Bayesian image deconvolution and denoising using complex wavelets

This paper proposes a new algorithm for image restoration (deconvolution and denoising) which employs the recently developed dual-tree complex wavelet transform in an iterative Bayesian framework. Complex wavelets are selected for their key features: shift invariance, directional selectivity and efficiency. The aim is to find an optimal description of the restored image in the complex wavelet domain, which minimises a quadratic energy function of the wavelet coefficients. The algorithm searches for this minimum using an efficient conjugate gradient method. We show that this can improve the SNR performance of a good minimax deconvolution method, WaRD, which is used to initialise the iterations, by typically 1.2 dB. Convergence is quite rapid, achieving 80% of the ultimate performance gain in about 20 iterations. Each iteration takes around 5 seconds using MatLab on a 400 MHz Pentium computer with 256×256 pixel images