Maximum Gain, Effective Area, and Directivity

Fundamental bounds on antenna gain are found via convex optimization of the current density in a prescribed region. Various constraints are considered, including self-resonance and only partial control of the current distribution. Derived formulas are valid for arbitrarily shaped radiators of a given conductivity. All the optimization tasks are reduced to eigenvalue problems, which are solved efficiently. The second part of the paper deals with superdirectivity and its associated minimal costs in efficiency and Q-factor. The paper is accompanied with a series of examples practically demonstrating the relevance of the theoretical framework and entirely spanning wide range of material parameters and electrical sizes used in antenna technology. Presented results are analyzed from a perspective of effectively radiating modes. In contrast to a common approach utilizing spherical modes, the radiating modes of a given body are directly evaluated and analyzed here. All crucial mathematical steps are reviewed in the appendices, including a series of important subroutines to be considered making it possible to reduce the computational burden associated with the evaluation of electrically large structures and structures of high conductivity.Comment: 12 pages, 15 figures, submitted to TA

Relaxed regularization for linear inverse problems

We consider regularized least-squares problems of the form $\min_{x} \frac{1}{2}\Vert Ax - b\Vert_2^2 + \mathcal{R}(Lx)$. Recently, Zheng et al., 2019, proposed an algorithm called Sparse Relaxed Regularized Regression (SR3) that employs a splitting strategy by introducing an auxiliary variable $y$ and solves $\min_{x,y} \frac{1}{2}\Vert Ax - b\Vert_2^2 + \frac{\kappa}{2}\Vert Lx - y\Vert_2^2 + \mathcal{R}(x)$. By minimizing out the variable $x$ we obtain an equivalent system $\min_{y} \frac{1}{2} \Vert F_{\kappa}y - g_{\kappa}\Vert_2^2+\mathcal{R}(y)$. In our work we view the SR3 method as a way to approximately solve the regularized problem. We analyze the conditioning of the relaxed problem in general and give an expression for the SVD of $F_{\kappa}$ as a function of $\kappa$. Furthermore, we relate the Pareto curve of the original problem to the relaxed problem and we quantify the error incurred by relaxation in terms of $\kappa$. Finally, we propose an efficient iterative method for solving the relaxed problem with inexact inner iterations. Numerical examples illustrate the approach.Comment: 25 pages, 14 figures, submitted to SIAM Journal for Scientific Computing special issue Sixteenth Copper Mountain Conference on Iterative Method

Modern GPR Target Recognition Methods

Traditional GPR target recognition methods include pre-processing the data by removal of noisy signatures, dewowing (high-pass filtering to remove low-frequency noise), filtering, deconvolution, migration (correction of the effect of survey geometry), and can rely on the simulation of GPR responses. The techniques usually suffer from the loss of information, inability to adapt from prior results, and inefficient performance in the presence of strong clutter and noise. To address these challenges, several advanced processing methods have been developed over the past decade to enhance GPR target recognition. In this chapter, we provide an overview of these modern GPR processing techniques. In particular, we focus on the following methods: adaptive receive processing of range profiles depending on the target environment; adoption of learning-based methods so that the radar utilizes the results from prior measurements; application of methods that exploit the fact that the target scene is sparse in some domain or dictionary; application of advanced classification techniques; and convolutional coding which provides succinct and representatives features of the targets. We describe each of these techniques or their combinations through a representative application of landmine detection.Comment: Book chapter, 56 pages, 17 figures, 12 tables. arXiv admin note: substantial text overlap with arXiv:1806.0459

PyLDM - An open source package for lifetime density analysis of time-resolved spectroscopic data

Ultrafast spectroscopy offers temporal resolution for probing processes in the femto- and picosecond regimes. This has allowed for investigation of energy and charge transfer in numerous photoactive compounds and complexes. However, analysis of the resultant data can be complicated, particularly in more complex biological systems, such as photosystems. Historically, the dual approach of global analysis and target modelling has been used to elucidate kinetic descriptions of the system, and the identity of transient species respectively. With regards to the former, the technique of lifetime density analysis (LDA) offers an appealing alternative. While global analysis approximates the data to the sum of a small number of exponential decays, typically on the order of 2-4, LDA uses a semi-continuous distribution of 100 lifetimes. This allows for the elucidation of lifetime distributions, which may be expected from investigation of complex systems with many chromophores, as opposed to averages. Furthermore, the inherent assumption of linear combinations of decays in global analysis means the technique is unable to describe dynamic motion, a process which is resolvable with LDA. The technique was introduced to the field of photosynthesis over a decade ago by the Holzwarth group. The analysis has been demonstrated to be an important tool to evaluate complex dynamics such as photosynthetic energy transfer, and complements traditional global and target analysis techniques. Although theory has been well described, no open source code has so far been available to perform lifetime density analysis. Therefore, we introduce a python (2.7) based package, PyLDM, to address this need. We furthermore provide a direct comparison of the capabilities of LDA with those of the more familiar global analysis, as well as providing a number of statistical techniques for dealing with the regularization of noisy data