In a photon counting detector spectral computed tomography (CT) scanner, the projection in each energy channel is generated using part of the received photons. The reconstructed channel image suffers from severe noise. Therefore, image reconstruction in spectral CT is considered as a big challenge. As a result, some regularization should be applied to obtain a better image quality for this ill-posed problem in spectral CT image reconstruction. Different edge-preserving regularization methods have been adopted for reconstructing high quality images in the last decade. In the first work, we numerically evaluate the performance of different regularizers in spectral CT, including total variation, non-local means and anisotropic diffusion. The goal is to provide some practical guidance to accurately reconstruct the attenuation distribution in each energy channel of the spectral CT data. In the second work, we propose an average-image-incorporated block-matching and 3D (aiiBM3D) filtering along with a low rank regularization for iterative spectral CT reconstruction. Because the inter-channel images are all from the same object but in different energy bins, there exists a strong correlation among these images. Moreover, it is suggested that there are similarities among various patches of CT images in spatial domain. The proposed algorithm makes use of the aforementioned correlation between the inter-channel images and the redundant information in spatial domain. Moreover, miscalibrated or imperfect detector elements in CT produce stripe artifacts in the sinogram. The stripe artifacts in Radon space are responsible for concentric ring artifacts in the reconstructed images. In our third work, a new optimization model using a novel ring total variation (RTV) regularization is developed to penalize the ring artifacts in the image domain.