Research And Application Of Compreeeive Sensing Theory

Compressive sensing, which processes information from the perspective of sparse representation, is a new theory that is popular in recent years. It breaks through the limitation of traditional sampling theory, and has attracted considerable attention in areas of signal processing, applied mathematics, pattern recognition and wireless communication. Compressive sensing takes full advantage of the fact that natural signals are sparse or compressible. It makes signal acquisition and compression process in one and it can accurately reconstruct original signals from a small quantity of measurements through approptiate optimization algorithm. After accessing and summarizing the relevant literature home and abroad, we carry out a research on it and its application of defects detection. The concerete steps are as follows:1. This paper studys the relevant basic theory of compressive sensing and then carries detailed analysis on the three core parts of compressive sensing theory that is signal sparse representation, design of the observation matrix and signal reconstruction. Basis pursuit, orthogonal matching pursuit, stagewise orthogonal matching pursuit, these three typical reconstruction algorithms’reconstruction performance can be analysed by simulation experiments.2. Based on compressive sensing theory from one-dimensional signal to two-dimensional matrix, namely Robust Principal Component Analysis (RPCA) of matrix recovery problem, two kinds of typical algorithm:Accelerated Proximal Gradient (APG) and Augmented Lagrange Multiplier (ALM) are studied and are applied in defect detection. RPCA utilizes the correlation between similar images to make up a low-rank matrix and searches abnormal points of the image to make up a sparse matrix. Defects can be identified accurately by decomposition of the low-rank matrix and the sparse matrix.3. Based on the problem of RPCA can only express data simply and be lack of learning ability, deep learning, another kind of compressive sensing method is studied. It takes advantage of layer-wise compressive sensing of Deep Belief Networks (DBN) to abstract feature representation of high-level from low-level data. Then, the original data can be reconstructed reversely from this small quantity of features, and also can be applied in defect detection. We verify the feasibility of the proposed method on detection of solar cells defects with experiments. Meanwhile, the experiments show that the method has the advantage of fast speed, high accuracy and universality.