Compressed Smooth Sparse Decomposition

Image-based anomaly detection systems are of vital importance in various manufacturing applications. The resolution and acquisition rate of such systems are increasing significant in recent years under the fast development of image sensing technology. This enables the detection of tiny anomalies in real time. However, such a high resolution and a high acquisition rate of image data not only slow down the speed of image processing algorithms but also, increase data storage and transmission cost. To tackle this problem, we propose a fast and data-efficient method with theoretical performance guarantee that is suitable for sparse anomaly detection in images with a smooth background (smooth plus sparse signal). The proposed method, named compressed smooth sparse decomposition (CSSD), is a one-step method that unifies the compressive image acquisition- and decomposition-based image processing techniques. To further enhance its performance in a high-dimensional scenario, a Kronecker compressed smooth sparse decomposition (KronCSSD) method is proposed. Compared with traditional smooth and sparse decomposition algorithms, significant transmission cost reduction and computational speed boost can be achieved with negligible performance loss. Simulation examples and several case studies in various applications illustrate the effectiveness of the proposed framework.