Pixel-level feature detection from images is an essential but challenging task encountered in domains such as detecting defects in manufacturing systems and detecting tumors in medical imaging. Often, the real image contains multiple feature types. The types with higher pixel intensities are termed as positive (extreme) features and the ones with lower pixel intensities as negative (extreme) features. For example, when planning a medical treatment, it is important to identify, (a) calcification (a pathological feature which can result in a post-surgical complications) as positive features, and (b) soft tissues (organ morphology, knowledge of which can support pre-surgical planning) as negative features, from a preoperative computed tomography image of the human heart. However, this is not an easy task because (a) conventional segmentation techniques require manual intervention and post-processing, and (b) existing automatic approaches do not distinguish positive features from negative. In this work, we propose a novel, automatic image decomposition-based sparse extreme pixel-level feature detection model to decompose an image into mean and extreme features. To estimate model parameters, a high-dimensional least squares regression with regularization and constraints is utilized. An efficient algorithm based on the alternating direction method of multipliers and the proximal gradient method is developed to solve the large-scale optimization problem. The effectiveness of the proposed model is demonstrated using synthetic tests and a real-world case study, where the model exhibits superior performance over existing methods.