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IPI

This paper presents a new method for the exponential Radon transform
inversion based on the harmonic analysis of the Euclidean motion
group of the plane. The proposed inversion method is based on the
observation that the exponential Radon transform can be modified to
obtain a new transform, defined as the modified exponential Radon
transform, that can be expressed as a convolution on the Euclidean
motion group. The convolution representation of the modified
exponential Radon transform is block diagonalized in the Euclidean
motion group Fourier domain. Further analysis of the block diagonal
representation provides a class of relationships between the
spherical harmonic decompositions of the Fourier transforms of the
function and its exponential Radon transform. These relationships
and the block diagonalization lead to three new reconstruction
algorithms. The proposed algorithms are implemented using the fast
implementation of the Euclidean motion group Fourier transform and
their performances are demonstrated in numerical simulations. Our
study shows that convolution representation and harmonic analysis
over groups motivates novel solutions for the inversion of the
exponential Radon transform.

IPI

We derive an optimal transmit waveform for filtered backprojection-based synthetic-aperture imaging. The waveform is optimal in terms of minimising the mean square error (MSE) in the resulting image. Our optimization is performed in two steps: First, we consider the minimum-mean-square-error (MMSE) for an arbitrary but fixed waveform, and derive the corresponding filter for the filtered backprojection reconstruction. Second, the MMSE is further reduced by finding an optimal transmit waveform.
The transmit waveform is derived for stochastic models of the scattering objects of interest (targets), other scattering objects (clutter), and additive noise. We express the waveform in terms of spatial spectra for the random fields associated with target and clutter, and the spectrum for the noise process.
This approach results in a constraint that involves only the amplitude of the Fourier transform of the
transmit waveform. Therefore, considerable flexibility is left for incorporating additional requirements, such as minimal variation of transmit amplitude and phase-coding.

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