Verification of optimal discretization in multi-plane phaseless diagnostics

Enhancing Deep Learning-Based Antenna Array Coefficient Reconstruction through Optimized Data Management

“…The resultant optimal ∆ z is non-uniform, meaning that the spacing between the first and second scanning plane differs from that between the second and third plane. The findings in [12] affirm that this non-uniform ∆ z yields more independent data compared to the uniform counterpart, significantly simplifying source reconstruction. We provide a concise summary of this approach below.…”

“…Subsequently, it establishes a discrete eigenvalue problem, illustrating that the most crucial portion of the singular system can be accurately computed by employing a slightly higher number of samples than the Shannon number. This pioneering strategy was initially devised for one-dimensional sources and was further refined for two-dimensional current sources in [12]. Generally, this scheme exploits the singular system of the continuous radiation operator described in function (1).…”

“…This introduces the critical question of determining the optimal ∆ z to position these planes effectively. This issue has been appropriately addressed in prior work [12]. The resultant optimal ∆ z is non-uniform, meaning that the spacing between the first and second scanning plane differs from that between the second and third plane.…”

“…This problem is exceptionally challenging because it is both nonlinear and ill-posed [8], demanding a substantial number of measurements to attain a satisfactory level of accuracy. Several methodologies have been devised to tackle such complex challenges, including phase retrieval algorithms [9], and optimization techniques [10,11,12,13]. Nonetheless, there remains plenty room for enhancement in terms of computational efficiency, robustness, and adaptability to diverse scenarios.…”

“…We assume that the optimality achieved by the ONUS approach facilitates the prediction of true solutions to inverse problems. Notably, the ONUS scheme, initially devised for 1D problems and later extended to 2D problems [12], focuses on creating an optimal scanning plane that minimizes the number of measurements while preserving reconstruction quality. The data points in this plane exhibit irregular spacing, diverging from the typical equally spaced distribution.…”