Filter design for filtered back-projection guided by the interpolation model

Horbelt, Stefan; Liebling, Michael; Unser, Michaël

doi:10.1117/12.467227

Cited by 11 publications

(3 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The convolution and backprojection method is a fast two-step approach. Initially, measured projections are convolved with a filter [64]. Subsequently, a backprojection operation is conducted.…”

Section: Ct Reconstruction Algorithmsmentioning

confidence: 99%

Tomographic Reconstruction: General Approach to Fast Back-Projection Algorithms

Polevoy,

Gilmanov,

Kazimirov

et al. 2023

Mathematics

View full text Add to dashboard Cite

Addressing contemporary challenges in computed tomography (CT) demands precise and efficient reconstruction. This necessitates the optimization of CT methods, particularly by improving the algorithmic efficiency of the most computationally demanding operators—forward projection and backprojection. Every measurement setup requires a unique pair of these operators. While fast algorithms for calculating forward projection operators are adaptable across various setups, they fall short in three-dimensional scanning scenarios. Hence, fast algorithms are imperative for backprojection, an integral aspect of all established reconstruction methods. This paper introduces a general method for the calculation of backprojection operators in any measurement setup. It introduces a versatile method for transposing summation-based algorithms, which rely exclusively on addition operations. The proposed approach allows for the transformation of algorithms designed for forward projection calculation into those suitable for backprojection, with the latter maintaining asymptotic algorithmic complexity. Employing this method, fast algorithms for both forward projection and backprojection have been developed for the 2D few-view parallel-beam CT as well as for the 3D cone-beam CT. The theoretically substantiated complexity values for the proposed algorithms align with their experimentally derived estimates.

show abstract

Section: Ct Reconstruction Algorithmsmentioning

confidence: 99%

Tomographic Reconstruction: General Approach to Fast Back-Projection Algorithms

Polevoy,

Gilmanov,

Kazimirov

et al. 2023

Mathematics

View full text Add to dashboard Cite

show abstract

“…Different interpolation methods have been proposed for FBP. Horbelt et al considered using spline interpolation to improve the standard FBP reconstruction [43]. Schaller et al presented a spiral interpolation approach for multislice spiral computed tomography [44].…”

Section: Introductionmentioning

confidence: 99%

Deep Filtered Back Projection for CT Reconstruction

Tan,

Liu,

Xiang

et al. 2024

IEEE Access

View full text Add to dashboard Cite

Filtered back projection (FBP) is a classic analytical algorithm for computed tomography (CT) reconstruction, with high computational efficiency. However, images reconstructed by FBP often suffer from excessive noise and artifacts. The original FBP algorithm uses a window function to smooth signals and a linear interpolation to estimate projection values at un-sampled locations. In this study, we propose a novel framework named DeepFBP in which an optimized filter and an optimized nonlinear interpolation operator are learned with neural networks. Specifically, the learned filter can be considered as the product of an optimized window function and the ramp filter, and the learned interpolation can be considered as an optimized way to utilize projection information of nearby locations through nonlinear combination. The proposed method remains the high computational efficiency of the original FBP and achieves much better reconstruction quality at different noise levels. It also outperforms the statistical iterative algorithm, with computational time being reduced in an order of two, and state-of-the-art postprocessing deep learning methods that have deeper and more complicated network structures.

show abstract

“…By those approaches the image quality was similar with or superior to that using the standard FBP technique. In [16], the spline interpolation and ramp filtering had been combined to improve the standard FBP algorithm, by which the image quality could also be improved somewhat.…”

Section: Introductionmentioning

confidence: 99%

A novel scheme to design the filter for CT reconstruction using FBP algorithm

Shi

Luo

2013

BioMed Eng OnLine

View full text Add to dashboard Cite

BackgroundThe Filtered Back-Projection (FBP) algorithm is the most important technique for computerized tomographic (CT) imaging, in which the ramp filter plays a key role. FBP algorithm had been derived using the continuous system model. However, it has to be discretized in practical applications, which necessarily produces distortion in the reconstructed images.MethodsA novel scheme is proposed to design the filters to substitute the standard ramp filter to improve the reconstruction performance for parallel beam tomography. The design scheme is presented under the discrete image model and discrete projection environment. The designs are achieved by constrained optimization procedures. The designed filter can be regarded as the optimal filter for the corresponding parameters in some ways.ResultsSome filters under given parameters (such as image size and scanning angles) have been designed. The performance evaluation of CT reconstruction shows that the designed filters are better than the ramp filter in term of some general criteria.ConclusionsThe 2-D or 3-D FBP algorithms for fan beam tomography used in most CT systems, are obtained by modifying the FBP algorithm for parallel beam tomography. Therefore, the designed filters can be used for fan beam tomography and have potential applications in practical CT systems.

show abstract

Filter design for filtered back-projection guided by the interpolation model

Cited by 11 publications

References 7 publications

Tomographic Reconstruction: General Approach to Fast Back-Projection Algorithms

Tomographic Reconstruction: General Approach to Fast Back-Projection Algorithms

Deep Filtered Back Projection for CT Reconstruction

A novel scheme to design the filter for CT reconstruction using FBP algorithm

Contact Info

Product

Resources

About