SayedMasoud Hashemi

Fast fan/parallel beam CS-based low-dose CT reconstruction

Low dose X-ray Computed Tomography (CT) is clinically desired to reduce the risk of cancer caused by X-ray radiation. Compressed Sensing (CS), which allows images to be formed from incomplete data, enables large dose reduction to be achieved. Though this remains to be clinically unrealized due to excessive computation times. In this paper we demonstrate a fast, complete CS-based ℓ2-TV minimizing CT reconstruction method applicable to both parallel and fan beam geometries to recover high quality images from highly undersampled (thus low-dose) data. We apply the fast pseudo-polar Fourier algorithm and the Central Slice Theorem to reduce the computation time of CS recovery. On a typical desktop computer, we are able to reconstruct a 512×512 CT image in approximately 30 seconds: a clinically-significant speedup compared to the many hours required by previous CS methods.

Adaptive image denoising by rigorous Bayesshrink thresholding

Optimum Bayes estimator for General Gaussian Distributed data is provided. The distribution describes a large class of signals including natural images. A wavelet thresholding method for image denoising is proposed. Interestingly we show that the Bayes estimator for this class of signals is behaving very similar to a thresholding approach. This will analytically confirm the importance of thresholding in these scenarios. In particular, when noise variance is less than the the noise-free signal variance, the Bayes estimator behaves similar to a soft thresholding method. We provide the optimum soft thresholding value that mimics the behavior of the Bayes estimator and minimizes the resulting error. The method denoted by Rigorous BayesShrink (R-BayesShrink) outperforms BayesShrink that is the existing most used and efficient soft thresholding method. While BayesShrink threshold is calculated by minimizing the Bayes risk numerically, our approach provides the optimum threshold analytically. Our simulation results show that R-BayesShrink outperforms the BayesShrink in most cases.

Adaptively Tuned Iterative Low Dose CT Image Denoising

Improving image quality is a critical objective in low dose computed tomography (CT) imaging and is the primary focus of CT image denoising. State-of-the-art CT denoising algorithms are mainly based on iterative minimization of an objective function, in which the performance is controlled by regularization parameters. To achieve the best results, these should be chosen carefully. However, the parameter selection is typically performed in an ad hoc manner, which can cause the algorithms to converge slowly or become trapped in a local minimum. To overcome these issues a noise confidence region evaluation (NCRE) method is used, which evaluates the denoising residuals iteratively and compares their statistics with those produced by additive noise. It then updates the parameters at the end of each iteration to achieve a better match to the noise statistics. By combining NCRE with the fundamentals of block matching and 3D filtering (BM3D) approach, a new iterative CT image denoising method is proposed. It is shown that this new denoising method improves the BM3D performance in terms of both the mean square error and a structural similarity index. Moreover, simulations and patient results show that this method preserves the clinically important details of low dose CT images together with a substantial noise reduction.

Adaptive updating of regularization parameters

Iterative minimization of an objective function is usually used for restoring a signal from its noisy measurements. The performance of such iterative algorithms is controlled by regularization parameters, such as Lagrange multipliers. Inappropriate choice of these parameters can either trap the algorithm in local minima and/or lead to a lower convergence rate. We propose a Noise Confidence Region Evaluation (NCRE) algorithm, which adaptively adjusts the regularization parameters. The adjustment is based on evaluation and comparison of error residuals and the considered noise statistics, at the end of each iteration. Moreover, it stops the iterations when the statistical characteristics of the residual match those of the considered noise. NCRE can be used with different algorithms, such as: wavelet soft thresholding, Total Variation denoising, Iterative Soft Thresholding compressed sensing recovery, that have been explained in this paper. In addition, NCRE enables Block Matching and 3D filtering denoising method to be used in an iterative scheme applied on low dose computed tomography images. Simulation results showed advantages of the NCRE in improving the performance of the discussed methods in sense of image quality and mean squared error. Moreover, NCRE enables these algorithms to converge in fewer iterations. HighlightsA new regularization parameter updating method is proposed for Lagrangian multipliers.An efficient stopping criterion is proposed for iterative optimization algorithms.The application of the above methods improves the iterative denoising algorithms.Subsequently, an effective computed tomography image denoising method is presented.

Accelerated Compressed Sensing Based CT Image Reconstruction

In X-ray computed tomography (CT) an important objective is to reduce the radiation dose without significantly degrading the image quality. Compressed sensing (CS) enables the radiation dose to be reduced by producing diagnostic images from a limited number of projections. However, conventional CS-based algorithms are computationally intensive and time-consuming. We propose a new algorithm that accelerates the CS-based reconstruction by using a fast pseudopolar Fourier based Radon transform and rebinning the diverging fan beams to parallel beams. The reconstruction process is analyzed using a maximum-a-posterior approach, which is transformed into a weighted CS problem. The weights involved in the proposed model are calculated based on the statistical characteristics of the reconstruction process, which is formulated in terms of the measurement noise and rebinning interpolation error. Therefore, the proposed method not only accelerates the reconstruction, but also removes the rebinning and interpolation errors. Simulation results are shown for phantoms and a patient. For example, a 512 × 512 Shepp-Logan phantom when reconstructed from 128 rebinned projections using a conventional CS method had 10% error, whereas with the proposed method the reconstruction error was less than 1%. Moreover, computation times of less than 30 sec were obtained using a standard desktop computer without numerical optimization.

Non-local total variation based low-dose Computed Tomography denoising

Radiation dose of X-ray Computed Tomography (CT) imaging has raised a worldwide health concern. Therefore, low-dose CT imaging has been of a huge interest in the last decade. However, lowering the radiation dose degrades the image quality by increasing the noise level, which may reduce the diagnostic performance of the images. As a result, image denoising is one of the fundamental tasks in low-dose CT imaging. One of the state of art denoising methods, which has been successfully used in this area, is Total Variation (TV) denoising. Nevertheless, if the parameters of the TV denoising are not optimally adjusted or the algorithm is not stopped in an appropriate point, some of the small structures will be removed by this method. Here, we provide a solution to this problem by proposing a modified nonlocal TV method, called probabilistic NLTV (PNLTV). Denoising performance of PNLTV is improved by using better weights and an appropriate stopping criterion based on statistics of image wavelet coefficients. Non-locality allows the algorithm to preserve the image texture, which combined with the proposed stopping criterion enables PNLTV to keep fine details unchanged.

Subband-dependent compressed sensing in local CT reconstruction

To achieve high-quality low-dose computed tomography (CT) images, compressed sensing (CS)-based CT reconstructions recover the images using fewer projections; and wavelet inverse Radon algorithms recover wavelet subbands of CT images from locally scanned projections. Moreover, it has been shown that subband CS algorithms accelerate the convergence of the CS recovery methods. Here, we propose an innovative combination of a newly developed accelerated wavelet inverse Radon transform and non-convex CS formulation to recover the wavelet subbands of CT images from a reduced number of locally scanned X-ray projections. Fast pseudo-polar Fourier transform is used to decrease the computational complexity of CS recovery. Therefore, the proposed method, denoted by AWiR-SISTA, reduces the radiation dose by simultaneously decreasing the X-ray exposure area and the number of projections, decreases the CS computational complexity, and accelerates the CS recovery convergence rate. Phantom-based simulations show that high-quality ultra-low-dose local CT images can be reconstructed using the proposed method in few seconds, without numerical optimization. Clinical chest CT images are used to demonstrate the practical potential of the method.

Retrieving quantized signal from its noisy version

In this paper we propose an algorithm to retrieve a quantized data from its noisy version. To find the optimum quantization levels, a multistage process minimizes the Mean Square Error (MSE) at each quantization level by using the Minimum Noiseless Description Length (MNDL) algorithm. Consequently, the procedure denoises and recovers the quantized data simultaneously. The prior knowledge that the original signal is a quantized data enables us to denoise the data more efficiently. We show that in high Signal to Noise Ratio (SNR) cases, the retrieved levels are the same as the original levels of the quantized signal. However, in low SNR cases, since the quantized signal has been highly effected by the additive noise, the optimum retrieved levels are less than the original quantization levels.

Two stage quantization of noisy hyperspectral images

A two-stage quantization approach for compression of noisy hyperspectral images is proposed. In the first stage, a multilevel denoising process uses the minimum noiseless description length (MNDL) approach to not only denoise the data, but also provide quantization levels for the noise dominant wavelet coefficients. In the second stage, the remaining noiseless dominant coefficients are quantized with the conventional quantization methods such as the high bit rate uniform quantization approach. Our simulation results show the advantages of the proposed method over separate “denoising and compression” approaches in both improving the output SNR and providing much less number of quantization levels.