Research On Compressive Sensing For Hyperspectral Images

In recent years, hyperspectral imaging technology has been widely used in many fields such as environmental monitoring, geological, agricultural, medical and military fields because the traditional multicolor image has been far from satisfying people's needs. In hyper-spectral imaging devices, the sensors detect reflection or radiation intensity of hundreds of different wavelengths from the targets, creating hundreds of continuous spectral bands. Hyperspectral image can be defined as a cubic data with two-dimensional space domain and one-dimensional frequency domain.Hyperspectral imaging has potential both in civilian areas and military aspects; however, it has a disadvantage that the data is very large. Especially when the spectral resolution increases, the imagery data increases sharply. Take the typical hyperspectral image of AVIRIS as an example, which is consisted of 224 bands with the wavelength ranging from 380nm to 2500nm; the spatial resolution of each band is 614×512 pixels, and each pixel is measured and recorded in 16 bits. It is easy to conclude that the size of each scene of the hyperspectral image is about 140MB. As a result, high quality compressed coding of hyperspectral images is becoming an important technique to ensure highly effective transmission and storage of hyperspectral images.After compression, a lot of non-essential coefficients of the image are discarded; this process of sampling and then compression bring on the increase of complexity of the system. So the implementation of analogue-to-digital converters becomes a choke point when the sampling rate is high. It comes naturally to us that: Is it possible to depict the signal in transform domains and establish a new theory framework of describing and processing signals, thus signals could be sampled at a rate much lower than what is specified by the Nyquist sampling theorem and recovered without losing information? In other words, can the sampling of signals be replaced by the sampling of information?The recent several years saw the emergence of a novel theory—Compressive sensing (CS). In the framework of CS, the sampling rate is not determined by the signal bandwidth, but by the contents of information in the signal. In CS, the image is sampled and compressed at a lower rate synchronously, making the cost of the sensors being reduced, while the recovery of image signal is a process of optimization. For hyperspectral images, which are compressible, it is possible to be sampled effectively by using observation matrixes not correlating to the sparse transform matrix to project the high-dimensional data to a lower-dimensional space, as long as the sparse representation is found out. By solving the optimization problem, the original signal could be reconstructed with high probability from the small number of CS measurements.In this dissertation, according to the problems addressed above, the research on reconstruction error for different sparse levels of the compressible signal and the relationship between the quantization precision of CS measurements and the relative reconstruction error are done. Research on the relationship between the CS measurements with additive Gaussian noises of different power and the relative reconstruction error is also made. Then a comparison of the performance of basis pursuit, orthogonal matching pursuit, Least Absolute Shrinkage and Selection Operator, and the Bayesian methods is made.Based on the properties of hyperspectral images, a novel method for classification of hyper-spectrums in CS domain is proposed. At last, a novel model for compressive hyperspectral sensing is derived. The novel method reduces the average reconstruction error by approximate 50%, compared with reconstruction without using the correlation among the spectrums.