Hybrid Thresholding for Image Deconvolution in Expectation Maximization framework

ABSTRACT

In this study, we proposed an image deconvolution method in the expectation maximization (EM) framework. This method involves two steps: (i) E-step: utilizing the fast Fourier transform (FFT) for computationally efficient inversion of the convolution operator and (ii) M-step: employing the discrete wavelet transform (DWT) for estimating the original image from the image obtained in the E-step. In M-step, we proposed a modified L₁-clipped penalty resulting in a hybrid thresholding scheme that integrates conventional hard and soft thresholds. This hybrid threshold ameliorates the inherent bias-variance trade-offs associated with traditional hard and soft thresholding schemes. The mathematical expressions for the risk, bias, and variance of the proposed hybrid threshold are derived and the performance is evaluated through simulation. Experimental results show that the proposed method achieves optimal values for variance and bias, thereby minimizing the risk. Moreover, the proposed method outperforms state-of-the-art methods in terms of performance metrics: PSNR, ISNR, and SSIM.

KEYWORDS:

• Expectation-maximization
• hard thresholding
• image deconvolution
• regularization
• soft thresholding
• wavelet
• deblurring
• risk analysis

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability

All data generated or analysed during this study are included in this published article.

Additional information

Notes on contributors

Ravi Pratap Singh

Ravi Pratap Singh received the B.Sc. (Hons) degree with Mathematics, and the M.Sc. degree in Computational science and application in signal processing from Banaras Hindu University, Varanasi, India, in 2012 and 2016 respectively. He is perusing the Ph.D. degree from Department of Science and Technology-Centre for Interdisciplinary Sciences (DST-CIMS) from Banaras Hindu University, Varanasi, India, (2017–present). His current research interests include image processing, imaging system, parameter estimation, time frequency analysis, machine leaning, Inverse Computational Imaging, Deep Neural networks in Image processing and affective computing.

Manoj Kumar Singh

Manoj Kumar Singh is Associate Professor at Department of Computer Science, Institute of Science, Banaras Hindu University, Varanasi, India. He received the Ph.D. degree from Gwangju Institute of Science and Technology (GIST), Gwangju, South Korea. Before joining Department of Computer Science, he worked as Assistant Professor at DST – Center for Interdisciplinary Mathematical Sciences (DST-CIMS), Banaras Hindu University, Varanasi, India from 2010 to 2017. From 2009 to 2010, he worked as BK-21 Post Doctoral Fellow at Sensor System Lab, GIST, South Korea. His research interests are Statistical Signal Processing, Image Processing, Inverse Problems, Computer Vision, Effective Computing and Artificial Intelligence.