The Dimension of Phaseless Near-Field Data by Asymptotic Investigation of the Lifting Operator

• Main Authors: Rocco Pierri, Giovanni Leone, Raffaele Moretta
• Format: Article
• Language: English
• Published: MDPI AG 2021-07-01
• Series: Electronics
• Subjects: phase retrieval; lifting technique; data space dimension; singular values; phaseless data; independent data
• Online Access: https://www.mdpi.com/2079-9292/10/14/1658

In this paper, the question of evaluating the dimension of data space in an inverse source problem from near-field phaseless data is addressed. The study is developed for a <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2</mn><mi>D</mi></mrow></semantics></math></inline-formula> scalar geometry made up by a magnetic current strip whose square magnitude of the radiated field is observed in near non-reactive zone on multiple lines parallel to the source. With the aim of estimating the dimension of data space, at first, the lifting technique is exploited to recast the quadratic model as a linear one. After, the singular values decomposition of such linear operator is introduced. Finally, the dimension of data space is evaluated by quantifying the number of “relevant” singular values. In the last part of the article, some numerical simulations that corroborate the analytical estimation of data space dimension are shown.