Abstract. Sparse signal models learned from data are widely used in audio, image, and video restoration. They have recently been generalized to discriminative image understanding tasks such as texture segmentation and feature selection. This paper extends this line of research by proposing a multiscale method to minimize least-squares reconstruction errors and discriminative cost functions under 0 or 1 regularization constraints. It is applied to edge detection, category-based edge selection and image classification tasks. Experiments on the Berkeley edge detection benchmark and the PASCAL VOC'05 and VOC'07 datasets demonstrate the computational efficiency of our algorithm and its ability to learn local image descriptions that effectively support demanding computer vision tasks.