We describe a unique approach for extracting the temporal profile of ultrashort laser pulses from typical autocorrelation measurements. The use of the constraint that intensity is a nonnegative quantity enables an iterative numerical algorithm to reconstruct pulse shapes in a one-dimensional procedure. With the reconstruction of the intensity profile, the Gerchberg–Saxton algorithm can be used ...

Abstract. The Papoulis-Gerchberg (PG) algorithm is well known for band-limited signal extrapolation. The authors consider the generalization of the PG algorithm to signals in the wavelet subspaces in this research. The uniqueness of the extrapolation for continuous-time signals is examined, and sufficient conditions on signals and wavelet bases for the generalized PG (GPG) algorithm to converge...

Abstract In this paper, the numerical solution of a mixed derivative type Hunter–Saxton equation is addressed. A given discretized transforming it into system ODEs with use cubic trigonometric B-splines based differential quadrature method. The further solved using fifth-order optimized one-step hybrid block Three illustrations validate efficiency proposed scheme and show its better performance...

The Camassa-Holm (CH) and Hunter-Saxton (HS) equations have an interpretation as geodesic flow equations on the group of diffeomorphisms, preserving the H and Ḣ right-invariant metrics correspondingly. There is an analogy to the Euler equations in hydrodynamics, which describe geodesic flow for a right-invariant metric on the infinitedimensional group of diffeomorphisms preserving the volume el...

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 ...