Blur is a significant problem in medical imaging which can hinder diagnosis and prevent further automated or manual processing. The problem of restoring an image from blur degradation remains a challenging task in image processing. Semi-blind deblurring is a useful technique which may be developed to restore the underlying sharp image given some assumed or known information about the cause of degradation. Existing models assume that the blur is of a particular type, such as Gaussian, and do not allow for the approximation of images corrupted by other blur types which are not easily incorporated into deblurring frameworks. We present an automated approach to image deconvolution which assumes that the cause of blur belongs to a set of common types. We develop a hierarchical approach with convolutional neural networks (CNNs) to distinguish between blur types, achieving an accuracy of 0.96 across a test set of 900 images, and to determine the blur strength, achieving accuracy of 0.77 across 1500 test images. Given this, we are able to reconstruct the underlying image to mean ISNR of 7.53.