Modern digital colour cameras are faced with a number of challenges in producing high-quality images, including noisy sensor measurements and chromatic aberration due to dispersion in the optics. In addition, most digital colour cameras use a single sensor combined with a set of colour filters to capture red, green and blue wavelengths of light at different spatial locations in a mosaic-like pattern. Hence, some form of interpolation, often called demosaicking, is required to produce a full colour image. These image restoration tasks are formulated as ill-posed inverse problems and solved through a regularisation inspired by the total variation (TV) denoising algorithm of Rudin, Osher and Fatemi. This leads to convex variational problems and edge-preserving image restorations. To solve these problems, an efficient primal-dual algorithm from convex analysis is adopted. In addition to some standard image restoration problems, we apply these methods to chromatic aberration and demosaicking. A TV-based demosaicking model is developed based on a decomposition of the image into luminance and chrominance components which are then regularised separately. The proposed method demonstrates improved results for demosaicking a set of standard test images.