Regularization-parameter-free optimization approach for image deconvolution.

Image deconvolution is often modeled as an optimization problem for a cost function involving two or more terms that represent the data fidelity and the image domain constraints (or penalties). While a number of choices for modeling the cost function and implementing the optimization algorithms exist, selection of the regularization parameter in the cost function usually involves empirical tuning, which is a tedious process. Any optimization framework provides a family of solutions, depending on the numerical value of the regularization parameter. The end-user has to perform the task of tuning the regularization parameter based on visual inspection of the recovered solutions and then use the suitable image for further applications. In this work, we present an image deconvolution framework using the methodology of mean gradient descent (MGD), which does not involve any regularization parameter. The aim of our approach is instead to arrive at a solution point where the different costs balance each other. This is achieved by progressing the solution in the direction that bisects the steepest descent directions corresponding to the two cost terms in each iteration. The methodology is illustrated with numerical simulations as well as with experimental image records from a bright-field microscope system and shows uniform deconvolution performance for data with different noise levels. MGD offers an efficient and user-friendly method that may be employed for a variety of image deconvolution tools. The MGD approach as discussed here may find applications in the context of more general optimization problems as well.