CT image reconstruction from sparse projections using adaptive total generalised variation with soft thresholding

The quantitative analysis of the blood flow in the brain tissue is one of the important problems in neurosurgery. It arises when diagnosing acute ischemic stroke. This problem can be solved using computed tomography (CT) perfusion imaging. There are various methods for extracting quantitative characteristics of cerebral blood flow from CT perfusion data, which differ in degrees of their noise resistance. More noise-resistant methods enable the reduction in radiation doses when conducting the examination of the patient. Hence, the development of noise-resistant methods is an important problem. This paper presents an algorithm for evaluating the quantitative characteristics of cerebral blood flow, based on the regularization using the projection onto a set of monotonic functions while minimizing the functional of total generalized variation (TGV). The proposed approach is tested on synthetic and real-world data. It yields better results than the singular value decomposition (SVD) method with Tikhonov regularization and methods of total variation (TV) minimization and TGV minimization.

Radiation dose reduction without losing CT image quality has been an increasing concern. Reducing the number of X-ray projections to reconstruct CT images, which is also called sparse-projection reconstruction, can potentially avoid excessive dose delivered to patients in CT examination. To overcome the disadvantages of total variation (TV) minimization method, in this work we introduce a novel adaptive TpV regularization into sparse-projection image reconstruction and use FISTA technique to accelerate iterative convergence. The numerical experiments demonstrate that the proposed method suppresses noise and artifacts more efficiently, and preserves structure information better than other existing reconstruction methods.

Spectral computed tomography (CT)-reconstructed images often exhibit severe noise and artifacts, which compromise the practical application of spectral CT imaging technology. Methods that use tensor dictionary learning (TDL) have shown superior performance, but it is difficult to obtain a high-quality pre-trained global tensor dictionary in practice. In order to resolve this problem, this paper develops an algorithm called tensor decomposition with total generalized variation (TGV) for sparse-view spectral CT reconstruction. In the process of constructing tensor volumes, the proposed algorithm utilizes the non-local similarity feature of images to construct fourth-order tensor volumes and uses Canonical Polyadic (CP) tensor decomposition instead of pre-trained tensor dictionaries to further explore the inter-channel correlation of images. Simultaneously, introducing the TGV regularization term to characterize spatial sparsity features, the use of higher-order derivatives can better adapt to different image structures and noise levels. The proposed objective minimization model has been addressed using the split-Bregman algorithm. To assess the performance of the proposed algorithm, several numerical simulations and actual preclinical mice are studied. The final results demonstrate that the proposed algorithm has an enormous improvement in the quality of spectral CT images when compared to several existing competing algorithms.

In this article, we developed and analyzed a thresholding method in which soft thresholding estimators are independently expanded by empirical scaling values. The scaling values have a common hyper-parameter that is an order of expansion of an ideal scaling value that achieves hard thresholding. We simply call this estimator a scaled soft thresholding estimator. The scaled soft thresholding is a general method that includes the soft thresholding and non-negative garrote as special cases and gives an another derivation of adaptive LASSO. We then derived the degree of freedom of the scaled soft thresholding by means of the Stein's unbiased risk estimate and found that it is decomposed into the degree of freedom of soft thresholding and the reminder connecting to hard thresholding. In this meaning, the scaled soft thresholding gives a natural bridge between soft and hard thresholding methods. Since the degree of freedom represents the degree of over-fitting, this result implies that there are two sources of over-fitting in the scaled soft thresholding. The first source originated from soft thresholding is determined by the number of un-removed coefficients and is a natural measure of the degree of over-fitting. We analyzed the second source in a particular case of the scaled soft thresholding by referring a known result for hard thresholding. We then found that, in a sparse, large sample and non-parametric setting, the second source is largely determined by coefficient estimates whose true values are zeros and has an influence on over-fitting when threshold levels are around noise levels in those coefficient estimates. In a simple numerical example, these theoretical implications has well explained the behavior of the degree of freedom. Moreover, based on the results here and some known facts, we explained the behaviors of risks of soft, hard and scaled soft thresholding methods.

Isotropic and anisotropic filtering norm-minimization: A generalization of the TV and TGV minimizations using NESTA

Wavelet denoising techniques with applications to experimental geophysical data

In the CT image reconstruction, the authors investigate the obtainable information content about object to be imaged from its finite number of projections and the structure of the reconstruction error due to the insufficient number of projections. They can explicitly demonstrate that the mechanism which limits the resolution of CT image is angular aliasing. Based on this investigation, a new CT image reconstruction algorithm is developed, which produces high quality artifactless images even in the case of a small number of projections. The image quality reconstructed by the proposed algorithm is superior to that by the conventional filtered backprojection (FBP) algorithm. >

To investigate the relationship between the number of basis projections for local computed tomography (CT) and the detection of proximal caries and to find a minimum number of projections needed to maintain diagnostic accuracy. We presented observers (n = 12) with stacks of both axial and vertical CT slices of 23 extracted teeth placed in a dry human mandible. The slices were prepared with 14, 20, 33 and 100 basis projections. The observers scored the proximal surfaces for the presence of caries on a 1-5 confidence scale. The performance of the varying number of projections was compared with conventional digital radiographs. The performance of all four CT modalities was significantly better than conventional radiographs (P = 0.005 to P = 0.021) and showed a consistent increase with the number of projections. Diagnostic performance depended significantly on lesion depth (P = 0.00), but not on observer. We conclude that the number of CT projections used can be reduced at least to 20 with the diagnostic performance still markedly better than that of conventional film, provided that the observer can make use of both axial and vertical stacks of CT slices.

The shrinkage function has an important effect on the image denoising results. An adaptive shrinkage function is developed in this paper to shrink the small coefficients properly for image denoising based on neighborhood characteristics. The shrinkage function is determined by the number of large coefficients near the current signal coefficients. In this way, different shrinkage functions can be adaptively used to deal with different coefficients in the process of image denoising, instead of using fixed shrinkage functions. Experimental results show that the SNR of the image processed by the adaptive shrink function algorithm is better than that processed by the soft threshold, hard threshold, and neighborhood shrink algorithm. Moreover, compared with the traditional soft threshold, hard threshold and neighborhood shrink algorithm, the PSNR of the algorithm using adaptive shrink function increases by 3.68dB, 2.28dB and 0.61dB, respectively. In addition, the proposed new algorithms, soft threshold and hard threshold, are combined with empirical Wiener filtering and shift invariant (TI) scheme to compare their image noise reduction effects. The results show that the PSNR can be improved significantly by using the adaptive shrink function algorithm combined with empirical Wiener filtering and shift invariant (TI) scheme.

In this paper, the noise of 3D computed tomography (CT) image reconstruction using QR-Decomposition is analyzed. There are several types of image noise that can interfere with the interpretation of an image. Here, the noise introduced by the reconstruction process is studied. In this analysis, condition numbers are calculated with different CT model parameters, three dimensional (3D) CT image reconstruction with simulated and real data are performed, image noise analysis is performed through various image quality parameters and the condition number of the linear system is related with the image quality parameters. Results show the condition number's dependence on the CT model. Image reconstructions with simulated data show errors significantly below the condition number theoretical bound and image reconstructions with real data show that quality improvements depend strongly on the condition number. This allows a reduction on the number of projections without compromising image quality and places this reconstruction method as a strong candidate for low-dose 3D CT imaging reconstruction.

Image De-noising is a problem of prime importance in the field of Image Processing ranging from Medical Imaging to Satellite imaging. The main purpose of an Image de-noising algorithm is to reduce the noise level to improve both the interpretability and visual aspect of the images. This paper propose to indicate the suitability of different Multi-resolution transforms, viz Wavelets, Ridgelets and Curvelets in de-noising various imaging modalities corrupted by Random noise, Gaussian noise, Speckle Noise, Salt and Pepper Noise and Poisson noise. Though the comparative study is based on various imaging modalities, due relevance is given to medical images like Computed Tomography (CT), Magnetic resonance Imaging (MRI) and X-ray images. Experiments are conducted on various image data sets namely Natural, Satellite and Medical Images with the Multi-resolution transforms using two existing thresholding strategies, namely Soft and Hard Thresholding. A comprehensive evaluation of three different types of Multiresolution transforms corrupted with different types of noise is provided and the quality of de-noising is measured in terms of Peak Signal to Noise ratio (PSNR). Experimental results indicate that the Curvelets reveal superior performance over wavelets and Ridgelets in terms of PSNR value and perceptible quality.

The air container CT inspection system has been developed as a high space-resolution, high density-resolution CT scanner. The design of CT reconstruction software based on the system uses the back project algorithm to construct the CT images, and the filter functions are also included to process the CT data. Because the system can be used to inspect the large objects that cannot be penetrated easily by gamma-ray, the reconstructed CT images may have some artifacts that may damage CT image. The digital subtraction method is used to realize the CT reconstruction for the edge parts of large object that has big gamma-ray attenuation in the center part of the object. The nonlinear effect while measuring is corrected using serials of thin ion plates. The CT images for large objects are improved obviously by using the plate correction. The CT images based on the back project algorithm are also obtained by using the non-perfect projection data. The obtained CT image can have a certain precision to meet the demand. And the principal of the CT reconstruction using the non-perfect project data is also analyzed. The noise influence to the CT imaging quality is also analyzed. Different kinds of noises were added to the signals of all channels or selected channel. The experiment showed that the CT construction realized by the paper has high density resolution and high spatial resolution. The designing for CT construction software is successful.

The nuclear norm minimization method emerged from a patch-based low-rank model leads to an excellent image denoising performance, where the non-local self-similarity over image patches is exploited. However, natural images are normally with complex and irregular image patches, which cannot be well represented using only a low-rank model, and thus most of them suffer from the over-penalty problem especially for images with lots of local irregular structures (e.g., fine details or sharp edges), and then results in over-smoothing problem after denoising. On the other hand, in order to represent the irregular components, edges defined over pixel level are often exploited. While the total variation (TV) is a well-known prior to remove noises and preserve edges, it might yield undesired staircase artifacts. The total generalized variation (TGV), a generalization of TV, can largely alleviate such staircase artifacts. Consequently, in order to deal with the over-smoothing problem aroused by a low-rank model, we propose a re-weighted TGV regularized nuclear norm minimization model for local structure preserving image denoising. Thanks to the split Bregman method, our proposed model can be effectively solved. A re-weighted strategy is developed to adaptively update the weight parameters of TGV regularization. The encouraging experimental results on noisy images demonstrate the effectiveness of our proposed method.

Natural image statistics indicate that we should use non-convex norms for most regularization tasks in image processing. Therefore, in order to restore the damaged image better, this paper proposes a new non-convex high variational image inpainting model. An iteratively reweighed minimization method is proposed to tackle this non-convex problem. Experimental results show that the proposed method yields quantitative and qualitative improvements compared to the current Total Variation (TV) method and convex second Total Generalized Variation (TGV) inpainting method.

Purpose:To develop and to test a method to generate a new 4D CT images of the treatment day from the old 4D CT and the portal images of the day when the motion extent exceeded from that represented by plan CTs.Methods:A motion vector of a moving tumor in a patient may be extended to reconstruct the tumor position when the motion extent exceeded from that represented by plan CTs. To test this, 1. a phantom that consists of a polystyrene cylinder (tumor) embedded in cork (lung) was placed on a moving platform with 4 sec/cycle and amplitudes of 1 cm and 2 cm, and was 4D‐scanned. 2. A 6MV photon beam was irradiated on the moving phantoms and cineEPID images were obtained. 3. A motion vector of the tumor was acquired from 4D CT images of the phantom with 1 cm amplitude. 4. From cine EPID images of the phantom with the 2 cm amplitude, various motion extents (0.3 cm, 0.5 cm, etc) were acquired and programmed into the motion vector, producing CT images at each position. 5. The reconstructed CT images were then compared with pre‐acquired “reference” 4D CT images at each position (i.e. phase).Results:The CT image was reconstructed and compared with the reference image, showing a slight mismatch in the transition direction limited by voxel size (slice thickness) in CT image. Due to the rigid nature of the phantom studied, the modeling the displacement of the center of object was sufficient. When deformable tumors are to be modeled, more complex scheme is necessary, which utilize cine EPID and 4D CT images.Conclusion:The new idea of CT image reconstruction was demonstrated. Deformable tumor movements need to be considered in the future.