In recent years, many scholars have been committed to improving the security and practicability of chaotic image encryption. In addition, their proposed schemes mainly focus on two aspects, new or improved chaotic systems and new or improved encryption processes. However, according to cryptanalysis works of scholars, encryption processes of chaotic image encryption schemes deserve more attentions. In this paper, a recently reported chaotic image encryption scheme named the 2D logistic-adjusted-sine-map-based image encryption scheme is comprehensively investigated, and some security, practicability, and rationality problems are found. Therefore, we first point out these problems existing in the reported encryption scheme and make some improvements in practicability and rationality. Next, under the conditions of chosen plaintext attack, we cryptanalyze it and propose a corresponding attack algorithm. For our attack algorithm, simulation test results show that it can completely recover plain images without knowing any secret key related information. Finally, we also present some possible improvements for the security problems of chaotic image encryption scheme under study.