In the age of big data, HBase which can store massive data is widely used. HBase only can optimize index for the rowkey and donot create indexes to the columns of non-rowkey, which has a serious impact on the efficiency of complicated condition query. In order to solve the problem, a new scheme about secondary indexes in HBase based on memory was proposed. The indexes of mapping to rowkey for the columns which needed to be queried were established, and these indexes were stored in memory environment which was built by Spark. The rowkey was firstly got by index during query time, then the rowkey was used to find the corresponding record quickly in HBase. Due to the cardinality size of the column and whether or not the scope query determined the type of index, and different types of indexes were constructed to deal with three different situations. Meanwhile, the memory computation and parallelization were used in Spark to improve the query efficiency of indexes. The experimental results show that the proposed secondary indexes in HBase can gain better query performance, and the query time is less than the secondary indexes based on Solr. The proposed secondary indexes can solve the problem of low query efficiency, which is caused by the lack of indexes of non-rowkey columns in HBase, and improve the query efficiency for large data analysis based on HBase storage.

In order to solve the problem of large correlation coefficients when obtaining the observation matrix from the optimized Gram matrix in Compressive Sensing (CS), based on the optimized Gram matrix obtained in the existing algorithm, the value of the row vector in the observation matrix when the objective function takes the extreme value was obtained based on the extreme value of the equivalent transformation of the objective function, the analytic formula of the row vector when the objective function takes the extreme value was elected from the values mentioned above by Singular Value Decomposition (SVD) of the error matrix, then a new observation matrix optimization algorithm was put forward by using the idea of optimizing the target matrix row by row in the K-SVD algorithm, the observation matrix was optimized iteratively row by row, and the difference between the correlations of the observation matrix generated by adjacent two iterations was taken as a measure of whether or not the iteration is completed. Simulation results show that the relevance between the observation matrix and the sparse base in the improved algorithm is better than that in the original algorithm, thus reducing the reconstruction error.