Sparse dynamic tomography: a shearlet-based approach for iodine perfusion in plant stems

Abstract

In this paper we propose a motion-aware variational approach to reconstruct moving objects from sparse dynamic data. The motivation of this work stems from X-ray imaging of plants perfused with a liquid contrast agent, aimed at increasing the contrast of the images and studying the phloem transport in plants over time.The key idea of our approach is to deploy 3D shearlets as a space-temporal prior, treating time as the third dimension. The rationale behind this model is that a continuous evolution of a cartoonlike object is well suited for the use of 3D shearlets. We provide a basic mathematical analysis of the variational model for the image reconstruction. The numerical minimization is carried out with primaldual scheme coupled with an automated choice of regularization parameter. We test our model on different measurement setups: a simulated phantom especially designed to resemble a plant stem, with spreading points to simulate a spreading contrast agent; a measured agarose gel phantom to demonstrate iodide diffusion and geometry prior to imaging living sample; a measured living tree grown in vitro and perfused with a liquid sugar-iodine-mix. The results, compared against a 2D static model, show that our approach provides reconstructions that capture well the time dynamic of the contrast agent onset and are encouraging to develop microCT as a tool to study phloem transport using iodine tracer.

4D Dual-Tree Complex Wavelets for Time-Dependent Data

“…Finally, we incidentally mention that the inclusion of the third spatial direction seems to improve the quality of robust- ness of the reconstructions compared to the similar 2D + time setup in [3]. While the angular sampling is definitely sparse (just 30 projections), this does not affect the 𝑧-direction which provides additional robustness and seems to decrease to some extent the ill-posedness of the problem.…”

“…One way to overcome illposedness, and therefore guarantee a stable (and unique) solution, is to add regularization to the problem [9]. In the latest years, sparse regularization strategies, based on the paradigm that for each class of data, there exists a sparsifying representation system (such as wavelets or shearlets), have been widely used in CT applications, including dynamic CT (see [3] and references therein).…”

“…Starting from the model first introduced in [3] for the 2D+time case, we extend it to the 4D case, using complex wavelets rather than shearlets as a regularizer.…”

“…This method was first introduced in [22] using Haar wavelet regularization in traditional 2D tomography regularization and contains a detailed explanation of the automated sparsity control. Recently we applied the method to 2D+time dynamic tomography setting using shearlets [3], where we also motivated the choice of this model further.…”

Review of high-speed imaging with lab-based x-ray computed tomography

“…All high-speed/in-situ publications included in figure 13 use FBP for fair comparative purposes, but there were 9 out of the 596 studies from the literature search that used iterative reconstruction methods that typically require a lower numbers of projections [55,[110][111][112][113][114][115][116][117]. For example Myers et al [113] experiments with two-phase fluid flow, used an iterative algorithm that exploits the a priori knowledge of the sample.…”