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In dynamic positron emission tomography (PET) imaging, the reconstructed image of a single frame often exhibits high noise due to limited counting statistics of projection data. This study proposed a median nonlocal means (MNLM)-based kernel method for dynamic PET image reconstruction. The kernel matrix is derived from median nonlocal means of pre-reconstructed composite images. Then the PET image intensities in all voxels were modeled as a kernel matrix multiplied by coefficients and incorporated into the forward model of PET projection data. Then, the coefficients of each feature were estimated by the maximum likelihood method. Using simulated low-count dynamic data of Zubal head phantom, the quantitative performance of the proposed MNLM kernel method was investigated and compared with the maximum-likelihood method, conventional kernel method with and without median filter, and nonlocal means (NLM) kernel method. Simulation results showed that the MNLM kernel method achieved visual and quantitative accuracy improvements (in terms of the ensemble mean squared error, bias versus variance, and contrast versus noise performances). Especially for frame 2 with the lowest count level of a single frame, the MNLM kernel method achieves lower ensemble mean squared error (10.43%) than the NLM kernel method (13.68%), conventional kernel method with and without median filter (11.88% and 23.50%), and MLEM algorithm (24.77%). The study on real low-dose 18F-FDG rat data also showed that the MNLM kernel method outperformed other methods in visual and quantitative accuracy improvements (in terms of regional noise versus intensity mean performance).

BACKGROUND: Dynamic positron emission tomography (PET) is a powerful tool that provides useful quantitative information on physiological and biochemical processes. However, the low signal-to-noise ratio (SNR) in short dynamic frames is a challenge. OBJECTIVE: To get high SNR in the dynamic PET and to achieve high-quality PET parametric image are the objective of this study. METHODS: Low-rank (LR) modeling and edge-preserving prior are incorporated in this study with a unified mathematical framework to improve the SNR of a dynamic PET image series. The proposed algorithm is designed to reduce noise in homogeneous areas while preserving the edges of regions of interest. RESULTS: The performance of the proposed method (LRH) is compared both visually and quantitatively by using the classic Gaussian filter and an LR expression filter on a digital brain phantom and in vivo rat study. Experimental results demonstrate that the proposed filter can achieve superior visual and quantitative performance without sacrificing spatial resolution. CONCLUSIONS: The proposed LRH is considerably effective and exhibits great potential in processing dynamic PET data with high noise levels.

The maximum-likelihood and expectation-maximization (ML-EM) algorithm as well as its accelerated variant ordered subset expectation-maximization (OS-EM) have been extensively used in positron emission tomography (PET) image reconstruction. The principal drawback of the ML-EM/OS-EM algorithm is the “checkerboard effect” with increasing iteration number. One approach to alleviate it is to filter reconstructed images during or after reconstruction process. This study investigated the applications of three advanced image-filtering algorithms, namely, total variation, bilateral filtering, and nonlocal means via an iterative correction (IC) scheme for addressing the drawback of ML-EM/OS-EM. Numerical simulated and physically acquired PET datasets were used to test the proposed IC scheme. Our results demonstrate that the IC with image-filtering scheme can achieve significant gains than the conventional ML-EM/OS-EM algorithm in reducing noise, preserving edges, and reducing the “checkerboard effect”.

Continuous loop averaging deconvolution (CLAD) is one of the proven methods for recovering transient auditory evoked potentials (AEPs) in rapid stimulation paradigms, which requires an elaborated stimulus sequence design to attenuate impacts from noise in data. The present study aimed to develop a new metric in gauging a CLAD sequence in terms of noise gain factor (NGF), which has been proposed previously but with less effectiveness in the presence of pink (1/f) noise. We derived the new metric by explicitly introducing the 1/f model into the proposed time-continuous sequence. We selected several representative CLAD sequences to test their noise property on typical EEG recordings, as well as on five real CLAD electroencephalogram (EEG) recordings to retrieve the middle latency responses. We also demonstrated the merit of the new metric in generating and quantifying optimized sequences using a classic genetic algorithm. The new metric shows evident improvements in measuring actual noise gains at different frequencies, and better performance than the original NGF in various aspects. The new metric is a generalized NGF measurement that can better quantify the performance of a CLAD sequence, and provide a more efficient mean of generating CLAD sequences via the incorporation with optimization algorithms. The present study can facilitate the specific application of CLAD paradigm with desired sequences in the clinic.

Objectives To evaluate the performance of region-of-interest (ROI)-based MRI R2* measurements by using the first-moment noise-corrected model (M1NCM) to correct the non-central Chi noise in magnitude images from phased arrays for hepatic iron content (HIC) assessment. Methods R2* values were quantified using the M1NCM model. Three approaches were employed to determine the representative R2*: fitting of the ROI-averaged signal (average-then-fit, ATF); outputting the median and mean of R2*s from the pixel-wise fitting of decay signals within the ROI (denoted as PWFmed and PWFmea, respectively). The accuracy and precision of the three approaches were evaluated on synthesized data. The agreement among these approaches and their intra- and inter-observer reproducibility were assessed on 105 thalassaemia major patients. Results Simulations showed that ATF consistently yielded the highest accuracy and precision at varying noise levels. By contrast, PWFmed and PWFmea slightly and significantly overestimated high R2* at poor signal-to-noise ratios, respectively. Patient study showed that ATF agreed well with PWFmed, whereas PWFmea produced high R2* measurements for patients with severe HIC. No significant difference was observed in the reproducibility of the three approaches. Conclusions PWFmea tends to overestimate high R2*, whereas ATF and PWFmed can produce more accurate R2* measurements for HIC assessment.

The Perona-Malik (PM) model, or the anisotropic diffusion, shows good performance for image restoration. However, it suffers from the so-called staircasing effect if the contrast parameter is small and otherwise cannot preserve edges. This paper proposes a modified Perona-Malik (MPM) model based on directional Laplacian, which diffuses image along the edge direction of the original image. A slightly weighted Laplacian is also integrated to suppress noise. The proposed model can alleviate the staircasing effect, preserve sharp discontinuities, and remove noise simultaneously. Experimental results compared with several relevant methods demonstrate the good performance of the proposed algorithm.

We present a new method to estimate noise for a single-slice sinogram of low-dose CT based on the homogenous patches centered at a special pixel, called center point, which has the smallest variance among all sinogram pixels. The homogenous patch, composed by homogenous points, is formed by the points similar to the center point using similarity sorting, similarity decreasing searching, and variance analysis in a very large neighborhood (VLN) to avoid manual selection of parameter for similarity measures.Homogenous pixels in the VLN allow us find the largest number of samples, who have the highest similarities to the center point, for noise estimation, and the noise level can be estimated according to unbiased estimation.Experimental results show that for the simulated noisy sinograms, the method proposed in this paper can obtain satisfied noise estimation results, especially for sinograms with relatively serious noises.

This letter presents an adaptive denoising method based on the singular value decomposition (SVD). By incorporating a global subspace analysis into the scheme of local basis selection, the problems of previous adaptive methods are effectively tackled. Experimental results show that the proposed method achieves outstanding preservation of image details, and at high noise levels it provides improvements in both objective and subjective quality of the denoised image when compared to the state-of-the-art methods.

We proposed a composite image guided filtering technique for dynamic PET denoising to enable quantitatively enhanced time frames. The guided filter computes the filtering output by considering the content of a guidance image, which can be the input image itself or a different image. In this paper, the composite image from the entire time series is considered as the guidance image. Thus, a local linear model is established between the composite image and individual PET time frames. Subsequently, linear ridge regression is exploited to derive an explicit composite image guided filter. For validation, 20 minute FDG PET data from a NEMA NU 4-2008 IQ phantom were acquired in the list-mode format via the Siemens Invoen micro PET, and were subsequently divided and reconstructed into 20 frames. We compared the performances (including visual and quantitative profiles) of the proposed composite image guide filter (CIGF) with a classic Gaussian filter (GF), and a highly constrained back projection (HYPR) filter. The experimental results demonstrated the proposed filter to achieve superior visual and quantitative performance without sacrificing spatial resolution. The proposed CIGF is considerably effective and has great potential to process the data with high noise for dynamic PET scans.

Due to the noisy measurement of the voxel-wise time activity curve (TAC), parametric imaging for dynamic positron emission tomography (PET) is a challenging task. To address this problem, some spatial filters, such as Gaussian filter, bilateral filter, wavelet-based filter, and so on, are often performed to reduce the noise of each frame. However, these filters usually just consider local properties of each frame without exploring the kinetic information. In this paper, aiming to improve the quantitative accuracy of parametric imaging, we present a kinetics-induced filter to lower the noise of dynamic PET images by incorporating the kinetic information. The present kinetics-induced filter is designed via the similarity between voxel-wise TACs under the framework of bilateral filter. Experimental results with a simulation study demonstrate that the present kinetics-induced filter can achieve noticeable gains than other existing methods for parametric images in terms of quantitative accuracy measures.

Sparse-view x-ray computed tomography (CT) imaging still is an interesting topic in CT field. In this paper, a new iterative image reconstruction approach for sparse-view CT with a normal-dose image was presented. The proposed cost-function which is under the criteria of penalized weighed least-square (PWLS) for CT image reconstruction mainly contains two terms, i.e., fidelity term and prior term. For the fidelity term, the weights of weighed least-square term are determined by considering the relationship between the variance and mean of the projection data in the presence of electronic background noise. For the prior term, a normal-dose image induced total variation (ndiTV) prior is proposed as an extension of the PICCS algorithm introduced by Chen et al 2008, which can relieve the requirement of misalignment reduction of the PICCS algorithm. For simplicity, the present approach is referred to as “PWLS-ndiTV”. Qualitative and quantitative evaluations were carried out on the present PWLS-ndiTV approach. Experimental results show that the present PWLS-ndiTV approach can achieve significant gains than the existing similar methods in noise and artifacts suppression.

In this paper, we propose a novel intensity-based similarity measure for medical image registration. Traditional intensity-based methods are sensitive to intensity distortions, contrast agent and noise. Although residual complexity can solve this problem in certain situations, relative modification of the parameter can generate dramatically different results. By introducing a specifically designed exponential weighting function to the residual term in residual complexity, the proposed similarity measure performed well due to automatically weighting the residual image between the reference image and the warped floating image. We utilized local variance of the reference image to model the exponential weighting function. The proposed technique was applied to brain magnetic resonance images, dynamic contrast enhanced magnetic resonance images (DCE-MRI) of breasts and contrast enhanced 3D CT liver images. The experimental results clearly indicated that the proposed approach has achieved more accurate and robust performance than mutual information, residual complexity and Jensen-Tsallis.

In X-ray computed tomography (CT) reconstruction, accurate statistical modeling of the measurement after linearity/nonlinearity calibration is essential to yield high quality diagnostic images, especially for low-dose CT. Due to the complicate noise distribution of after-log projection data or sinogram data, direct image reconstruction by filtered backprojection (FBP) approach is a very challenging task for noise reduction. As studied in our previous work, a (alpha) divergence as an important information metric has shown its advantages in describing the statistical distribution of sinogram data. In practice, the estimation of sinogram data is relevant to each detector bin, and the mismatched measure between the estimated and measured sinogram data should be balanced by using data-dependent weight factor at different detector bins, such as weighted least-square approach. With above observations, based on our previous work, in this paper, we propose a penalized weighted alpha-divergence (PWAD) approach for low-dose (i.e., low-mAs) CT sinogram iterative restoration. To test the performance of the present PWAD approach, a modified digital Shepp-Logan phantom and a physical phantom were used in our study. The results show that the present PWAD approach could significantly reduce the noise with less sacrificing image resolution. As a conclusion, the weighted alpha-divergence metric may be an interesting choice for building more reasonable cost-function in low-dose CT image reconstruction.

Reducing radiation dose as more as possible has been a significant concern in CT imaging field. Although lower the X-ray tube current (mAs) is an easy way to reduce the radiation dose directly, the associated reconstructed image quality will degrade significantly due to the excessive noise in projection data. For high quality low-dose CT reconstruction, the projection data restoration methods can adaptively suppress the noise in the highest attenuation regions. However, these methods remove not only the noise but also some edge information, which result in the reconstructed image suffers noticeable resolutions loss. In addition, it is known that a high-performance filtering methods for low-dose CT image restoration can achieve noticeable noise suppression without a significant resolution loss, but the noise-induced artifacts cannot be removed effectively due to the complex artifacts characteristics in low-dose CT image. Based on above observations, in this paper, we propose an image fusion method for low-dose CT reconstruction by making full use of the advantages of both the low-dose CT sinogram data restoration and image domain advanced edge-preserving filtering. Simulated and clinical experimental results demonstrate the presented method performs better than the existing methods in lowering the noise and preserving the image edge, without noticeable sacrifice of the spatial resolution.

How to reduce the radiation dose delivered to the patients is always an important concern since the introduction of computed tomography (CT). With respect to patients' care, the least possible radiation dose is demanded. Though clinically desired, low-dose CT (LDCT) images tend to be severely degraded by quantum noise and artifacts under low dose scan protocols. This paper proposes to improve the LDCT images by Weighted Intensity Averaging over Large-scale Neighborhoods (WIA-LN). In the implementation of the proposed WIA-LN method, the processed pixel intensities are from a selective weighted intensity averaging of the pixels belonging to different organs or attenuation tissues within large-scale neighborhoods. Effective suppression of noise and artifacts in LDCT images without obvious loss of fine anatomic features are realized. In experiment, CT images of different doses from a Siemens CT with 16 detector rows are used. Results validate an excellent performance of the proposed approach in improving clinical LDCT images.

Purpose Though highly desirable in radiologic procedures, low-dose CT (LDCT) images tend to be severely degraded by quantum noise and non-stationary artifacts. The purpose of this paper is to improve the abdominal LDCT images by the approach of Weighted Intensity Averaging over Large-scale Neighborhoods (WIA-LN). Materials and methods In the implementation of the proposed WIA-LN method, the processed pixel intensities are adaptively calculated as the weighted intensity averaging of the pixels with similar surrounding structures throughout a large-scale neighborhood. Both phantom and clinical abdominal CT images from a 16 detector rows Siemens CT were acquired at standard and 80% reduced tube current time products (150 mA s and 30 mA s corresponding to standard-dose and low-dose protocols, respectively). Visual comparison, statistical qualitative analysis (image quality scores and hepatic cyst diagnosis), and quantitative calculation (noise and contrast-to-noise ratio) are made. Results Better vision and quantitative performance are realized using the proposed WIA-LN method. Compared to original LDCT and standard-dose CT (SDCT) images, statistically significant improvement of noise/artifacts suppression, contrast preservation and hepatic cyst detection in LDCT images are achieved by using the proposed method ( P Conclusion With the tube current reduced to approximate one-fifth of the standard tube current setting, clinically acceptable images can still be obtained by using the proposed method.

Bayesian methods have been widely applied to the ill-posed problem of image reconstruction. Typically the prior information of the objective image is needed to produce reasonable reconstructions. In this paper, we propose a novel generalized Gibbs prior (GG-Prior), which exploits the basic affinity structure information in an image. The motivation for using the GG-Prior is that it has been shown to suppress noise effectively while capturing sharp edges without oscillations. This feature makes it particularly attractive for those applications of Positron Emission Tomographic (PET) where the objective is to identify the shape of objects (e.g.tumors) that are distinguished from the background by sharp edges. We show that the standard paraboloidal surrogate coordinate ascent (PSCA) algorithm can be modified to incorporate the GG-Prior using a local linearized scheme in each iteration process. The proposed GG-Prior MAP reconstruction algorithm based on PSCA algorithm has been tested on simulated, real phantom data. Comparisons the GG-Prior model with other existing prior model clearly demonstrate that the proposed GG-Prior performs better in lowering the noise, and preserving the edge and detail in the image.

To decrease the effects of the Rician noise, we propose to consider the wavelet-based diffusion method to denoise multichannel typed diffusion weighted (DW) images. The presented smoothing strategy, which utilizes complex diffusion in wavelet domain, successfully removes noise while preserving both texture and edges. To evaluate quantitatively the efficiency of the presented method in accounting for the Rician noise introduced into the DW images, the peak-to-peak signal-to-noise ratio (PSNR) and signal-to-mean squared error ratio (SMSE) metrics are adopted. Based on the synthetic and real data, we calculated the apparent diffusion coefficient (ADC) and tracked the fibers. We made comparisons between the presented model, the wave shrinkage and complex diffusion smoothing method. All the experiment results prove quantitatively and visually the better performance of the presented filter.

Fuzzy c-means (FCM) clustering algorithm is a popular model widely used in segmentation of magnetic imaging (MRI) data. The conventional FCM does not take into account the spatial information of image and get the unexpected results of segmentation when dealing with some MRI contaminated by noise. Considering the intensities of ideal MRI are piecewise constant, we present an improved model to fuzzy c-means algorithm using membership smoothing constraint. The proposed algorithm can reasonably use the spatial information of image and improve the accuracy of segmentation. Simulation MR brain image with different noise levels and real MR brain image are presented in the experiments. The results of experiments show better robustness of our algorithms to noise than other segmentation algorithms.

Parallel imaging methods provide accelerated multiple coil MR image acquisitions via reconstruction of sub-sampled It- space data. However, the images from component array coil may have strong artifacts due to motion, which in turn have the significant effect on reconstructed composite image. The least squares solution can get arbitrarily wrong when high residual errors are used in the estimation. In this article, these corrupted data are regarded as outliers in observed datum. We present a new algorithm for SENSE which is optimal in presence of artifacts or noise. We apply annealing M-estimator to make solutions insensitive to the influence caused by outliers. Phantom as well as in vivo experiments show significant improvements image quality using the new method. In addition, the benefits are demonstrated compared with conventional SENSE technique.

Summary form only given. For medical image sequences, the method of contour-based tracking proved to be a powerful tool for boundary delineation. During contour evolution, the particle filter (PF) can be used to track the feature points by enforcing spatio-temporal local constraints to handle the observation noise. To optimize the importance ratios (IR) of PF and improve its capability, a new approach of generalized fuzzy particle filter (GFPF) is presented. Compared with the unscented particle filter (UPF) that is currently a good method for object tracking, GFPF shows more advantages, including lower particle degeneracy, higher precision and so on. In addition, a likelihood estimation model is constructed to provide the observation data for GFPF. By theoretic analysis and contrast experiments, it is clear that GFPF is a good method for left ventricle tracking.

Purpose: To study the noise correlation properties of cone-beam CT (CBCT) projection data and to incorporate the noise correlation information to a statistics-based projection restoration algorithm for noise reduction in low-dose CBCT. Methods: In this study, we systematically investigated the noise correlation properties among detector bins of CBCT projection data by analyzing repeated projection measurements. The measurements were performed on a TrueBeam on-board CBCT imaging system with a 4030CB flat panel detector. An anthropomorphic male pelvis phantom was used to acquire 500 repeated projection data at six different dose levels from 0.1 mAs to 1.6 mAs per projection at three fixed angles. To minimize the influence of the lag effect, lag correction was performed on the consecutively acquired projection data. The noise correlation coefficient between detector bin pairs was calculated from the corrected projection data. The noise correlation among CBCT projection data was then incorporated into the covariance matrix of the penalized weighted least-squares (PWLS) criterion for noise reduction of low-dose CBCT. Results: The analyses of the repeated measurements show that noise correlation coefficients are non-zero between the nearest neighboring bins of CBCT projection data. The average noise correlation coefficients for the first- and second- order neighbors are about 0.20 and 0.06, respectively. The noise correlation coefficients are independent of the dose level. Reconstruction of the pelvis phantom shows that the PWLS criterion with consideration of noise correlation (PWLS-Cor) results in a lower noise level as compared to the PWLS criterion without considering the noise correlation (PWLS-Dia) at the matched resolution. Conclusion: Noise is correlated among nearest neighboring detector bins of CBCT projection data. An accurate noise model of CBCT projection data can improve the performance of the statistics-based projection restoration algorithm for low-dose CBCT.

Purpose: To study the noise correlation properties of cone-beam CT (CBCT) projection data and to incorporate the noise correlation information to a statistics-based projection restoration algorithm for noise reduction in low-dose CBCT. Methods: In this study, the authors systematically investigated the noise correlation properties among detector bins of CBCT projection data by analyzing repeated projection measurements. The measurements were performed on a TrueBeam onboard CBCT imaging system with a 4030CB flat panel detector. An anthropomorphic male pelvis phantom was used to acquire 500 repeated projection data at six different dose levels from 0.1 to 1.6 mAs per projection at three fixed angles. To minimize the influence of the lag effect, lag correction was performed on the consecutively acquired projection data. The noise correlation coefficient between detector bin pairs was calculated from the corrected projection data. The noise correlation among CBCT projection data was then incorporated into the covariance matrix of the penalized weighted least-squares (PWLS) criterion for noise reduction of low-dose CBCT. Results: The analyses of the repeated measurements show that noise correlation coefficients are nonzero between the nearest neighboring bins of CBCT projection data. The average noise correlation coefficients for the first- and second-order neighbors are 0.20 and 0.06, respectively. The noise correlation coefficients are independent of the dose level. Reconstruction of the pelvis phantom shows that the PWLS criterion with consideration of noise correlation (PWLS-Cor) results in a lower noise level as compared to the PWLS criterion without considering the noise correlation (PWLS-Dia) at the matched resolution. At the 2.0 mm resolution level in the axial-plane noise resolution tradeoff analysis, the noise level of the PWLS-Cor reconstruction is 6.3% lower than that of the PWLS-Dia reconstruction. Conclusions: Noise is correlated among nearest neighboring detector bins of CBCT projection data. An accurate noise model of CBCT projection data can improve the performance of the statistics-based projection restoration algorithm for low-dose CBCT.