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Comparing implementations of penalized weighted least-squares sinogram restoration.

ABSTRACT: A CT scanner measures the energy that is deposited in each channel of a detector array by x rays that have been partially absorbed on their way through the object. The measurement process is complex and quantitative measurements are always and inevitably associated with errors, so CT data must be preprocessed prior to reconstruction. In recent years, the authors have formulated CT sinogram preprocessing as a statistical restoration problem in which the goal is to obtain the best estimate of the line integrals needed for reconstruction from the set of noisy, degraded measurements. The authors have explored both penalized Poisson likelihood (PL) and penalized weighted least-squares (PWLS) objective functions. At low doses, the authors found that the PL approach outperforms PWLS in terms of resolution-noise tradeoffs, but at standard doses they perform similarly. The PWLS objective function, being quadratic, is more amenable to computational acceleration than the PL objective. In this work, the authors develop and compare two different methods for implementing PWLS sinogram restoration with the hope of improving computational performance relative to PL in the standard-dose regime. Sinogram restoration is still significant in the standard-dose regime since it can still outperform standard approaches and it allows for correction of effects that are not usually modeled in standard CT preprocessing.The authors have explored and compared two implementation strategies for PWLS sinogram restoration: (1) A direct matrix-inversion strategy based on the closed-form solution to the PWLS optimization problem and (2) an iterative approach based on the conjugate-gradient algorithm. Obtaining optimal performance from each strategy required modifying the naive off-the-shelf implementations of the algorithms to exploit the particular symmetry and sparseness of the sinogram-restoration problem. For the closed-form approach, the authors subdivided the large matrix inversion into smaller coupled problems and exploited sparseness to minimize matrix operations. For the conjugate-gradient approach, the authors exploited sparseness and preconditioned the problem to speed up convergence.All methods produced qualitatively and quantitatively similar images as measured by resolution-variance tradeoffs and difference images. Despite the acceleration strategies, the direct matrix-inversion approach was found to be uncompetitive with iterative approaches, with a computational burden higher by an order of magnitude or more. The iterative conjugate-gradient approach, however, does appear promising, with computation times half that of the authors' previous penalized-likelihood implementation.Iterative conjugate-gradient based PWLS sinogram restoration with careful matrix optimizations has computational advantages over direct matrix PWLS inversion and over penalized-likelihood sinogram restoration and can be considered a good alternative in standard-dose regimes.

SUBMITTER: Forthmann P

PROVIDER: S-EPMC2988831 | biostudies-other | 2010 Nov

REPOSITORIES: biostudies-other

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Project description:The suppression of noise in x-ray computed tomography (CT) imaging is of clinical relevance for diagnostic image quality and the potential for radiation dose saving. Toward this purpose, statistical noise reduction methods in either the image or projection domain have been proposed, which employ a multiscale decomposition to enhance the performance of noise suppression while maintaining image sharpness. Recognizing the advantages of noise suppression in the projection domain, the authors propose a projection domain multiscale penalized weighted least squares (PWLS) method, in which the angular sampling rate is explicitly taken into consideration to account for the possible variation of interview sampling rate in advanced clinical or preclinical applications.The projection domain multiscale PWLS method is derived by converting an isotropic diffusion partial differential equation in the image domain into the projection domain, wherein a multiscale decomposition is carried out. With adoption of the Markov random field or soft thresholding objective function, the projection domain multiscale PWLS method deals with noise at each scale. To compensate for the degradation in image sharpness caused by the projection domain multiscale PWLS method, an edge enhancement is carried out following the noise reduction. The performance of the proposed method is experimentally evaluated and verified using the projection data simulated by computer and acquired by a CT scanner.The preliminary results show that the proposed projection domain multiscale PWLS method outperforms the projection domain single-scale PWLS method and the image domain multiscale anisotropic diffusion method in noise reduction. In addition, the proposed method can preserve image sharpness very well while the occurrence of "salt-and-pepper" noise and mosaic artifacts can be avoided.Since the interview sampling rate is taken into account in the projection domain multiscale decomposition, the proposed method is anticipated to be useful in advanced clinical and preclinical applications where the interview sampling rate varies.

Project description:Repeated computed tomography (CT) scans are required for some clinical applications such as image-guided interventions. To optimize radiation dose utility, a normal-dose scan is often first performed to set up reference, followed by a series of low-dose scans for intervention. One common strategy to achieve the low-dose scan is to lower the x-ray tube current and exposure time (mAs) or tube voltage (kVp) setting in the scanning protocol, but the resulted image quality by the conventional filtered back-projection (FBP) method may be severely degraded due to the excessive noise. Penalized weighted least-squares (PWLS) image reconstruction has shown the potential to significantly improve the image quality from low-mAs acquisitions, where the penalty plays an important role. In this work, the authors' explore an adaptive Markov random field (MRF)-based penalty term by utilizing previous normal-dose scan to improve the subsequent low-dose scans image reconstruction.In this work, the authors employ the widely-used quadratic-form MRF as the penalty model and explore a novel idea of using the previous normal-dose scan to obtain the MRF coefficients for adaptive reconstruction of the low-dose images. In the coefficients determination, the authors further explore another novel idea of using the normal-dose scan to obtain a scale map, which describes an optimal neighborhood for the coefficients determination such that a local uniform region has a small spread of frequency spectrum and, therefore, a small MRF window, and vice versa. The proposed penalty term is incorporated into the PWLS image reconstruction framework, and the low-dose images are reconstructed via the PWLS minimization.The presented adaptive MRF based PWLS algorithm was validated by physical phantom and patient data. The experimental results demonstrated that the presented algorithm is superior to the PWLS reconstruction using the conventional Gaussian MRF penalty or the edge-preserving Huber penalty and the conventional FBP method, in terms of image noise reduction and edge/detail/contrast preservation.This study demonstrated the feasibility and efficacy of the proposed scheme in utilizing previous normal-dose CT scan to improve the subsequent low-dose scans.

Project description:This paper concentrates on the study of the Weighted Least-squares (WLS) approaches for the generation of ground displacement time-series through Differential Interferometric SAR (DInSAR) methods. Usually, within the DInSAR framework, the Weighted Least-squares (WLS) techniques have principally been applied for improving the performance of the phase unwrapping operations as well as for better conveying the inversion of sequences of unwrapped interferograms to generate ground displacement maps. In both cases, the identification of low-coherent areas, where the standard deviation of the phase is high, is requested. In this paper, a WLS method that extends the usability of the Multi-Temporal InSAR (MT-InSAR) Small Baseline Subset (SBAS) algorithm in regions with medium-to-low coherence is presented. In particular, the proposed method relies on the adaptive selection and exploitation, pixel-by-pixel, of the medium-to-high coherent interferograms, only, so as to discard the noisy phase measurements. The selected interferometric phase values are then inverted by solving a WLS optimization problem. Noteworthy, the adopted, pixel-dependent selection of the "good" interferograms to be inverted may lead the available SAR data to be grouped into several disjointed subsets, which are then connected, exploiting the Weighted Singular Value Decomposition (WSVD) method. However, in some critical noisy regions, it may also happen that discarding of the incoherent interferograms may lead to rejecting some SAR acquisitions from the generated ground displacement time-series, at the cost of the reduced temporal sampling of the data measurements. Thus, variable-length ground displacement time-series are generated. The mathematical framework of the developed technique, which is named Weighted Adaptive Variable-lEngth (WAVE), is detailed in the manuscript. The presented experiments have been carried out by applying the WAVE technique to a SAR dataset acquired by the COSMO-SkyMed (CSK) sensors over the Basilicata region, Southern Italy. A cross-comparison analysis between the conventional and the WAVE method has also been provided.

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Comparing implementations of penalized weighted least-squares sinogram restoration.

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