Image deconvolution using hybrid threshold based on modified L1-clipped penalty in EM framework

Image deconvolution remains a challenging task due to its inherent ill-posedness. While existing algorithms show strong numerical performance, their complexity often complicates analysis and implementation. This paper introduces a computationally efficient image deconvolution method within the expectation maximization (EM) framework. The proposed algorithm alternates between an E-step leveraging the fast Fourier transform (FFT) and an M-step utilizing the discrete wavelet transform (DWT). In the M-step, we introduce a novel L₁-clipped penalty to compute the maximum a posteriori (MAP) estimate, resulting in a hybrid threshold that combines the strengths of soft and hard thresholding. This hybrid threshold is mathematically derived, overcoming the high variance of hard-thresholding and the high bias of soft-thresholding, thus optimizing the trade-off between variance and bias. Extensive experiments demonstrate that our method significantly outperforms state-of-the-art techniques in terms of improved signal-to-noise ratio (ISNR) and peak signal-to-noise ratio (PSNR), as well as visual quality. Notably, the proposed method shows average PSNR improvements of 3.49 dB, 4.23 dB, and 1.44 dB for uniform blur and 0.76 dB, 3.57 dB, and 0.66 dB for Gaussian blur on the Set12, BSD68, and Set14 datasets, respectively.