Image restoration and reconstruction with a Bayesian approach

Restoration of Tc-99m methyl diphosphonate bone scan image using Richardson-Lucy algorithm

INTRODUCTION

In this study, the optimal input parameters point spread function (PSF) and the number of iterations of the Richardson-Lucy algorithm were experimentally determined to restore Tc-99 m methyl diphosphonate (MDP) whole-body bone scan images.

MATERIALS AND METHODS

The experiment was performed on 60 anonymized Tc-99 m MDP whole-body bone scan images. Ten images were used for estimating the optimum value of PSF and the number of iterations to restore scintigraphic images. The remaining 50 images were used for validation of estimated parameters. The image quality of observed and restored images was assessed objectively using blind/referenceless image spatial quality evaluator (BRISQUE), mean brightness (MB), discrete entropy (DE), and edge-based contrast measure (EBCM) image quality metrics. Image quality was subjectively assessed by two nuclear medicine physicians (NMPs) by comparing the restored image quality with observed image quality and assigning a score to each image on the scale of 0-5.

RESULTS

Based on BRISQUE, MB, DE, and EBCM scores, the restored images were significantly sharper, less bright, had more detailed information, and had less contrast around edges compared to the input images. The restored images had improved resolution based on visual assessment as well; NMPs assigned an average image quality score of 4.00 to restored images. Maximum resolution enhancement was noticed at PSF (size: 11 pixels, sigma: 1.75 pixels) and the number of iterations = 10. With the increase in the number of iterations, noise also gets amplified along with resolution enhancement and affects the detectability of small lesions; in the case of relatively low noisy input images, the number of iterations = 5 gave better results.

CONCLUSION

Tc-99 m MDP bone scan images were restored to improve image quality using the Richardson-Lucy algorithm. The optimum value of the PSF parameter was found to be of size = 11 pixels and sigma = 1.75 pixels.

Image Reconstruction: From Sparsity to Data-adaptive Methods and Machine Learning

The field of medical image reconstruction has seen roughly four types of methods. The first type tended to be analytical methods, such as filtered back-projection (FBP) for X-ray computed tomography (CT) and the inverse Fourier transform for magnetic resonance imaging (MRI), based on simple mathematical models for the imaging systems. These methods are typically fast, but have suboptimal properties such as poor resolution-noise trade-off for CT. A second type is iterative reconstruction methods based on more complete models for the imaging system physics and, where appropriate, models for the sensor statistics. These iterative methods improved image quality by reducing noise and artifacts. The FDA-approved methods among these have been based on relatively simple regularization models. A third type of methods has been designed to accommodate modified data acquisition methods, such as reduced sampling in MRI and CT to reduce scan time or radiation dose. These methods typically involve mathematical image models involving assumptions such as sparsity or low-rank. A fourth type of methods replaces mathematically designed models of signals and systems with data-driven or adaptive models inspired by the field of machine learning. This paper focuses on the two most recent trends in medical image reconstruction: methods based on sparsity or low-rank models, and data-driven methods based on machine learning techniques.

Edge-preserving PET image reconstruction using trust optimization transfer

Iterative image reconstruction for positron emission tomography can improve image quality by using spatial regularization. The most commonly used quadratic penalty often oversmoothes sharp edges and fine features in reconstructed images, while nonquadratic penalties can preserve edges and achieve higher contrast recovery. Existing optimization algorithms such as the expectation maximization (EM) and preconditioned conjugate gradient (PCG) algorithms work well for the quadratic penalty, but are less efficient for high-curvature or nonsmooth edge-preserving regularizations. This paper proposes a new algorithm to accelerate edge-preserving image reconstruction by using two strategies: trust surrogate and optimization transfer descent. Trust surrogate approximates the original penalty by a smoother function at each iteration, but guarantees the algorithm to descend monotonically; Optimization transfer descent accelerates a conventional optimization transfer algorithm by using conjugate gradient and line search. Results of computer simulations and real 3-D data show that the proposed algorithm converges much faster than the conventional EM and PCG for smooth edge-preserving regularization and can also be more efficient than the current state-of-art algorithms for the nonsmooth l1 regularization.

Penalized likelihood PET image reconstruction using patch-based edge-preserving regularization

Iterative image reconstruction for positron emission tomography (PET) can improve image quality by using spatial regularization that penalizes image intensity difference between neighboring pixels. The most commonly used quadratic penalty often oversmoothes edges and fine features in reconstructed images. Nonquadratic penalties can preserve edges but often introduce piece-wise constant blocky artifacts and the results are also sensitive to the hyper-parameter that controls the shape of the penalty function. This paper presents a patch-based regularization for iterative image reconstruction that uses neighborhood patches instead of individual pixels in computing the nonquadratic penalty. The new regularization is more robust than the conventional pixel-based regularization in differentiating sharp edges from random fluctuations due to noise. An optimization transfer algorithm is developed for the penalized maximum likelihood estimation. Each iteration of the algorithm can be implemented in three simple steps: an EM-like image update, an image smoothing and a pixel-by-pixel image fusion. Computer simulations show that the proposed patch-based regularization can achieve higher contrast recovery for small objects without increasing background variation compared with the quadratic regularization. The reconstruction is also more robust to the hyper-parameter than conventional pixel-based nonquadratic regularizations. The proposed regularization method has been applied to real 3-D PET data.

Development and evaluation of MRI based Bayesian image reconstruction methods for PET

A maximum a posteriori algorithm, which incorporates correlated magnetic resonance images into the processing of positron emission tomography reconstruction with the aim of improving image quality was developed. The line site map from MRI a priori is made up of a modified Markov random field or Canny edge detector with Gaussian smoothing filter. It is used in the MAP algorithm by a weighted line site method. We evaluate and compare the performance of these reconstruction methods. The results show that the Bayesian methods produce reconstructed images with less noise and better spatial resolution than those produced by the maximum likelihood-expectation maximization method.