The Fast Multipole Method for Sparse Solution of Linear Inverse Scattering Problems

2018-11-02
Miran, Emre Alp
Koç, Seyit Sencer
The sparse solution for the linear inverse problems provide useful results for many fundamental engineering applications such as radar imaging. The studies in the literature has shown that the computational methods for the sparse solution tend to be slow as the imaging problem gets electromagnetically large, therefore the image reconstruction gets harder for the existing computational resources. The fast multipole method (FMM) can reduce the number of operations and the memory requirement for the solution of the system. In this study, we apply the FMM to accelerate the sparse solution of the inverse scattering problem.

Suggestions

Performance Comparison of Different Sparse Array Configurations for Ultra-Wideband, Near-field Imaging Applications
Cetin, Beyzat Talat; Alatan, Lale (2017-03-24)
The aim of this study is to compare the performance of different multiple-input multiple-output (MIMO) array topologies, intended to be used in ultra-wideband (UWB) near-field imaging applications, by using an analysis method that does not include the effects of image reconstruction algorithm. For this purpose, maximum projection method, previously proposed for the analysis of UWB arrays under far-field conditions, is utilized and modified to obtain two way beam patterns of UWB arrays operating in the near-...
Evaluation of Sparsity-based Methods for Parameterized Source Separation
Baskaya, Hasan Can; Öktem, Sevinç Figen (2020-10-07)
Parametric reconstruction problems arise in many areas such as array processing, wireless communication, source separation, and spectroscopy. In a parametric recovery problem, the unknown model parameters in each superimposed signal are estimated from noisy observations. Sparsity-based methods used in compressive sensing are also applied to parametric recovery problems. These methods discretize the parameter space to form a dictionary whose atoms correspond to candidate parameter values, represent the data ...
A Bayesian approach to inclusion and performance analysis of using extra information in bioelectric inverse problems
Serinağaoğlu Doğrusöz, Yeşim; Macleod, Robert S. (The Institute of Electrical and Electronics Engineers Signa Processing Society (IEEE); 2003-12-16)
Due to attenuation and spatial smoothing that occurs in the conducting media, the bioelectric inverse problem of estimating sources from remote measurements is ill-posed and solution requires regularization. Recent studies showed that employing Bayesian methods could help increase accuracy. The basic limitations are the availability of good a priori information about the solution, and the lack of a "good" error metric. In this paper, we employ Bayesian methods, and present the mathematical framework for inc...
Evaluation of classical and sparsity-based methods for parametric recovery problems
Başkaya, Hasan Can; Öktem, Figen S..; Department of Electrical and Electronics Engineering (2020)
Parametric reconstruction problems arise in many areas such as array processing, wireless communication, source separation, and spectroscopy. In a parametric recovery problem, the unknown model parameters in each superimposed signal are estimated from noisy observations. Classical methods perform the recovery over directly on the continuous-valued parameter space by solving a nonlinear inverse problem. Recently sparsity-based methods have also been applied to parametric recovery problems. These methods disc...
Evaluation of discrete ordinates method for radiative transfer in rectangular furnaces
Selçuk, Nevin (1997-01-01)
The discrete ordinates method (DOM) and discrete transfer method (DTM) were evaluated from the viewpoints of both predictive accuracy and computational economy by comparing their predictions with exact solutions available from a box-shaped enclosure problem with steep temperature gradients. Comparative testing shows that the S-4 approximation produces better accuracy in radiative energy source term than in flux density in three orders of magnitude less CPU time than that required by the DTM. The S-4 approxi...
Citation Formats
E. A. Miran and S. S. Koç, “The Fast Multipole Method for Sparse Solution of Linear Inverse Scattering Problems,” 2018, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/55625.