Tone mapping operators aim to compress high dynamic range (HDR) images to low dynamic range ones so as to visualize HDR images on standard displays. Most existing works were demonstrated on specific examples without being thoroughly tested on well-established and subject-validated image quality assessment models. A recent tone mapped image quality index (TMQI) made the first attempt on objective quality assessment of tone mapped images. TMQI consists of two fundamental building blocks: structural fidelity and statistical naturalness. In this thesis, we propose an enhanced tone mapped image quality index (eTMQI) by 1) constructing an improved nonlinear mapping function to better account for the local contrast visibility of HDR images and 2) developing an image dependent statistical naturalness model to quantify the unnaturalness of tone mapped images based on a subjective study. Experiments show that the modified structural fidelity and statistical naturalness terms in eTMQI better correlate with subjective quality evaluations. Furthermore, we propose an iterative optimization algorithm for tone mapping. The advantages of this algorithm are twofold: 1) eTMQI and TMQI can be compared in a more straightforward way; 2) better quality tone mapped images can be automatically generated by using eTMQI as the optimization goal. Numerical and subjective experiments demonstrate that eTMQI is a superior objective quality assessment metric for tone mapped images and consistently outperforms TMQI.