  Many algorithms and methods have been proposed for inverse problems
particularly with the recent surge of interest in machine learning and deep
learning methods. Among all proposed methods, the most popular and effective
method is the convolutional neural network (CNN) with mean square error (MSE).
This method has been proven effective in super-resolution, image de-noising,
and image reconstruction. However, this method is known to over-smooth images
due to the nature of MSE. MSE based methods minimize Euclidean distance for all
pixels between a baseline image and a generated image by CNN and ignore the
spatial information of the pixels such as image texture. In this paper, we
proposed a new method based on Wasserstein GAN (WGAN) for inverse problems. We
showed that the WGAN-based method was effective to preserve image texture. It
also used a maximum likelihood estimation (MLE) regularizer to preserve pixel
fidelity. Maintaining image texture and pixel fidelity is the most important
requirement for medical imaging. We used Peak Signal to Noise Ratio (PSNR) and
Structure Similarity (SSIM) to evaluate the proposed method quantitatively. We
also conducted first-order and second-order statistical image texture analysis
to assess image texture.
