New approximated inversion of spherical Radon transform in SAR imaging

Régnier, Rémi; Rigaud, Gaël; Nguyen, Maï K.

doi:10.1109/icip.2013.6738494

Cited by 1 publication

(1 citation statement)

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“…In addition, we show that inversion of the spherical Radon transform is well-posed for signals that exhibit antipodal symmetry. While techniques that attempt to invert the spherical Radon transform are typically approximate [56]- [59], our approach is exact.…”

Section: Introductionmentioning

confidence: 99%

Scale-discretised ridgelet transform on the sphere

McEwen

Price

2019

2019 27th European Signal Processing Conference (EUSIPCO)

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We first revisit the spherical Radon transform, also called the Funk-Radon transform, viewing it as an axisymmetric convolution on the sphere. Viewing the spherical Radon transform in this manner leads to a straightforward derivation of its spherical harmonic representation, from which we show the spherical Radon transform can be inverted exactly for signals exhibiting antipodal symmetry. We then construct a spherical ridgelet transform by composing the spherical Radon and scalediscretised wavelet transforms on the sphere. The resulting spherical ridgelet transform also admits exact inversion for antipodal signals. The restriction to antipodal signals is expected since the spherical Radon and ridgelet transforms themselves result in signals that exhibit antipodal symmetry. Our ridgelet transform is defined natively on the sphere, probes signal content globally along great circles, does not exhibit blocking artefacts, does not rely of any ad hoc parameters and exhibits an explicit inverse transform. No alternative ridgelet construction on the sphere satisfies all of these properties. Our implementation of the spherical Radon and ridgelet transforms is made publicly available. Finally, we illustrate the effectiveness of spherical ridgelets for diffusion magnetic resonance imaging of white matter fibers in the brain.

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Section: Introductionmentioning

confidence: 99%