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

Isernia, Tommaso; Leone, Giovanni; Pierri, Rocco; Soldovieri, Francesco

doi:10.1364/josaa.16.001845

Cited by 41 publications

(42 citation statements)

References 30 publications

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“…Zeros in Fourier space are candidates (necessary but not sufficient condition) for the location of phase vortices, phase discontinuities, which are known to cause stagnation [33]. Analytical [32], statistical [3,33,34], and deterministic [30,31] methods have been proposed to overcome such singularities.…”

Section: Discussionmentioning

confidence: 99%

Phase retrieval and saddle-point optimization

Marchesini

2007

J. Opt. Soc. Am. A

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Iterative algorithms with feedback are amongst the most powerful and versatile optimization methods for phase retrieval. Among these, the hybrid inputoutput algorithm has demonstrated practical solutions to giga-element nonlinear phase retrieval problems, escaping local minima and producing images at resolutions beyond the capabilities of lens-based optical methods. Here the input-output iteration is improved by a lower dimensional subspace saddlepoint optimization.

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Section: Discussionmentioning

confidence: 99%

Phase retrieval and saddle-point optimization

Marchesini

2007

J. Opt. Soc. Am. A

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“…The GA optimization procedure was employed with the parameters listed in Table 5, while COPAS was employed with the parameters selected as in Table 6; Figure 13 depicts the excitation coefficients [I] obtained by using GA and COPAS. We have verified that the fields obtained with excitation coefficients resulting from the global GA optimization fulfill the convex constraints in (9)- (11). For the sake of brevity, we do not report the QI parameters for this solution in view of the fact that there are no significant changes with respect the results obtained with COPAS and depicted in Figures 8-10, and 11.…”

Section: Verification Of Overall Convexity Under Convex Constraintsmentioning

confidence: 65%

“…On the other hand, other useful theoretical results come into play which further simplify the solution of the problem, and justify a convex (deterministic) optimization. In fact, functionals of this kind have been extensively studied in the framework of the solution of quadratic inverse problems including array antenna synthesis [10] and phase retrieval [11], showing that fourth-order polynomial functionals of this kind can be assumed to be convex whenever the number of unknowns is much less than the number of (independent) contributions to the cost functional.…”

Section: Joint Optimization Methodsmentioning

confidence: 99%

“…Therefore, any local optimization procedure will be able to get the globally optimal solution to the problem at hand. To get the maximum reliability of such a conclusion, such a result (based on [10,11]) has also been successfully checked by comparing results of the proposed Convex Programming Approach to Shimming (COPAS), (which does not require global optimizations), with the ones resulting from a global optimization procedures based on genetic algorithm (GA). In Section 4.2 we will verify the convexity under given constraints.…”

Section: Joint Optimization Methodsmentioning

confidence: 99%

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FIELD SYNTHESIS IN INHOMOGENEOUS MEDIA: JOINT CONTROL OF POLARIZATION, UNIFORMITY AND SAR IN MRI B<sub>1</sub>-FIELD

Attardo¹,

Isernia²,

Vecchi³

2011

PIER

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Abstract-The homogeneity of the amplitude of one of the polarizations of the RF field B 1 is a crucial issue in Magnetic Resonance Imaging (MRI), and several methods have been proposed for enhancing this uniformity ("Shimming"). The existing approaches aim at controlling the homogeneity of B + 1 and limiting the Specific Absorption Rate (SAR) of the RF field by independently controlling magnitude and phase of individual excitation currents in MRI scanners, either birdcage or TEM coil system. A novel approach is presented here which allows a joint control of B + 1 uniformity, SAR, and purity of polarization of the total RF B 1 field. We propose a convex optimization procedure with convex constraints, and special attention has been devoted to the issue of convexity of the proposed functional. The method is applied to MRI brain imaging; numerical tests have been performed on a realistic head model at low, medium, and high RF field in order to assess the effectiveness of the proposed method. We found that maintaining a specific polarization plays an important role also in maintaining the homogeneity of B + 1 amplitude.

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“…Therefore, as for the thermal imaging, GPR imaging relies upon the fact that the electromagnetic signal is capable of penetrating inside opaque materials. Starting from the knowledge of the scattered field, a reconstruction of the electromagnetic properties of the investigated scene can be achieved by solving an electromagnetic inverse scattering problem, which is is nonlinear (Isernia et al, 1996(Isernia et al, , 1999 and ill-posed (Soldovieri et al, 2009).…”

Section: N Le Touz Et Al: a Joint Thermal And Electromagnetic Diagnmentioning

confidence: 99%

A joint thermal and electromagnetic diagnostics approach for the inspection of thick walls

Touz

Dumoulin

Gennarelli

et al. 2017

Geosci. Instrum. Method. Data Syst.

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Abstract. In this study, we present an inversion approach to detect and localize inclusions in thick walls under natural solicitations. The approach is based on a preliminary analysis of surface temperature field evolution with time (for instance acquired by infrared thermography); subsequently, this analysis is improved by taking advantage of a priori information provided by ground-penetrating radar reconstruction of the structure under investigation. In this way, it is possible to improve the accuracy of the images achievable with the standalone thermal reconstruction method in the case of quasiperiodic natural excitation.

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

Cited by 41 publications

References 30 publications

Phase retrieval and saddle-point optimization

Phase retrieval and saddle-point optimization

FIELD SYNTHESIS IN INHOMOGENEOUS MEDIA: JOINT CONTROL OF POLARIZATION, UNIFORMITY AND SAR IN MRI B<sub>1</sub>-FIELD

A joint thermal and electromagnetic diagnostics approach for the inspection of thick walls

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