A Tensor Factorization Method for 3D Super-Resolution with Application to Dental CT

TL;DR

A recently introduced tensor-factorization-based approach offers a fast solution without the use of known image pairs or strict prior assumptions for single image resolution enhancement with an offline estimate of the system point spread function.

Abstract

Available super-resolution techniques for 3D images are either computationally inefficient prior-knowledge-based iterative techniques or deep learning methods which require a large database of known low- and high-resolution image pairs. A recently introduced tensor-factorization-based approach offers a fast solution without the use of known image pairs or strict prior assumptions. In this article this factorization framework is investigated for single image resolution enhancement with an off-line estimate of the system point spread function. The technique is applied to 3D cone beam computed tomography for dental image resolution enhancement. To demonstrate the efficiency of our method, it is compared to a recent state-of-the-art iterative technique using low-rank and total variation regularizations. In contrast to this comparative technique, the proposed reconstruction technique gives a 2-order-of-magnitude improvement in running time -- 2 minutes compared to 2 hours for a dental volume of 282$\times$266$\times$392 voxels. Furthermore, it also offers slightly improved quantitative results (peak signal-to-noise ratio, segmentation quality). Another advantage of the presented technique is the low number of hyperparameters. As demonstrated in this paper, the framework is not sensitive to small changes of its parameters, proposing an ease of use.

Figures (7)

• Figure 1: Illustration of tensor factorization. $F$ is the number of outer products formed by mode-1 ($U^1_i := U^1(:,i)$), mode-2 ($U^2_i := U^2(:,i)$) and mode-3 ($U_i^3 := U^3(:,i)$) fibers summing up to a rank-$F$ tensor.
• Figure 2: Illustration of the mode-1 product. The mode-1 fibers of the 3D tensor are extracted and pre-multiplied by the 2D matrix. This example can illustrate a downsample operation with rate 2 in the first dimension.
• Figure 3: Tensor rank and image complexity. In example a) a single dark pixel (representing 1) in the white (representing 0) volume can be expressed by one outer product. In b) two neighboring pixels are dark, making one outer product sufficient for their description. In c) the pixel value is printed on the cell, equals 0 if not present. Two fibers are linearly dependent ($2\times$ [21,35] = [42,70]), so the volume can be decomposed using a tensor rank of $F=1$.
• Figure 4: Results on Sample #1. In the rows the CBCT, LRTV output, TF-SISR output and µCT images can be seen, whereas the columns correspond to one axial, a coronal and a sagittal slice. The CBCT image is shown on the same scale as the HR images, for better comparison. The location of the slices within the volume is illustrated on the CBCT images in colored lines.
• Figure 5: Segmentation results for CBCT, LRTV and TF-SISR for the 3 samples. The color-bar visualizes the distance between the estimated surface of the canal and the one obtained with µCT segmentation.