  Image-based anomaly detection systems are of vital importance in various
manufacturing applications. The resolution and acquisition rate of such systems
is increasing significantly in recent years under the fast development of image
sensing technology. This enables the detection of tiny defects in real-time.
However, such a high resolution and acquisition rate of image data not only
slows down the speed of image processing algorithms but also increases 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 to
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.
