Abstract. Existing deblurring methods mainly focus on developing effective image priors and assume that blurred images contain insignificant amounts of noise. However, state-of-the-art deblurring methods do not perform well on real-world images degraded with significant noise or outliers. To address these issues, we show that it is critical to learn data fitting terms beyond the commonly used ?1 or ?2 norm. We propose a simple and effective discriminative framework to learn data terms that can adaptively handle blurred images in the presence of severe noise and outliers. Instead of learning the distribution of the data fitting errors, we directly learn the associated shrinkage function for the data term using a cascaded architecture, which is more flexible and efficient. Our analysis shows that the shrinkage functions learned at the intermediate stages can effectively suppress noise and preserve image structures. Extensive experimental results show that the proposed algorithm performs favorably against state-of-the-art methods