Face Recognition Based On Compressed Sensing Theory

The Shannon/Nyquist sampling theorem specifies that to avoid losing information when capturing a signal, one must sample at least two times faster than the signal bandwidth. In many applications, including digital image and video cameras, the Nyquist rate is so high that too many samples result, making compression a necessity prior to storage or transmission. In other applications, including imaging systems(medical scanners and radars) and high-speed analog-to-digital converters, increasing the sampling rate is very expensive.Compressive sampling, also known as compressed sensing of CS, a novel sensing/sampling paradigm that goes against the common wisdom in data acquisition. CS theory asserts that one can recover certain signals and images from far fewer samples or measurements than traditional method use.Face Recognition(FR) is a technology that identities people’s ID based on human visual information. FR technology has developed more than 30 years. Due to FR’s unique advantages to the other biometric identification: non-mandatory, non-contact and concurrency, FR technology has been widely applied in various fields. However, the traditional FR techniques have a very low correct recognition rate in the different face illumination, different expressions, and even the pollution and occlusion in the face images.Combining with the CS theory and traditional FR technology, J.Wright proposed a sparse-based representation classifier(SRC). It has a very high recognition rate, especially for the occlusion and corruption face images. Additionally, the correct recognition rate is non-relevant to the selection of feature space.Based on SRC algorithm, this paper analysis and study the corresponding modified algorithms in the existence of different types of noise in order to improve the FR rate. For the small and dense noise, we assert a new method of determining the identity of test image: counting the number of small noise. The method above outperforms SRC algorithm with the increasing the dimension of feature. On the other hand, we extend the SRC algorithm(ESRC) that we consider the noise as a sparse signal for the abstract large and sparse noise. It indicates the ESRC algorithm is much better than the traditional FR algorithms in the simulation. Furtherly, we analysis and modify the SRC algorithm as weighted SRC(WSRC) which is based on the noise amplitude via the Bayesian perspective in the case of the presence of two types of noise above. This paper present a continuous WSRC(CWSRC) by taking advantage of continuity and relevance of noise and CWSRC is better than both WSRC and SRC algorithm. Finally, we propose a double weighted SRC algorithm(DWSRC) taking into account the different noise weight and the relationship between the test sample and the training samples set, and the simulation shows that DWSRC outperforms SRC in some case.The prerequisite for success of SRC algorithm is that a lot of training samples of every class. However, it cost a lot time when there are many people and samples of per class. In order to diminish the size of training matrix we need retrain the training samples. Combining the K Nearest Neighbors(KNN), Linear Regression Classifier(LRC) and Dictionary Learning(DL), we get the KNN-SRC, LRC-SRC, DL-SRC algorithm and they have the similar performance comparing the SRC algorithm and cost much less time at the same time. The performance of SRC algorithm reduces greatly with decreasing the number of training samples. Therefore, we generate the new synthetic images according the original images and call it as SSRC algorithm. It improves the performance of the SRC algorithm.In Summary, CS-based FR is an emerging research area. CS-based FR will become more and more in our life and it is meaningful to do something research about CS-based FR with the constantly improvement of CS theory and the wider scope of the application of FR technology.