Inverse problems are where you have some data that has interacted with a system of interest and you try and work out the details of the system from the data. This may sound dry but it includes lots of really interesting practical applications including X-Ray imaging.

This is a collection of essay-style papers on the subject of inverse problems applied to imaging - vision and tomography.

The first paper is a round up and introduction to the general problem. If you have never encountered the inverse problem posed in its complete generality then you will appreciate this chapter. It covers not only the details of the continuous case but aspects of the discrete model derived from the continuous case. It is good enough to serve as your only introduction to the subject.

From here the book is composed of a set of focused applications of the general method. Topics include noise removal and contour detection; blind image deconvolution; Markov chains and image segmentation; object recognition; motion estimation; super resolution image construction; surface reconstruction; microwave imaging; shape from shading;image separation; stereo reconstruction from aerial images; and fusion of multi-modal images. What should surprise you from this list is the wide range of topics that inverse problems cover. The idea of treating the merging of multiple low resolution images to create a single high resolution image was, for example, new to me.

Although Tomography appears on the title, the book doesn't have much about specifically tomographic techniques. Instead it is more focused on imaging, and pattern recognition by reconstruction than tomography. However, given the availability of low cost 3D imaging sensors such as the Kinect this might be a good area to emphasise.

The big problem is that the quality of the writing and explanation varies from paper-to-paper and they are all very mathematical and academic - this is not for the geneal reader. In the main, however, the authors make the attempt to communicate and not just wrap the ideas up in academic language to make them seem harder.

Apart from the high price I can recommend this book if you are interested in imaging or artificial vision.