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Dynamical machine learning volumetric reconstruction of objects' interiors from limited angular views.

ABSTRACT: Limited-angle tomography of an interior volume is a challenging, highly ill-posed problem with practical implications in medical and biological imaging, manufacturing, automation, and environmental and food security. Regularizing priors are necessary to reduce artifacts by improving the condition of such problems. Recently, it was shown that one effective way to learn the priors for strongly scattering yet highly structured 3D objects, e.g. layered and Manhattan, is by a static neural network [Goy et al. Proc. Natl. Acad. Sci. 116, 19848-19856 (2019)]. Here, we present a radically different approach where the collection of raw images from multiple angles is viewed analogously to a dynamical system driven by the object-dependent forward scattering operator. The sequence index in the angle of illumination plays the role of discrete time in the dynamical system analogy. Thus, the imaging problem turns into a problem of nonlinear system identification, which also suggests dynamical learning as a better fit to regularize the reconstructions. We devised a Recurrent Neural Network (RNN) architecture with a novel Separable-Convolution Gated Recurrent Unit (SC-GRU) as the fundamental building block. Through a comprehensive comparison of several quantitative metrics, we show that the dynamic method is suitable for a generic interior-volumetric reconstruction under a limited-angle scheme. We show that this approach accurately reconstructs volume interiors under two conditions: weak scattering, when the Radon transform approximation is applicable and the forward operator well defined; and strong scattering, which is nonlinear with respect to the 3D refractive index distribution and includes uncertainty in the forward operator.

SUBMITTER: Kang I

PROVIDER: S-EPMC8027224 | biostudies-literature |

REPOSITORIES: biostudies-literature

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Project description:Despite the rapid developments of X-ray cone-beam CT (CBCT), image noise still remains a major issue for the low dose CBCT. To suppress the noise effectively while retain the structures well for low dose CBCT image, in this paper, a sparse constraint based on the 3-D dictionary is incorporated into a regularized iterative reconstruction framework, defining the 3-D dictionary learning (3-DDL) method. In addition, by analyzing the sparsity level curve associated with different regularization parameters, a new adaptive parameter selection strategy is proposed to facilitate our 3-DDL method. To justify the proposed method, we first analyze the distributions of the representation coefficients associated with the 3-D dictionary and the conventional 2-D dictionary to compare their efficiencies in representing volumetric images. Then, multiple real data experiments are conducted for performance validation. Based on these results, we found: 1) the 3-D dictionary-based sparse coefficients have three orders narrower Laplacian distribution compared with the 2-D dictionary, suggesting the higher representation efficiencies of the 3-D dictionary; 2) the sparsity level curve demonstrates a clear Z-shape, and hence referred to as Z-curve, in this paper; 3) the parameter associated with the maximum curvature point of the Z-curve suggests a nice parameter choice, which could be adaptively located with the proposed Z-index parameterization (ZIP) method; 4) the proposed 3-DDL algorithm equipped with the ZIP method could deliver reconstructions with the lowest root mean squared errors and the highest structural similarity index compared with the competing methods; 5) similar noise performance as the regular dose FDK reconstruction regarding the standard deviation metric could be achieved with the proposed method using (1/2)/(1/4)/(1/8) dose level projections. The contrast-noise ratio is improved by ~2.5/3.5 times with respect to two different cases under the (1/8) dose level compared with the low dose FDK reconstruction. The proposed method is expected to reduce the radiation dose by a factor of 8 for CBCT, considering the voted strongly discriminated low contrast tissues.

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Dynamical machine learning volumetric reconstruction of objects' interiors from limited angular views.

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