Abstract
All imaging modalities such as computed tomography, emission tomography and magnetic resonance imaging require a reconstruction approach to produce an image. A common image processing task for applications that utilise those modalities is image segmentation, typically performed posterior to the reconstruction. Recently, the idea of tackling both problems jointly has been proposed. We explore a new approach that combines reconstruction and segmentation in a unified framework. We derive a variational model that consists of a total variation regularised reconstruction from undersampled measurements and a Chan–Vese-based segmentation. We extend the variational regularisation scheme to a Bregman iteration framework to improve the reconstruction and therefore the segmentation. We develop a novel alternating minimisation scheme that solves the non-convex optimisation problem with provable convergence guarantees. Our results for synthetic and real data show that both reconstruction and segmentation are improved compared to the classical sequential approach.
Highlights
Image reconstruction plays a central role in many imaging modalities for medical and non-medical applications
We focus on the specific magnetic resonance imaging (MRI) application; our proposed joint method can be applied to other imaging problems in which the measured data is connected to the image via a linear and bounded forward operator, cf
We show the total variation (TV) reconstruction 2b, where the parameter α has been optimised with respect to peak signal to noise ratio (PSNR) and its sequential segmentation 2f with optimal β with respect to relative segmentation error (RSE)
Summary
Image reconstruction plays a central role in many imaging modalities for medical and non-medical applications. The underlying idea is to incorporate prior knowledge about the objects that we want to segment in the reconstruction step, introducing additional regularity in our solution In this unified framework, we expect that the segmentation will benefit from sharper reconstructions. We investigated the performance of our model for two different applications: bubbly flow and cancer imaging We show that both reconstruction and segmentation benefit from this method, compared to the traditional sequential approaches, suggesting that error propagation is reduced. We consider the edge-preserving total variation regularisation for both the reconstruction and segmentation term using Bregman distances In this unified Bregman iteration framework, we have the advantage of improving the reconstruction by reducing the contrast bias in the TV formulation, which leads to more accurate segmentation. We investigate the robustness of our model by testing the undersampling rate up to its limit and by considering different noise levels
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