RECONSTRUCTING IMAGES FROM SPARSE DATA

In this dissertation, the process of recovering structure from sparse data is dis-cussed. Specifically, studies are undertaken for the case of X-ray imaging with weak signal. The limit of interest is when each image (or data frame) is so sparsely populated with X-ray photons that the structure of the object is not discernable. These techniques will be required to perform single molecule imaging using X-ray free electron lasers and serial microcrystallography experiments at synchrotron sources. An overview of the problem and the reconstruction algorithm is given in Chapter 1. In Chapters 2, 3 and 4, three different experiments are discussed, each with a different imaging geometry. All three experiments have the same prop-erty in that there are many data frames all of whom are very sparsely occupied. In Chapter 2, a shadowgraphy experiment is performed with a randomly rotated mask whose projected shadow on the detector is reconstructed from a large num-ber of images with a signal level as low as 2.5 photons per data frame. In Chap-ter 3, using a computed tomography (CT) setup with unrecorded orientations