Evaluation of penalty design in penalized maximum-likelihood image reconstruction for lesion detection

An improved patch-based regularization method for PET image reconstruction

Background

Statistical reconstruction methods based on penalized maximum likelihood (PML) are being increasingly used in positron emission tomography (PET) imaging to reduce noise and improve image quality. Wang and Qi proposed a patch-based edge-preserving penalties algorithm that can be implemented in three simple steps: a maximum-likelihood expectation-maximization (MLEM) image update, an image smoothing step, and a pixel-by-pixel image fusion step. The pixel-by-pixel image fusion step, which fuses the MLEM updated image and the smoothed image, involves a trade-off between preserving the fine structural features of an image and suppressing noise. Particularly when reconstructing images from low-count data, this step cannot preserve fine structural features in detail. To better preserve these features and accelerate the algorithm convergence, we proposed to improve the patch-based regularization reconstruction method.

Methods

Our improved method involved adding a total variation (TV) regularization step following the MLEM image update in the patch-based algorithm. A feature refinement (FR) step was then used to extract the lost fine structural features from the residual image between the TV regularized image and the fused image based on patch regularization. These structural features would then be added back to the fused image. With the addition of these steps, each iteration of the image should gain more structural information. A brain phantom simulation experiment and a mouse study were conducted to evaluate our proposed improved method. Brain phantom simulation with added noise were used to determine the feasibility of the proposed algorithm and its acceleration of convergence. Data obtained from the mouse study were divided into event count sets to validate the performance of the proposed algorithm when reconstructing images from low-count data. Five criteria were used for quantitative evaluation: signal-to-noise ratio (SNR), covariance (COV), contrast recovery coefficient (CRC), regional relative bias, and relative variance.

Results

The bias and variance of the phantom brain image reconstructed using the patch-based method were 0.421 and 5.035, respectively, and this process took 83.637 seconds. The bias and variance of the image reconstructed by the proposed improved method, however, were 0.396 and 4.568, respectively, and this process took 41.851 seconds. This demonstrates that the proposed algorithm accelerated the reconstruction convergence. The CRC of the phantom brain image reconstructed using the patch-based method was iterated 20 times and reached 0.284, compared with the proposed method, which reached 0.446. When using a count of 5,000 K data obtained from the mouse study, both the patch-based method and the proposed method reconstructed images similar to the ground truth image. The intensity of the ground truth image was 88.3, and it was located in the 102^nd row and the 116^th column. However, when the count was reduced to below 40 K, and the patch-based method was used, image quality was significantly reduced. This effect was not observed when the proposed method was used. When a count of 40 K was used, the image intensity was 58.79 when iterated 100 times by the patch-based method, and it was located in the 102^nd row and the 116^th column, while the intensity when iterated 50 times by the proposed method was 63.83. This suggests that the proposed method improves image reconstruction from low-count data.

Conclusions

This improved method of PET image reconstruction could potentially improve the quality of PET images faster than other methods and also produce better reconstructions from low-count data.

Positron emission tomography image reconstruction using feature extraction

PURPOSE

To reduce the cost of positron emission tomography (PET) scanning systems, image reconstruction algorithms for low-sampled data have been extensively studied. However, the current method based on total variation (TV) minimization regularization nested in the maximum likelihood-expectation maximization (MLEM) algorithm cannot distinguish true structures from noise resulting losing some fine features in the images. Thus, this work aims to recover fine features lost in the MLEM-TV algorithm from low-sampled data.

METHOD

A feature refinement (FR) approach previously developed for statistical interior computed tomography (CT) reconstruction is applied to PET imaging to recover fine features in this study. The proposed method starts with a constant initial image and the FR step is performed after each MLEM-TV iteration to extract the desired structural information lost during TV minimization. A feature descriptor is specifically designed to distinguish structure from noise and artifacts. A modified steepest descent method is adopted to minimize the objective function. After evaluating the impacts of different patch sizes on the outcome of the presented method, an optimal patch size of 7×7 is selected in this study to balance structure-detection ability and computational efficiency.

RESULTS

Applying MLEM-TV-FR algorithm to the simulated brain PET imaging using an emission activity phantom, a standard Shepp-Logan phantom, and mouse results in the increased peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) as comparing to using the conventional MLEM-TV algorithm, as well as the substantial reduction of the used sampling numbers, which improves the computational efficiency.

CONCLUSIONS

The presented algorithm can achieve image quality superior to that of the MLEM and MLEM-TV approaches in terms of the preservation of fine structure and the suppression of undesired artifacts and noise, indicating its useful potential for low-sampled data in PET imaging.

Theoretical Analysis of Penalized Maximum-Likelihood Patlak Parametric Image Reconstruction in Dynamic PET for Lesion Detection

Detecting cancerous lesions is a major clinical application of emission tomography. In a previous work, we studied penalized maximum-likelihood (PML) image reconstruction for lesion detection in static PET. Here we extend our theoretical analysis of static PET reconstruction to dynamic PET. We study both the conventional indirect reconstruction and direct reconstruction for Patlak parametric image estimation. In indirect reconstruction, Patlak parametric images are generated by first reconstructing a sequence of dynamic PET images, and then performing Patlak analysis on the time activity curves (TACs) pixel-by-pixel. In direct reconstruction, Patlak parametric images are estimated directly from raw sinogram data by incorporating the Patlak model into the image reconstruction procedure. PML reconstruction is used in both the indirect and direct reconstruction methods. We use a channelized Hotelling observer (CHO) to assess lesion detectability in Patlak parametric images. Simplified expressions for evaluating the lesion detectability have been derived and applied to the selection of the regularization parameter value to maximize detection performance. The proposed method is validated using computer-based Monte Carlo simulations. Good agreements between the theoretical predictions and the Monte Carlo results are observed. Both theoretical predictions and Monte Carlo simulation results show the benefit of the indirect and direct methods under optimized regularization parameters in dynamic PET reconstruction for lesion detection, when compared with the conventional static PET reconstruction.