Poissonian Image Deconvolution via Sparse and Redundant Representations and Framelet Regularization

Abstract

Poissonian image deconvolution is a key issue in various applications, such as astronomical imaging, medical imaging, and electronic microscope imaging. A large amount of literature on this subject is analysis-based methods. These methods assign various forward measurements of the image. Meanwhile, synthesis-based methods are another well-known class of methods. These methods seek a reconstruction of the image. In this paper, we propose an approach that combines analysis with synthesis methods. The method is proposed to address Poissonian image deconvolution problem by minimizing the energy functional, which is composed of a sparse representation prior over a learned dictionary, the data fidelity term, and framelet based analysis prior constraint as the regularization term. The minimization problem can be efficiently solved by the split Bregman technique. Experiments demonstrate that our approach achieves better results than many state-of-the-art methods, in terms of both restoration accuracy and visual perception.

Multiplicative noise removal via adaptive learned dictionaries and TV regularization

“…Note that in all experiments, the iteration for the proposed method is terminated, unless the following stopping criterion is met. Namely, (24) where ε is a fixed threshold. We stop the inner loop of Algorithm 1 when ε ≤ 10 −4 .…”

“…It first learns a dictionary from the noisy image patches, and then recovers each image patch by using the linear combinations of a few atoms in the learned dictionary. This method provides the state-of-the-art results, and it has been generalized to handle image sequence denoising, deblurring, decomposition, reducing artifacts [22][23][24][25][26][27][28]. For example, Zhao and Yang [28] proposed a hyperspectral image (HSI) denoising method by jointly utilizing sparse representation and low-rank constraint.…”

Image Restoration under Cauchy Noise with Sparse Representation Prior and Total Generalized Variation

“…Moreover, it was implemented in [31] to remove additive Gaussian noise. This denoising method preserved textural patterns and fine features well and has been generalized to handle various image processing problems including image sequence denoising [32][33][34], deblurring [35,36], decomposition [37], and restoration problems under different non-Gaussian noise, e.g., multiplicative [38,39], Poisson [40][41][42] or impulsive noise [43].…”