A Novel Iterative MLEM Image Reconstruction Algorithm Based on Beltrami Filter: Application to ECT Images.

The implementation of emission-computed tomography (ECT), including positron emission tomography and single-photon emission-computed tomography, has been an important research topic in recent years and is of significant and practical importance. However, the slow rate of convergence and the computational complexity have severely impeded the efficient implementation of iterative reconstruction. By combining the maximum-likelihood expectation maximization (MLEM) iteratively along with the Beltrami filter, this paper proposes a new approach to reformulate the MLEM algorithm. Beltrami filtering is applied to an image obtained using the MLEM algorithm for each iteration. The role of Beltrami filtering is to remove mainly out-of-focus slice blurs, which are artifacts present in most existing images. To improve the quality of an image reconstructed using MLEM, the Beltrami filter employs similar structures, which in turn reduce the number of errors in the reconstructed image. Numerical image reconstruction tomography experiments have demonstrated the performance capability of the proposed algorithm in terms of an increase in signal-to-noise ratio (SNR) and the recovery of fine details that can be hidden in the data. The SNR and visual inspections of the reconstructed images are significantly improved compared to those of a standard MLEM. We conclude that the proposed algorithm provides an edge-preserving image reconstruction and substantially suppress noise and edge artifacts.

Iterative Bayesian denoising based on variance stabilization using Contourlet Transform with Sharp Frequency Localization: application to EFTEM images.

BACKGROUND: Due to the presence of high noise level in tomographic series of energy filtered transmission electron microscopy (EFTEM) images, alignment and 3D reconstruction steps become so difficult. To improve the alignment process which will in turn allow a more accurate and better three dimensional tomography reconstructions, a preprocessing step should be applied to the EFTEM data series. RESULTS: Experiments with real EFTEM data series at low SNR, show the feasibility and the accuracy of the proposed denoising approach being competitive with the best existing methods for Poisson image denoising. The effectiveness of the proposed denoising approach is thanks to the use of a nonparametric Bayesian estimation in the Contourlet Transform with Sharp Frequency Localization Domain (CTSD) and variance stabilizing transformation (VST). Furthermore, the optimal inverse Anscome transformation to obtain the final estimate of the denoised images, has allowed an accurate tomography reconstruction. CONCLUSION: The proposed approach provides qualitative information on the 3D distribution of individual chemical elements on the considered sample.

Iterative Variance Stabilizing Transformation Denoising of Spectral Domain Optical Coherence Tomography Images Applied to Retinoblastoma.

BACKGROUND: Due to the presence of speckle Poisson noise, the interpretation of spectral domain-optical coherence tomography (SD-OCT) images frequently requires the use of data averaging to improve the signal-to-noise ratio. This implies long acquisition times and requires patient sedation in some cases. Iterative variance stabilizing transformation (VST) is a possible approach by which to remove speckle Poisson noise on single images. METHODS: We used SD-OCT images of human and murine (LH Beta-Tag mouse model) retinas with and without retinoblastoma acquired with 2 different imaging devices (Bioptigen and Micron IV). These images were processed using a denoising workflow implemented in Matlab. RESULTS: We demonstrated the presence of speckle Poisson noise, which can be removed by a VST-based approach. This approach is robust as it works in all used imaging devices and in both human and mouse retinas, independently of the tumor status. The implemented algorithm is freely available from the authors on demand. CONCLUSIONS: On a single denoised image, the proposed method provides results similar to those expected from the SD-OCT averaging. Because of the friendly user interface, it can be easily used by clinicians and researchers in ophthalmology.

Improved Simultaneous Algebraic Reconstruction Technique Algorithm for Positron-Emission Tomography Image Reconstruction via Minimizing the Fast Total Variation.

CONTEXT: There has been considerable progress in the instrumentation for data measurement and computer methods for generating images of measured PET data. These computer methods have been developed to solve the inverse problem, also known as the "image reconstruction from projections" problem. AIM: In this paper, we propose a modified Simultaneous Algebraic Reconstruction Technique (SART) algorithm to improve the quality of image reconstruction by incorporating total variation (TV) minimization into the iterative SART algorithm. METHODOLOGY: The SART updates the estimated image by forward projecting the initial image onto the sinogram space. Then, the difference between the estimated sinogram and the given sinogram is back-projected onto the image domain. This difference is then subtracted from the initial image to obtain a corrected image. Fast total variation (FTV) minimization is applied to the image obtained in the SART step. The second step is the result obtained from the previous FTV update. The SART and the FTV minimization steps run iteratively in an alternating manner. Fifty iterations were applied to the SART algorithm used in each of the regularization-based methods. In addition to the conventional SART algorithm, spatial smoothing was used to enhance the quality of the image. All images were sized at 128 × 128 pixels. RESULTS: The proposed algorithm successfully accomplished edge preservation. A detailed scrutiny revealed that the reconstruction algorithms differed; for example, the SART and the proposed FTV-SART algorithm effectively preserved the hot lesion edges, whereas artifacts and deviations were more likely to occur in the ART algorithm than in the other algorithms. CONCLUSIONS: Compared to the standard SART, the proposed algorithm is more robust in removing background noise while preserving edges to suppress the existent image artifacts. The quality measurements and visual inspections show a significant improvement in image quality compared to the conventional SART and Algebraic Reconstruction Technique (ART) algorithms.