The ROI CT problem: a shearlet-based regularization approach

Abstract

Abstract. The possibility to significantly reduce the X-ray radiation dose and shorten the scanning time is particularly appealing, especially for the medical imaging community. Regionof-interest Computed Tomography (ROI CT) has this potential and, for this reason, is currently receiving increasing attention. Due to the truncation of projection images, ROI CT is a rather challenging problem. Indeed, the ROI reconstruction problem is severely ill-posed in general and naive local reconstruction algorithms tend to be very unstable. To obtain a stable and reliable reconstruction, under suitable noise circumstances, we formulate the ROI CT problem as a convex optimization problem with a regularization term based on shearlets, and possibly nonsmooth. For the solution, we propose and analyze an iterative approach based on the variable metric inexact line-search algorithm (VMILA). The reconstruction performance of VMILA is compared against different regularization conditions, in the case of fan-beam CT simulated data. The numerical tests show that our approach is insensitive to the location of the ROI and remains very stable also when the ROI size is rather small. IntroductionRegion-of-interest Computed Tomography (ROI CT) is an X-ray based incomplete data imaging acquisition modality [1]. Since X-ray radiation exposure comes with health hazards for patients, the possibility to reconstruct only a small ROI using truncated projection data is particularly appealing, especially in biomedical application, due to its potential to lower the X-ray radiation dose and reduce the scanning time. However, reconstructing a density function from its projections is an ill-posed problem, with the ill-posedness becoming more severe when projections are truncated, as in the case of ROI CT. Therefore, traditional approaches, like Filtered BackProjection, in general produce unacceptable visual artifacts and are unstable to noise.To address the problem of ROI reconstruction from truncated projections, a variety of ad hoc methods, both analytic and algebraic, were proposed in the last years (see [2] and the references therein), but usually require restrictive hypothesis on the ROI or are rather sensitive to noise.To overcome these drawbacks, we formulate ROI CT as a convex optimization problem with a regularized objective function, possibly nonsmooth, and based on a very recently introduced multiscale method called shearlets [3]. The use of less recent multiscale methods is not new in CT application, even combined with analytic approaches [4]. The approach we present

A nonsmooth regularization approach based on shearlets for Poisson noise removal in ROI tomography

“…To this end, the ROI reconstruction problem can be seen as an extrapolation problem, following the same idea presented in [34,35,21]:…”

Data-Consistent Local Superresolution for Medical Imaging

“…Medical tomographic imaging is one of the pillar area in healthcare. Unlike other application scenarios in general computational imaging, medical imaging practitioners pay significant more attentions and cares in critical areas, aka, regions-of-interest (ROI) (Bubba et al, 2016). Very often, observing the abnormal (for example, a tumor or a tiny crack of some bone) in a patient is much more critical than reconstructing a overall clean image (Antun et al, 2020).…”

An Automatic Regularization Method: An Application for 3-D X-Ray Micro-CT Reconstruction Using Sparse Data

“…Total variation regularization and shearlet sparsity have been successfully combined for 2D tomographic data in [20], [21], including sparse data with a minimum of 128 angles. Shearlets have been shown to be useful for 2D region-of-interest tomography in [22] and for limited-angle tomography in [23].…”