Phase retrieval by power iterations

I show that the power iteration method applied to the phase retrieval problem converges under special conditions. One is given the relative phases between small non-overlapping groups of pixels of a recorded intensity pattern, but no information on the phase between the groups of pixels. Numerical tests show that the inverse block iteration recovers the solution in 1 iteration.Comment: 4 pages, 6 figure

Ab initio compressive phase retrieval

Any object on earth has two fundamental properties: it is finite, and it is made of atoms. Structural information about an object can be obtained from diffraction amplitude measurements that account for either one of these traits. Nyquist-sampling of the Fourier amplitudes is sufficient to image single particles of finite size at any resolution. Atomic resolution data is routinely used to image molecules replicated in a crystal structure. Here we report an algorithm that requires neither information, but uses the fact that an image of a natural object is compressible. Intended applications include tomographic diffractive imaging, crystallography, powder diffraction, small angle x-ray scattering and random Fourier amplitude measurements.Comment: 7 pages, 4 figures, presented at the XXI IUCr Congress, Aug. 2008, Osaka Japa

Hard QCD: some results

I recall some points on the present status of QCD results in the short distance regions and illustrate the case of event shape in QCD radiationComment: 11 pages, talk given at XXXI International Symposium on Multiparticle Dynamics, Sept 1-7, 2001, Datong China. URL http://ismd31.ccnu.edu.cn

Jet-shape observables

Studies of jet-shape observables in hard processes are summarized together with future developmentsComment: 4 pages, talk at ICHEP2004, Beijing, August 200