Attenuated Vector Tomography -- An Approach to Image Flow Vector Fields with Doppler Ultrasonic Imaging

Huang, Qiu; Peng, Qiyu; Huang, Bin; Cheryauka, Arvi; Gullberg, Grant T.

doi:10.2172/943972

Cited by 4 publications

(4 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We refer also to the equivalent result provided by Natterer in [7]. Many further contributions followed up, without being exhaustive, we may cite [8][9][10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Approximate inverse and Sobolev estimates for the attenuated Radon transform

Rigaud

Lakhal

2015

Inverse Problems

View full text Add to dashboard Cite

The ill-posedness of the attenuated Radon transform is a challenging issue in practice due to the Poisson noise and the high level of attenuation. The investigation of the smoothing properties of the underlying operator is essential for developing a stable inversion. In this paper, we consider the framework of Sobolev spaces and derive analytically a reconstruction algorithm based on the method of the approximate inverse. The derived method inherits the efficiency and stability of the approximate inverse and supplies a method of extraction of contours. These algorithms appear to be efficient for an attenuation of human body type. However, for higher attenuations the ill-posedness increases exponentially what deteriorates accordingly the quality of reconstructions. Nevertheless, a high attenuation map affects less the contour extraction of a high contrast function and so can be neglected. This leads to simplifying the proposed method and circumvents in this case the artifacts due to the attenuation as attested by simulation results.

show abstract

“…We refer also to the equivalent result provided by Natterer in [7]. Many further contributions followed up, without being exhaustive, we may cite [8][9][10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Approximate inverse and Sobolev estimates for the attenuated Radon transform

Rigaud

Lakhal

2015

Inverse Problems

View full text Add to dashboard Cite

show abstract

“…Later Natterer [63] showed that transverse scalar projections would only be required; however, in practice these measurements can be difficult to acquire. Previously we investigated this for vector [64] and tensor [65] fields by simulating attenuated projections of scalar measurements around one orbit. The results indicated that the elements of the vectors are recovered, whereas components of the tensor field are not fully recovered.…”

Section: Helmholtz Decompositionmentioning

confidence: 99%

An Analytical Algorithm for Tensor Tomography From Projections Acquired About Three Axes

Tao

Rohmer

Gullberg

et al. 2022

IEEE Trans. Med. Imaging

View full text Add to dashboard Cite

Tensor fields are useful for modeling the structure of biological tissues. The challenge to measure tensor fields involves acquiring sufficient data of scalar measurements that are physically achievable and reconstructing tensors from as few projections as possible for efficient applications in medical imaging. In this paper, we present a filtered back-projection algorithm for the reconstruction of a symmetric second-rank tensor field from directional X-ray projections about three axes. The tensor field is decomposed into a solenoidal and irrotational component, each of three unknowns. Using the Fourier projection theorem, a filtered back-projection algorithm is derived to reconstruct the solenoidal and irrotational components from projections acquired around three axes. A simple illustrative phantom consisting of two spherical shells and a 3D digital cardiac diffusion image obtained from diffusion tensor MRI of an excised human heart are used to simulate directional X-ray projections. The simulations validate the mathematical derivations and demonstrate reasonable noise properties of the algorithm. The decomposition of the tensor field into solenoidal and irrotational components provides insight into the development of algorithms for reconstructing tensor fields with sufficient samples in terms of the type of directional projections and the necessary orbits for the acquisition of the projections of the tensor field. Index Terms-Filtered back-projection algorithm, solenoidal and irrotational components, tensor tomography, directional X-ray projections. I. INTRODUCTION T ENSOR tomography has found important applications in the physical sciences [1], [2], mathematics [3], and medicine [4]. Here we consider the tensor tomography problem as Manuscript

show abstract

“…Vector field tomography has not received much attention in the area of medical applications. There are only a few papers [29,22,12,13,6,33] and one PhD thesis [14] which present relevant methods. The main area of research according to these papers are Doppler back scattering for blood flow estimation, although till now there are only simulations and theoretical formulations without performing any real experiment or employing real data.…”

Section: Vector Field Reconstruction and Biomedical Imagingmentioning

confidence: 99%

Overcoming the ill-posedness through discretization in vector tomography: Reconstruction of irrotational vector fields

Koulouri¹

2017

Preprint

View full text Add to dashboard Cite

Attenuated Vector Tomography -- An Approach to Image Flow Vector Fields with Doppler Ultrasonic Imaging

Cited by 4 publications

References 5 publications

Approximate inverse and Sobolev estimates for the attenuated Radon transform

Approximate inverse and Sobolev estimates for the attenuated Radon transform

An Analytical Algorithm for Tensor Tomography From Projections Acquired About Three Axes

Overcoming the ill-posedness through discretization in vector tomography: Reconstruction of irrotational vector fields

Contact Info

Product

Resources

About