Robust Hyperspectral Image Reconstruction Based On Separable Dictionary Learning

Hyperspectral Image(HSI)plays an important role in many fields such as environmental monitoring,geological exploration,and biological research.Due to the limitations of Nyquist Sampling Theorem,spectroscopy imagers are confronted with a problem that high spatial resolution and high spectral resolution can not be achieved together.Compressive sensing breaks the bounds of the Nyquist Sampling Theorem,combines sampling and compression processes,which greatly reduces the sampling rate and saves system resources.Compressive sensing spectral imaging has two parts: obtain a small amount of observed data(compression sampling)by compression sampling,and then reconstruct the original threedimensional hyperspectral image from it.This thesis focuses on how to reconstruct the original three-dimensional hyperspectral image from the observed data.The technology of compression sampling used in this thesis is Coding Aperture Snapshot Spectral Imager developed by Duke University.The main work and contribution of this thesis are outlined as follow:Firstly,this thesis proposes a hyperspectral image reconstruction algorithm based on separable dictionary learning.In the reconstruction algorithm based on dictionary learning,the traditional dictionary learning methods is to learn a PCA dictionary based on image blocks.However,when the size of image block or the number of spectral segment is large,the dictionary dimension will be huge,causing dimension disaster.To solve this problem,this thesis proposes a hyperspectral image reconstruction algorithm based on separable dictionary learning.The basic idea is to cluster image blocks by utilizing nonlocal selfsimilarity,learn a spatial domain dictionary and a spectral domain dictionary for each kind of image blocks to reduce the dictionary dimension and reduce the complexity of the algorithm.The simulation results demonstrate the efficiency of the proposed algorithm is better than other algorithms.Secondly,this thesis proposes a robust hyperspectral image reconstruction algorithm based on Laplacian Scale Mixture.There are many causes in the imaging process that will lead to observation errors such as system noise,atmospheric effects,and imager jitter.In this thesis,we analyze the error caused by the jitter of the imager platform during the hyperspectral imaging,by simulating the horizontal,vertical and rotation jitter of the platform.By observing the statistical distribution of the observed error,we find that it obeys the Laplacian distribution.In order to reduce the effect of observation error on reconstruction effect,this thesis proposes a robust hyperspectral image reconstruction algorithm based on l1-norm.The algorithm considers the prior acknowledge about the Laplace distribution of the observation error and constrain it by the l1-norm.But it’s too simple to,which is equivalent to only guarantee the sparsity of the observation error.In order to overcome this problem,this thesis proposes a robust hyperspectral image reconstruction algorithm based on Laplacian Scale Mixture.In this algorithm,the observation error is decomposed into the product of a Laplacian vector and a positive scalar multiplier.The simulation results demonstrate that the algorithm still has good reconstruction quality when the imager is jittery.