Phaseless Data Research Articles

Role of support information and zero locations in phase retrieval by a quadratic approach

A recently introduced approach to phase-retrieval problems is applied to present a unified discussion of support information and zero locations in the reconstruction of a discrete complex image from Fourier-transform phaseless data. The choice of the square-modulus function of the Fourier transform of the unknown as the problem datum results in a quadratic operator that has to be inverted, i.e., a simple nonlinearity. This circumstance makes it possible to consider and to point out some relevant factors that affect the local minima problem that arises in the solution procedure (which amounts to minimizing a quartic functional). Simple modifications of the basic procedure help to explain the role of support information and zeros in the data and to develop suitable strategies for avoiding the local minima problem. All results can be summarized by reference to the ratio between the effective dimensions of the data space and the space of unknowns. Numerical results identify the approach’s considerable robustness against false solutions, starting from completely random first guesses, if the above ratio is larger than 3. The algorithm also ensures robust performance in the presence of noise in the data.

Far field reconstruction from phaseless measurement data

A new method on phase inverse problem in near field far field transformation is presented in this paper. It makes the relation very clear between phase and amplitude on a curve surface and another surface by describing the relation of the fields on two closed curve surfaces by matrix. Comparing with the other created functionals, the functional based on this method belongs in real space rather than complex space, its form is simple and it is easy to deal with. The relation between two sets of near field is consided while creating the functional, so it enlightens greatly work of the data processing. The conjugate gradient method (CGM) is taken to minimize the object functional, An analytical model validates the feasibilities of the theory and the algorithm.

On the local minima in phase reconstruction algorithms

Signal reconstruction from phaseless data occurs in electromagnetics both in the diagnostics of large reflector antennas and in the near‐field testing of microwave and millimeter wave antennas. The main difficulty in solving such problems arises from its inherent nonlinearity. Because of the latter, in fact, the solution procedure can converge to a function which has nothing to deal with the actual solution. In this paper we review and summarize the properties of a recently proposed approach to phase retrieval problems which allows to understand and possibly avoid the false solution problem. To this end, ill‐posedness of the problem is briefly recalled, and a convenient generalized solution is introduced as the global minimum of a proper functional whose local minima are indeed the false solutions of the problem. Then the geometrical meaning of such a functional is considered, and properties of the solution are discussed according to the formulation of the problem as a quadratic inverse one. In particular, the relevance of using nonredundant representations for the unknown of the problem and as many independent data as possible are discussed in full detail from both a theoretical and a numerical point of view. Finally, it is shown how the proposed solution procedure, descending from the adopted formulation based on a weaker nonlinearity with respect to the other ones, has indeed a better behavior as far as local minima problem is concerned.

Radiation pattern evaluation from near-field intensities on planes

This paper describes, analyzes, and implements an approach to far-field determination from phaseless measurements over two planar surfaces. A proper formulation of the problem is considered as a quadratic inverse one whose data is the square amplitude of the near field. A solution is introduced as the global minimum of an appropriate functional. Next, to perform such a minimization procedure, a finite dimensional representation of the field radiated by sources whose plane-wave spectrum becomes negligible outside a fixed angular domain is used. A detailed investigation of the properties of the mapping connecting the unknowns to the data makes it possible to analyze how to escape from the local minima possibly met in the course of the minimization procedure. To this end, the crucial role of the availability of phaseless data over two different sarfa,ces and of appropriate weights in the functional definition is emphasized, and a reliable iterative procedure converging on the solution, regardless of the starting point, is thus obtained. This property is confirmed by experimental results concerning near-zone data from a shaped reflector at 9 Ghz. It can be readily appreciated that when only the field intensity is detected the complexity and the cost of the equipment required for near-field techniques in antenna testing and diagnostics can be reduced to a very large extent.

Results for a truncated phaseless near field technique

Radiation pattern determination from phaseless near field data distributions collected over limited domains on planar surfaces is addressed as a nonlinear inverse problem. Numerical results show the good performances of the considered approach suggesting new possibilities for simplifying measurement setups in near field techniques.

New approach to antenna testing from near field phaseless data: the cylindrical scanning

A new method for recovering the complex near and far field from amplitude distributions collected over two near zone surfaces is proposed. By exploiting the mathematical properties of the radiated fields and choosing an appropriate functional of the data, the solution is found through the minimisation of the introduced functional. All details of the resulting iterative procedure are worked out for the cylindrical scanning in the three dimensional vector case where the implementation turns out to be effective thanks to a proper use of the FFT algorithm. It is shown that this new approach allows the solution to be obtained starting from a completely arbitrary point, so avoiding the local minima problem.

New technique for estimation of farfield from near-zone phaseless data

A new method for the estimation of the far field from two amplitude distributions in near zone is presented. The crucial point of the proposed approach relies on the choice of an appropriate function of the data, which is minimised in order to find the solution. It turns out that, although the problem is nonlinear, the global minimum can be found efficiently by a Newton-like minimisation procedure.