Compressed Smooth Sparse Decomposition

TL;DR

This paper introduces CSSD and KronCSSD, innovative methods that enable fast, data-efficient, and high-performance sparse anomaly detection in high-resolution images, reducing transmission costs and processing time.

Contribution

The paper presents a unified compressive and decomposition-based approach for smooth sparse image decomposition with theoretical guarantees, including a high-dimensional Kronecker extension.

Findings

Significant reduction in transmission costs

Enhanced computational speed with negligible performance loss

Effective in various application case studies

Abstract

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.