An Efficient Hybrid Threshold for Image Deconvolution in Expectation Maximization Framework

Abstract

In this paper, we present a computationally efficient hybrid thresholding method for image deconvolution in the expectation maximization (EM) framework. The proposed method alternates between two key steps: an E-step that exploits the fast Fourier transform (FFT) for inversion of the convolution operator and an M-step that uses the discrete wavelet transform (DWT) for denoising. A modified L<inf>1</inf>-clipped penalty is introduced in the M-step for the computation of the maximum a posteriori (MAP) estimate, leading to a hybrid thresholding scheme, which is a combination of both hard and soft thresholds. Hard thresholding gives high variance, while soft thresholding leads to high bias in the restored image. The proposed hybrid threshold ameliorates the bias and variance trade-offs of the hard and soft thresholding schemes. Also, we performed a detailed mathematical and statistical analysis of the proposed hybrid threshold and computed the risk. The experimental results show that the proposed method attains optimal values for both variance and bias, leading to minimum risk, and also outperforms the state-of-the-art methods by a significant margin in terms of the performance metrics peak signal-to-noise ratio (PSNR) and improved signal-to-noise ratio (ISNR), as well as the visual quality. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.