This paper describes an expectation-maximization(EM) algorithm for wavelet-based image restoratio... more This paper describes an expectation-maximization(EM) algorithm for wavelet-based image restoration (deconvolution). The observed image is assumed to be a convolved (e.g., blurred) and noisy ver- sion of the original image. Regularization is achieved by using a complexity penalty/prior in the wavelet domain, taking advantage of the well known sparsity of wavelet representations. The EM algorithm herein proposed combines the efficient image represen- tation offered by the discrete wavelet transform (DWT) with the diagonalization of the convolution operator in the discrete Fourier domain. The algorithm alternates between an FFT-based E-step and a DWT-based M-step, resulting in a very efficient iterative process requiring operations per iteration (where stands for the numper of pixels). The algorithm, which also esti- mates the noise variance, is called WAFER, standing for Wavelet and Fourier EM Restoration. The conditions for convergence of the proposed algorithm are also presented.
This paper describes an expectation-maximization(EM) algorithm for wavelet-based image restoratio... more This paper describes an expectation-maximization(EM) algorithm for wavelet-based image restoration (deconvolution). The observed image is assumed to be a convolved (e.g., blurred) and noisy ver- sion of the original image. Regularization is achieved by using a complexity penalty/prior in the wavelet domain, taking advantage of the well known sparsity of wavelet representations. The EM algorithm herein proposed combines the efficient image represen- tation offered by the discrete wavelet transform (DWT) with the diagonalization of the convolution operator in the discrete Fourier domain. The algorithm alternates between an FFT-based E-step and a DWT-based M-step, resulting in a very efficient iterative process requiring operations per iteration (where stands for the numper of pixels). The algorithm, which also esti- mates the noise variance, is called WAFER, standing for Wavelet and Fourier EM Restoration. The conditions for convergence of the proposed algorithm are also presented.
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