It is difficult to reconstruct an image of a complex-valued object from the modulus of its Fourier transform (i.e., retrieve the Fourier phase) except in some special cases. By using additionally a low-resolution intensity image from a telescope with a small aperture, a fine-resolution image of a general object can be reconstructed in a two-step approach. First the Fourier phase over the small ...

In application of tomography imaging, limited-angle problem is a quite practical and important issue. In this paper, an iterative reprojection-reconstruction (IRR) algorithm using a modified Papoulis-Gerchberg (PG) iterative scheme is developed for reconstruction from limited-angle projections which contain noise. The proposed algorithm has two iterative update processes, one is the extrapolati...

In this paper we give a short proof of the Random Ramsey Theorem of Rödl and Ruciński: for any graph F which contains a cycle and r ≥ 2, there exist constants c, C > 0 such that P[Gn,p → (F )r] = { 1− o(1), p ≥ Cn−1/m2(F ) o(1), p ≤ cn−1/m2(F , where m2(F ) = maxJ⊆F,vJ≥2 eJ−1 vJ−2 . The proof of the 1-statement is based on the recent beautiful hypergraph container theorems by Saxton/Thomason an...

Motivated by his work on the classification of countable homogeneous oriented graphs, Cherlin asked about the typical structure of oriented graphs (i) without a transitive triangle, or (ii) without an oriented triangle. We give an answer to these questions (which is not quite the predicted one). Our approach is based on the recent ‘hypergraph containers’ method, developed independently by Saxto...

A procedure for designing and fabricating holograms which are used for generating free space optical interconnections is described. The design process uses the Gerchberg-Saxton algorithm and a random search (simulated annealing) method. Fabrication is performed by electron beam lithography and acetone etch of a polymethyl methacrylate film. The use of holograms fabricated by this method in an o...

A color holographic reconstruction technique by using three light emitting diodes (LEDs) is described. Reflective type phase-only spatial light modulators (SLMs) are used since they are suitable for in-line phase holograms. Gerchberg-Saxton iterative algorithm is used for computing phase holograms. Three phase holograms are calculated separately for red, green and blue colors, for a color recon...