National Geographic expects that in 2015 Americans will take over 100 billion photos, half of which captured with mobile phones. While these devices provide a very easy and fast way to take pictures, they also suffer from high noise levels due to their limited lens aperture. Noise can be reduced by using long exposures. However, this also makes mobile phones extremely sensitive to hand movements, which, together with the high resolution of the sensor, can result in visibly blurry pictures. Thus, in recent years, the task of removing image blur has become a fundamental one.

The general problem of removing image blur is called blind deconvolution, and in the past 30 years has enjoyed widespread attention in the fields of computer vision, computer graphics, signal processing, mathematics and optics. In its simplest instance, blind deconvolution involves the estimation of a sharp image given only a blurry observation. The problem is extremely challenging due to its ill-posedness, but in the last decade steps forward have been made. Several methods that can successfully recover sharp images are now available.

This tutorial aims at introducing this fascinating field to beginning graduate students and engineers in industry. The main objective is to illustrate how the blur removal problem can be cast, what has been achieved so far, what we really know about blind deconvolution, and what the next challenges are. Overall we envision that investigation of these topics can lead to enhancements, extensions, and more transparent deployment of Bayesian-inspired algorithms both for blind deblurring problems and beyond. Also, the underlying insights carry over to a wide variety of bilinear models common in the computer vision literature such as independent component analysis, dictionary learning/sparse coding, and non-negative matrix factorization, just to name a few.