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We propose novel convolutional sparse and low-rank coding-based methods for cartoon and texture decomposition. In our method, we first learn a set of generic filters that can efficiently represent cartoon-and texture-type images. Then, using these learned filters, we propose two optimization frameworks to decompose a given image into cartoon and texture components: convolutional sparse coding-based image decomposition; and convolutional low-rank coding-based image decomposition. By working directly on the whole image, the proposed image separation algorithms do not need to divide the image into overlapping patches for leaning local dictionaries. The shift-invariance property is directly modeled into the objective function for learning filters. Extensive experiments show that the proposed methods perform favorably compared with state-of-the-art image separation methods.