Research On Sparse Optimization Modeling And High Performance Algorithm And Its Applications

With the rapid development of science and technology,a large number of complex datasets(including image,video and genomics data)have emerged in many application fields.In big data era,although the amount of data is huge,each data has its own structural characteristics and expresses different information.How to use the internal structure information of the data to find a sparse expression form has become a common concern in many engineering application field.The meaning of sparse is not just that there are very few non-zero components.It also means that the data contains a simple structure.Since the sparse representation of the data under certain conditions have been found in machine learning,data mining,image processing,data integration,and other fields,many sparse optimization based models have been established.These models have played a great role in solving practical problems and become a research hot in recent years.In this paper,we aim to establish sparse optimization based model to handle remote sensing image destripe,chromosome image classification,biological information data integration.We design algorithm to solve the corresponding problems.The main contents are listed as follows:1.We propose a variational based sparse regularization model to remove the stripe noise in remote sensing images.This model combines unidirectional total variation and second order total variation regularization to play their respective strengths.For example,the unidirectional total variation can employ the directional information of the stripes and the second order total variation can handle the wide stripes well.The split Bregman iteration method was used to solve the proposed model.Experimental results demonstrate that the proposed model can remove stripe noise well.2.In the study of chromosomes,how to classify the 46 chromosomes into 23 classes(Because the sex chromosomes X,Y belong to two classes,a male cell have 24 classes chromosomes)efficiently is the key to improve the accuracy of chromosome diagnosis.For normal cells,the pixels on the same chromosome belong to the same class.We use a 3-dimensional patch to represent the center pixel's information,by which we can use the correlations of neighbouring pixels and the structural information across different spectral channels for the classification.A training tensor was constructed according to the three modes “pixel-sample-class”.The feature vectors of each class were extracted by using higher order singular value decomposition,which can be used to classify the unknown chromosome pixels.Numerical experiments show that the proposed method can effectively classify chromosomes and achieve a higher correct classification ratio than the traditional methods.3.In the biological data integration for the study of schizophrenia,we adopt a joint nonnegative matrix factorization method to integrate single nucleotide polymorphism data,functional magnetic resonance imaging data and DNA methylation data.This method projects multiple datasets onto a common subspace.We can find out the correlated biomarkers among the datasets by analysing the expression coefficients of each variables.These biomarkers can be mapped to genes and brain regions.We identified a module that contain three kinds of biomarkers,which are significantly correlated and associated with schizophrenia.By analyzing these biomarkers,we obtain some candidate genes and candidate brain regions associated with the disease.These genes and brain regions provide the references for subsequent clinical studies of schizophrenia.4.We proposed a group sparse joint nonnegative matrix factorization model,which is an improved version of which presented in part 3.We add a group sparse constraint to employ the structure information in the data and the results are more easily to be interpreted.We identified four modules containing biomarkers which are significantly correlated and associated with schizophrenia.By analyzing these biomarkers,we identified some candidate genes and candidate brain regions associated with the schizophrenia.