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

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

High energy gravitational scattering: a numerical study

The S-matrix in gravitational high energy scattering is computed from the region of large impact parameters b down to the regime where classical gravitational collapse is expected to occur. By solving the equation of an effective action introduced by Amati, Ciafaloni and Veneziano we find that the perturbative expansion around the leading eikonal result diverges at a critical value signalling the onset of a new regime. We then discuss the main features of our explicitly unitary S-matrix down to the Schwarzschild's radius R=2G s^(1/2), where it diverges at a critical value b ~ 2.22 R of the impact parameter. The nature of the singularity is studied with particular attention to the scaling behaviour of various observables at the transition. The numerical approach is validated by reproducing the known exact solution in the axially symmetric case to high accuracy.Comment: 11 pages, 6 figure

The CCFM Monte Carlo generator CASCADE

CASCADE is a full hadron level Monte Carlo event generator for e-p, gamma-p and p-p_bar processes, which uses the CCFM evolution equation for the initial state cascade in a backward evolution approach supplemented with off-shell matrix elements for the hard scattering. A detailed program description is given, with emphasis on parameters the user wants to change and common block variables which completely specify the generated events.Comment: Program manual, 14 page