A Robust Variational Model for Positive Image Deconvolution
This work addresses image restoration for applications requiring positivity constraints, but it is incremental as it builds on existing variational interpretations and methods.
The paper tackles the problem of robust deconvolution with positivity constraints by modifying the Richardson-Lucy method to include a robust penaliser and regulariser, achieving image restoration quality comparable to state-of-the-art methods while maintaining computational efficiency similar to the original method.
In this paper, an iterative method for robust deconvolution with positivity constraints is discussed. It is based on the known variational interpretation of the Richardson-Lucy iterative deconvolution as fixed-point iteration for the minimisation of an information divergence functional under a multiplicative perturbation model. The asymmetric penaliser function involved in this functional is then modified into a robust penaliser, and complemented with a regulariser. The resulting functional gives rise to a fixed point iteration that we call robust and regularised Richardson-Lucy deconvolution. It achieves an image restoration quality comparable to state-of-the-art robust variational deconvolution with a computational efficiency similar to that of the original Richardson-Lucy method. Experiments on synthetic and real-world image data demonstrate the performance of the proposed method.