects. The main problem encountered in regularized reconstruction of images is the estimation of the regularization parameter, as the quality and fidelity of the reconstructed images and their details are affected with this parameter. The problem is less severe with signals. A more global regularization parameter can be used for signal reconstruction from convolution and noise degradations. There are several methods for evaluation of this parameter in image reconstruction. This process requires knowledge of the noise variance in the degraded image. After evaluating this parameter, regularized restoration is implemented by applying a regularization filter on the degraded image. In this paper, we have two contributions. The first one is investigation of an iterative method for evaluation of the regularization parameter, and this process is implemented on images. This method depends on the maximization of the power of the restored image by the coincidence of the passband of the regularization filter with the frequency band in which most of the image power exists. It does not necessitate a priori knowledge about the noise variance. We come to a conclusion about the range of the regularization parameter that is most appropriate for solving the deconvolution problem in the presence of noise as an inverse problem. According to the obtained solution, we can solve the problem in a general sense for other types of signals such as speech signals. Hence, the other contribution is the generalization of the obtained conclusion about the regularization problem solution for speech deconvolution.

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Authors and Affiliations

  1. Department of Electronics and Electrical Communications Engineering, Faculty of Electronic Engineering, Menoufia University, Menouf, 32952, Egypt

    Marwa A. Elsayed, Walid El-Shafai, Moawad I. Dessouky, Adel S. El-Fishawy & Fathi E. Abd El-Samie

  2. Security Engineering Lab, Computer Science Department, Prince Sultan University, Riyadh, 11586, Saudi Arabia

    Walid El-Shafai

  3. Department of Electronics and Electrical Communications Engineering, Faculty of Engineering, Cairo University, Giza, 12613, Egypt

    Mohsen A. Rashwan

  4. Department of Information Technology, College of Computer and Information Sciences, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh, 11671, Saudi Arabia

    Fathi E. Abd El-Samie

Authors
  1. Marwa A. Elsayed
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  2. Walid El-Shafai
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  3. Mohsen A. Rashwan
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  4. Moawad I. Dessouky
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  5. Adel S. El-Fishawy
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  6. Fathi E. Abd El-Samie
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Correspondence to Marwa A. Elsayed.

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Elsayed, M.A., El-Shafai, W., Rashwan, M.A. et al. Efficient iterative implementation of regularized solutions for image and signal reconstruction problems. J Opt (2023). https://doi.org/10.1007/s12596-023-01179-w

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