Analysis sparse representation (ASR) and synthesis sparse representation (SSR) are two representative approaches for sparsity-based image modeling. An image is described mainly by the non-zero coefficients in SSR, while is mainly characterized by the indices of zeros in ASR. To exploit the complementary representation mechanisms of ASR and SSR, we integrate the two models and propose a joint convolutional analysis and synthesis (JCAS) sparse representation model. The convolutional implementation is adopted to more effectively exploit the image global information. In JCAS, a single image is decomposed into two layers, one is approximated by ASR to represent image large-scale structures, and the other by SSR to represent image fine-scale textures. The synthesis dictionary is adaptively learned in JCAS to describe the texture patterns for different single image layer separation tasks. We evaluate the proposed JCAS model on a variety of applications, including rain streak removal, high dynamic range image tone mapping, etc. The results show that our JCAS method outperforms state-of-the-arts in these applications in terms of both quantitative measure and visual perception quality.