Blind deconvolution in model-based iterative reconstruction for CT using a normalized sparsity measure

Abstract

Model-based iterative reconstruction techniques for CT that include a description of the noise statistics and a physical forward model of the image formation process have proven to increase image quality for many applications. Specifically, including models of the system blur into the physical forward model and thus implicitly performing a deconvolution of the projections during tomographic reconstruction, could demonstrate distinct improvements, especially in terms of resolution. However, the results strongly rely on an exact characterization of all components contributing to the system blur. Such characterizations can be laborious and even a slight mismatch can diminish image quality significantly. Therefore, we introduce a novel objective function, which enables us to jointly estimate system blur parameters during tomographic reconstruction. Conventional objective functions are biased in terms of blur and can yield lowest cost to blurred reconstructions with low noise levels. A key feature of our objective function is a new normalized sparsity measure for CT based on total-variation regularization, constructed to be less biased in terms of blur. We outline a solving strategy for jointly recovering low-dimensional blur parameters during tomographic reconstruction. We perform an extensive simulation study, evaluating the performance of the regularization and the dependency of the different parts of the objective function on the blur parameters. Scenarios with different regularization strengths and system blurs are investigated, demonstrating that we can recover the blur parameter used for the simulations. The proposed strategy is validated and the dependency of the objective function with the number of iterations is analyzed. Finally, our approach is experimentally validated on test-bench data of a human wrist phantom, where the estimated blur parameter coincides well with visual inspection. Our findings are not restricted to attenuation-based CT and may facilitate the recovery of more complex imaging model parameters.

Nanoscopic X-ray tomography for correlative microscopy of a small meiofaunal sea-cucumber

“…Thus, for this NanoCT data set of a resin-embedded specimen, an alternative alignment algorithm was devised and compared to a centre shift correction. Our approach is based on a sparsity metric recently developed for blind deconvolution in CT reconstruction 20 . Thereby, the detector offset is optimized iteratively for every view until the reconstruction employs most sparsity according to the metric.…”

“…Unlike these methods, however, our alignment routine is not restricted to merely compensating for positional shifts but can, in principle, correct for any desired geometry parameter 30 . Furthermore, it does not revolve around a parallel beam assumption 20,30 and can thereby prove beneficial to a broader range of imaging systems.…”

“…For the overview NanoCT data, only a centre shift correction was used. For the high-resolution NanoCT data, a sparsity metric to evaluate the alignment of the projections was employed 20 . Thereby, the detector offset was optimized iteratively using a gradient-free line-search algorithm to give the optimal response with respect to the metric.…”

Photon-Counting CT Reconstruction With a Learned Forward Operator

“…A number of algorithms have been developed for detector blurring in single energy CT. For example, [4] combine twostep reconstruction with deconvolution of a known detector blur, and [5] device a one-step scheme for blind deconvolution. Likewise, there is a growing body of research on reconstruction methods for spectral CT [6].…”

Ultrasonic Image Optimization based on Double Constraint Algorithm

“…In 2019, Chen et al [9] proposed a blind deblurring method based on a prior local maximum gradient (LMG), which calculates the local maximum gradient and an effective optimization scheme by introducing a linear operator. In 2020, Zhou et al [10] proposed a joint prior model for the case that the pixel values of the dark channel and bright channel in some images are not concentrated on 0 and 1 respectively. The model combines the prior extreme channel and L 0 normalized intensity and gradient to remove the blur of blind images.…”