Classification of brain tumors using MRI images along with medical knowledge can lead to proper decision-making on the patient's condition. Also, classification of benign or malignant tumors is one of the challenging issues due to the need for detailed analysis of tumor tissue. Therefore, addressing this field using image processing techniques can be very important. In this paper, various types of texture-based and statistical-based features are used to determine the type of brain tumor and different types of features are applied in this classification procedure. Sparse non-negative matrix factorization algorithm is used to learn the over-complete models based on the characteristics of each data category. Also, Sparse structured principal component analysis algorithm is applied to reduce the dimension of training data. The classification process is carried out based on the calculated energy of the Sparse coefficients. Also, the results of this categorization are compared with the results of the classification based on the neural network and support vector machine. The simulation results show that the proposed method based on the selected combinational features and learning the over-complete dictionaries can be able to classify the types of brain tumors precisely.

Rice classification and detection of its quality as a main field in the modern agriculture is attracted many researchers in recent years. This problem is a major issue in the scientific and commercial fields associated with modern agriculture. Different processing techniques in recent years are applied to recognize various types of agricultural products. There are also several color-based and texture-based features to achieve the desired results in this classification procedure. In this paper, the problem of rice categorization and quality detection is considered using Sparse non-negative matrix factorization algorithm. This technique includes non-negative matrix factorization method with sparsity constraint to achieve dictionaries that represent the structural content of rice variety. Also, these dictionaries are corrected in such a way to yield the dictionaries with least coherence values to each other. The results of the proposed classifier based on the learned models are compared with the results obtained from the neural network and support vector machine classifiers. Simulation results show that the proposed method based on the combinational features is able to identify the type of rice grain and determine its quality with high accuracy rate.

In this paper, a new algorithm to solve a symmetric positive definite linear system of equations is proposed. Then, by exploiting the algorithm a new approach to compute a Sparse approximate inverse M of a symmetric positive definite matrix A is presented. The new approach is based on minimizing the Frobenius norm of the residual matrix AM - I and can be decoupled into n subproblems, where n is the dimension of A and I is identity matrix. Hence the computation of the preconditioner can be done in parallel. In this approach the sparsity of the approximate inverse is preserved only by specifying the number of the nonzero elements of each column of M in advance. Some numerical experiments on test matrices from Harwell-Boeing collection are presented to make a comparison with the similar available methods.

Classification of ECG arrhythmia along with medical knowledge can lead to proper decision-making on the patientchr('39')s condition. Also, classification of arrhythmia types is one of the challenging issues due to the need for detailed analysis of the extracted feature from ECG signal. Therefore, addressing this field using signal processing techniques can be very important. In this paper, various types of morphological features are used to determine the type of ECG arrhythmia. Sparse structured principal component analysis and Sparse non-negative matrix factorization algorithms are used to learn the over-complete models based on the characteristics of each data category. Also, the wavelet packet transform coefficients are calculated in different decomposition level to learn over-complete dictionaries. The results of this categorization are compared with the results of the classification based on the neural network, support vector machine another methods presented in this processing field. The simulation results show that the proposed method based on the selected combinational features and learning the over-complete dictionaries can be able to classify the types of ECG arrhythmia precisely.

Sparse matrix-vector multiplication (SpMV) is the key operation in the iterative methods for solving linear systems of equations. Almost all numerical methods need to solve such a system in their solution procedure. There have been a lot of researches on this subject and it is still a very hot research area. One of the best methods to increase the performance of this operation is using graphics processing units (GPUs). These processors have had a great improvement in their processing capabilities. In this research, a new method to perform this operation using open computing language (OpenCL) is presented. The results show that by optimizing the parameters of this method one can gain a much higher performance compared to CPUs, even when using the open multi-processing standard (OpenMP). Also, the results show that there is not much sensitivity near the optimal parameters, which paves the way to estimate them from the matrix properties.

A new single channel singing voice separation algorithm is presented in this paper. This field of signal processing provides important capability in various areas dealing with singer identification, voice recognition, data retrieval. This separation procedure is done using a decomposition model based on the spectrogram of singing voice signals. The novelty of the proposed separation algorithm is related to different issues listed in the following: 1) The decomposition scheme employs the vocal and music models learned using Sparse non-negative matrix factorization algorithm. The vocal signal and music accompaniment can be considered as Sparse and low-rank components of a singing voice segment, respectively. 2) An alternating factorization algorithm is used to decompose input data based on the modeled structures of the vocal and musical components. 3) A voice activity detection algorithm is introduced based on the energy of coding coefficients matrix in the training step to learn the basis vectors that are related to instrumental parts. 4) In the separation phase, these non-vocal atoms are updated to the new test conditions using the domain transfer approach to result in a proper separation procedure with low reconstruction error. The performance evaluation of the proposed algorithm is done using different measures and leads to significantly better results in comparison with the earlier methods in this context and the traditional procedures. The average improvement values of the proposed separation algorithm for PESQ, fwSegSNR, SDI, and GNSDR measures in comparison with previous separation methods in two defined test scenario and three mentioned SMR levels are 0. 53, 0. 84, 0. 39, and 2. 19, respectively.

In multiple regression analysis, the population multiple correlation coefficient (PMCC) is widely used to measure the correlation between a variable and a set of variables. To evaluate the existence or non-existence of this type of correlation, testing the hypothesis of zero PMCC can be very useful. In high-dimensional data, due to the singularity of the sample covariance matrix, traditional testing procedures to test this hypothesis lose their applicability. A simple test statistic was proposed for zero PMCC based on a plug-in estimator of the sample covariance matrix inverse. Then, a permutation test was constructed based on the proposed test statistic to test the null hypothesis. A simulation study was carried out to evaluate the performance of the proposed test in both high-dimensional and low-dimensional normal data sets. This study was finally ended by applying the proposed approach to mice tumour volumes data.

The difficulties in the measurement of rainfall interception in forests confirm the necessity of presenting models. The widely used models for estimating rainfall interception are physical-based models, among which the Sparse Gash is the most commonly used. We evaluated the Sparse Gash model for estimating the rainfall interception of five forest stands (two chestnut-leaved oak stands, two oriental beech stands, and one velvet maple stand) in the Hyrcanian region. In each stand, the gross rainfall and throughfall were measured using 5 and 20 rainfall collectors, respectively, and rainfall interception was calculated by subtracting the throughfall from gross rainfall. To evaluate the performance of the model, we used statistical metrics: Error percentage (Error), Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and the Model Efficiency coefficient (CE). Based on the Pearson correlation coefficient, the correlation between the values estimated by the model and the observed values was statistically significant at a 95% confidence interval. In all forests, the values of the CE were higher than 0. 5, indicating the appropriate efficiency of the model. Based on the Error, the model showed good capability in estimating the rainfall interception of four forest stands (i. e., oriental beech in Lajim, chestnut-leaved oak in Kohmiyan and Sari, and velvet maple in Sari Error metric were found to be-10. 3%, +12. 7%, +10. 8%, and +15. 4%, respectively). Studying the performance of physically-based models in forests with different species and different allometric, climatic and rainfall characteristics completes the information gap about the efficiency of models to estimate rainfall interception.