The relationship between backprojection and best linear unbiased estimation in synthetic-aperture radar imaging

Muller, Kaitlyn

doi:10.3934/ipi.2016011

Cited by 2 publications

(2 citation statements)

References 11 publications

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“…The bias piece of the MSE of the back-projected image is directly related to the resolution of the image. As was shown in [16], constraining the image to be unbiased results in the same constraint as choosing the back-projection filter such that the PSF is as close as possible to the delta function in the microlocal sense [9]. This constraint is precisely how one creates a PSF that is approximately the product of two sinc functions and leads to the standard (no attenuation) SAR resolution results [9].…”

Section: Resolution and Noise Tradeoffmentioning

confidence: 96%

Precursors for synthetic aperture radar

Cartwright

Muller

2023

Inverse Problems

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In this paper we study waveform design for synthetic-aperture radar (SAR) imaging through dispersive media. Under the assumptions of scalar wave propagation through a causal dielectric medium and single-scattering from an isotropic point scatterer, we use asymptotic analysis to derive the asymptotic approximation to the scattered electric field. From this asymptotic approximation, we define a sensing precursor that we propose for the transmit waveform for SAR imaging through dispersive material. We compare our sensing precursor with previously defined optimal waveforms (Varslot, Morales, and Cheney, Waveform design for synthetic-aperture radar imaging through dispersive media, SIAM J. Appl. Math., 71 (2011), pp. 1780 - 1800) in terms of both propagation and scattering capabilities, as well as imaging performance. With the filtered back-projection imaging algorithm that we use, we find that for high levels of signal-to-noise ratio (SNR), the optimal waveforms contain higher frequencies and thus produce better images. For low levels of SNR, the transmitted optimal waveforms and the sensing precursors are similar, thus giving comparable images.

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Section: Resolution and Noise Tradeoffmentioning

confidence: 96%

Precursors for synthetic aperture radar

Cartwright

Muller

2023

Inverse Problems

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“…where the second equality holds when we are able to integrate over the entire ξ plane. This constraint arises in other contexts, for example when we seek to find the best linear unbiased estimator of T [11] we find that the unbiased constraint is given by…”

Section: Filtered Backprojectionmentioning

confidence: 99%

A reproducing kernel Hilbert space framework for inverse scattering problems within the Born approximation

Muller¹

2019

Inverse Problems &Amp; Imaging

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In this work we develop a new reproducing kernel Hilbert space (RKHS) framework for inverse scattering problems using the Born approximation. We assume we have backscattered data of a field that is dependent on an unknown scattering potential. Our goal is to reconstruct or image this scattering potential. Assuming the scattering potential lies in a RKHS, we find that the imaging equation can be rewritten as the inner product of the desired unknown function with the adjoint of the forward operator applied to the kernel of the imaging operator. We therefore may choose the kernel of the imaging operator such that the adjoint applied to this kernel is precisely the reproducing kernel of the Hilbert space the reflectivity function lies in. In this way we are able to obtain an alternative definition of an ideal image. We will demonstrate this theory using synthetic aperture radar imaging as an example, though there are other applicable imaging modalities i.e. inverse diffraction and diffraction tomography [1,6]. We choose SAR as it was the motivating application for this work. We will compare the RKHS ideal imaging technique to the standard microlocal analytic ideal image from backprojection theory. Note this method requires a variation of the standard SAR data model with the assumption of a full two dimensional data collection surface as opposed to a one dimensional flight path, however we are able to perform imaging with a single frequency and avoid the approximations made in the backprojection imaging operator derivation.1. Introduction. In this paper we develop a new reproducing kernel Hilbert space framework for inverse scattering problems using the Born approximation. We assume we have backscattered data of some field that is dependent on an unknown scattering potential. Our goal is to reconstruct or image this scattering potential. We will use synthetic-aperture radar imaging as an example to demonstrate the theory developed in this work in terms of a real application.There are two main mathematical tasks to consider for imaging, first developing a forward model and then creating a method to invert that model to obtain information about the unknown function of interest. We will assume our collected data is in the form of a scattered field which is related to an unknown function to be reconstructed. We will therefore assume our field of interest satisfies the inhomogeneous scalar wave equation in the time domain and the inhomogeneous Helmholtz equation in the frequency domain. Thus we may use a Green's function

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The relationship between backprojection and best linear unbiased estimation in synthetic-aperture radar imaging

Cited by 2 publications

References 11 publications

Precursors for synthetic aperture radar

Precursors for synthetic aperture radar

A reproducing kernel Hilbert space framework for inverse scattering problems within the Born approximation

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