# Optimizing Parameters for Enhanced Iterative Image Reconstruction Using Extended Power Divergence
## 1 Introduction  
X-ray computed tomography (CT) scanners and nuclear medicine CT scanners are technologies used to reconstruct tomographic images from projection data acquired through radiation transmission and emission, respectively. Image reconstruction methods can be broadly categorized into transform methods and iterative methods [1, 2]. A transform method generates images analytically from projection data using Fourier transforms (or convolution integrals) and back-projection. When the CT inverse problem is consistent, an image equal to the true value of the inverse problem is obtained; however, when it is not consistent, artifacts may occur in the image. Meanwhile, iterative methods aim to reduce the differences between forward projections and measured projections through iterative calculations of pixel values. These methods are based on optimization principles and produce high-quality images even when the inverse problem cannot be analytically solved. Iterative methods include algebraic reconstruction technique [3], maximum-likelihood expectation-maximization (MLEM) [4], and multiplicative algebraic reconstruction technique [5], each with its unique characteristics. MLEM, in particular, is widely used in nuclear medicine diagnostic equipment due to its compatibility with noise models of nuclear disintegration and detection. In diagnostic X-ray CT, although iterative methods enable highly accurate image reconstruction, they are not mainstream due to the computational burden associated with the large number of pixels [6]. However, in recent years, iterative reconstruction hasreceived much attention because it requires fewer radiation doses [6; 7; 8; 9; 10] while maintaining image quality. Additionally, as machine-learning techniques continue to evolve, there is a growing need for high-quality training data [11; 12], which can be generated through advanced imaging methods. Therefore, the utility of high-performance iterative methods is expected to gain even more attention in the future. In iterative reconstruction algorithms, convergence and image quality are influenced by the iterative calculations based on the objective function. Notably, the MLEM method is well-known for deriving its objective function from the Kullback-Leibler (KL) divergence [13]. Some of the authors previously proposed an iterative algorithm, the power divergence-based expectation-maximization (PDEM) method [14], which uses an extended power-divergence (EPD) measure as the objective function and demonstrated that it provides higher convergence performance and image quality than the traditional MLEM method. In the PDEM method, appropriately selecting the adjustable parameters in the iterative process is crucial for obtaining effective reconstruction results based on the projection conditions, which include factors such as the noise levels arising from the imaging conditions, as well as the concentration values of the object being scanned. Previous studies have proposed methods such as machine learning and sequential estimation for determining these parameters [15; 16], but each has its pros and cons, and a complete solution has not yet been achieved. In this study, we propose a method to determine effective parameters before executing the reconstruction procedure by optimizing the evaluation function for projection data with common characteristics at a specified number of iterations. In the numerical experiments, we examined projection noise and evaluated the results using the structural similarity index measure (SSIM) between the reconstructed images and the true images. The results revealed that using Euclidean distance or KL-divergence as distance functions did not yield satisfactory quality, but using EPD and weighted EPD (WEPD) resulted in high-quality reconstructed images. Although the Euclidean distance between forward and measured projections is commonly used for evaluating reconstruction performance, the results of this study suggest that this approach may need to be reconsidered.