This study deals with the 3D recovering of magnetic susceptibility model by incorporating the SPARSITY-based CONSTRAINTS in the inversion algorithm. For this purpose, the area under prospect was divided into a large number of rectangular prisms in a mesh with unknown susceptibilities. Tikhonov cost functions with two SPARSITY functions were used to recover the smooth parts as well as the sharp boundaries of model parameters. A pre-selected basis namely wavelet can recover the region of smooth behaviour of susceptibility distribution while Haar or finite-difference (FD) domains yield a solution with rough boundaries. Therefore, a regularizer function which can benefit from the advantages of both wavelets and Haar/FD operators in representation of the 3D magnetic susceptibility distributionwas chosen as a candidate for modeling magnetic anomalies. The optimum wavelet and parameter b which controls the weight of the two sparsifying operators were also considered. The algorithm assumed that there was no remanent magnetization and observed that magnetometry data represent only induced magnetization effect. The proposed approach is applied to a noise-corrupted synthetic data in order to demonstrate its suitability for 3D inversion of magnetic data. On obtaining satisfactory results, a case study pertaining to the ground based measurement of magnetic anomaly over a porphyry-Cu deposit located in Kerman providence of Iran. Now Chun deposit was presented to be 3D inverted. The low susceptibility in the constructed model coincides with the known location of copper ore mineralization.

In order to exploit the advantages of the massive MIMO systems, it is vital to apply the channel estimation task. The huge number of antennas at the base station of a massive MIMO system produces a large set of channel paths which requires to be estimated. Therefore, the channel estimation in such systems is more troublesome. In this paper, we propose to leverage the temporal joint SPARSITY of the massive MIMO channels to offer a more accurate channel estimation. To attain this goal, we would model the problem to exploit the spatial correlation among different antennas of the BS as well as the inter-user similarity of the channel supports. In addition, by assuming a slow time-varying channel, the supports of the channel matrices of various snapshots would be equal which enables us to impose the temporal joint SPARSITY on the channel submatrices. The simulation results validate the efficiency and superiority of the suggested scheme over its rivals.

We present a modified examplar-based inpainting method in the framework of patch SPARSITY. In the examplar-based algorithms, the unknown blocks of target region are inpainted by the most similar blocks extracted from the source region, using the available information. Defining a priority term to decide the filling order of missing pixels ensures the connectivity of the object boundaries. In the exemplar-based patch SPARSITY approach, a sparse representation of missing pixels is considered to define a new priority term and the unknown pixels of the fill-front patch is inpainted by a sparse combination of the most similar patches. Here, we modify this representation of the priority term and take a measure to compute the similarities between fill-front and candidate patches. Also, a new definition is proposed for updating the confidence term to illustrate the amount of the reliable information surrounding pixels. Comparative reconstructed test images show the effectiveness of our proposed approach in providing high quality inpainted images.

Generally, the presence of noise in geophysical measurements is inevitable and depending on the type and the level it affects the results of geophysical studies. So, denoising is an important part of the processing of geophysical data. On the other hand, geophysicists make inferences about the physical properties of the earth interior based on the indirect measurements (data) collected at or near the surface of the earth. So, an inverse problem must be solved in order to take estimates of the physical properties in the earth. The vast majority of inverse problems which arise in geophysics are ill-posed; in other words, they have not unique and stable solutions. Regularization tools are used to find a unique and stable solution for such problems. The regularization uses a priori information about the solution to make it stable and to suppress high-frequency oscillations generated by the noise. One of the common ways to perform the regularization is expanding the unknown model (i.e. solution) with respect to an orthonormal basis, separating the model coefficients from that of the noise, and finally recovering the model.In singular value decomposition, the specific physical nature of the model under study is not considered when defining the basis. For homogeneous operators, such basis does not provide a parsimonious approximation of models which are smooth in some regions while having sharp local changes in others. This is due to the non-localized properties of the SVD basis vectors in space (time) domain.Wavelet-vaguelette decomposition (WVD) was introduced as a first approach for adapting wavelet methods to the framework of ill-posed inverse problems. It is a linear projection method based on wavelet-like function systems which have similar properties as the singular value decompositions. WVD are compared to the SVD construct near the orthogonal basis where the vectors are well localized in space (time) and frequency, thus producing less Gibbs-phenomenon at discontinuities. This property and existence of fast algorithm to compute the basis make wavelets a suitable candidate for solving inverse problems.Vaguelette-wavelet decomposition (VWD) is an alternative to WVD for solving illposed inverse problems. It is a linear projection method based on wavelet function systems. In VWD the noisy data are expanded in a wavelet series, generated wavelet coefficients are thresholded to obtain an estimate of the wavelet expansion of noise free data, and then the resulting coefficients are transformed back for smoothed data. Later on, the smoothed data are inverted for the desired model. In this paper we discuss: 1. The performance of sparsifying transforms (e.g. wavelet transform) for the denoising problem and their application to solve other linear inverse problems including WVD and VWD. 2. Comparing nonlinear Amplitude-scale-invariant Bayes Estimator (ABE) and hard- and soft-shrinkage filters to estimate signal coefficients in sparse domain for different levels of noise. 3. Introducing an efficient method to estimate the standard deviation of noise which is an important task in the experiments with single realization. The obtained standard deviation is then used to determine the regularization parameter in both wavelet- and SVD- based inversion methods. Finally, inversion of integration operator to find the variation rate of a function is used to show the performance of the introduced methods in comparison to the popular SVD method. The results indicate that a simple non-linear operation of weighting and thresholding of wavelet coefficients can consistently outperform classical linear inverse methods.

The SPARSITY of the Gram matrix in linear regression can influence the model's accuracy. Sparse matrices reduce computational complexity and improve generalization by minimizing overfitting. This advantage is particularly beneficial in high-dimensional data where the number of features exceeds the number of observations. This paper explores the integration of Radial Basis Functions (RBFs) in developing sparse Gram matrix fuzzy regression models. RBFs are powerful tools for function approximation, defined by their dependence on the distance from a center point, which allows for flexible modeling of nonlinear relationships. The focus will be on compactly supported RBF kernels, which facilitate SPARSITY in the Gram matrix, thereby improving computational efficiency and memory usage. By leveraging the properties of RBFs, particularly their ability to localize influence and reduce dimensionality, we aim to enhance the performance of fuzzy regression models. This study will present theoretical insights and empirical results demonstrating how the adoption of RBFs can lead to significant improvements in model accuracy and computational speed, making them a valuable asset in the field of fuzzy regression analysis.

Deep neural networks (DNNs) have achieved great interest due to their success in various applications. However, the computation complexity and memory size are considered to be the main obstacles for implementing such models on embedded devices with limited memory and computational resources. Network compression techniques can overcome these challenges. Quantization and pruning methods are the most important compression techniques among them. One of the famous quantization methods in DNNs is the multi-level binary quantization, which not only exploits simple bit-wise logical operations, but also reduces the accuracy gap between binary neural networks and full precision DNNs. Since, multi-level binary can’t represent the zero value, this quantization does’nt take advantage of SPARSITY. On the other hand, it has been shown that DNNs are sparse, and by pruning the parameters of the DNNs, the amount of data storage in memory is reduced while computation speedup is also achieved. In this paper, we propose a pruning and quantization-aware training method for multi-level ternary quantization that takes advantage of both multi-level quantization and data SPARSITY. In addition to increasing the accuracy of the network compared to the binary multi-level networks, it gives the network the ability to be sparse. To save memory size and computation complexity, we increase the SPARSITY in the quantized network by pruning until the accuracy loss is negligible. The results show that the potential speedup of computation for our model at the bit and word-level SPARSITY can be increased by 15x and 45x compared to the basic multi-level binary networks.

Background: DNA microarray is a useful technology that simultaneously assesses the expression of thousands of genes. It can be utilized for the detection of cancer types and cancer biomarkers. This study aimed to predict blood cancer using leukemia gene expression data and a robust ℓ, 2, p-norm SPARSITY-based gene selection method. Materials and Methods: In this descriptive study, the microarray gene expression data of 72 patients with acute myeloid leukemia (AML) and lymphoblastic leukemia (ALL) was used. To remove the redundant genes and identify the most important genes in the prediction of AML and ALL, a robust ℓ, 2, p-norm (0 < p ≤, 1) SPARSITYbased gene selection method was applied, in which the parameter p method was implemented from 1/4, 1/2, 3/4 and 1. Then, the most important genes were used by the random forest (RF) and support vector machine (SVM) classifiers for prediction of AML and ALL. Results: The RF and SVM classifiers correctly classified all AML and ALL samples. The RF classifier obtained the performance of 100% using 10 genes selected by the ℓ, 2, 1/2-norm and ℓ, 2, 1-norm SPARSITY-based gene selection methods. Moreover, the SVM classifier obtained a performance of 100% using 10 genes selected by the ℓ, 2, 1/2norm method. Seven common genes were identified by all four values of parameter p in the ℓ, 2, p-norm method as the most important genes in the classification of AML and ALL, and the gene with the description “, PRTN3 Proteinase 3 (serine proteinase, neutrophil, Wegener granulomatosis autoantigen”,was identified as the most important gene. Conclusion: The results obtained in this study indicated that the prediction of blood cancer from leukemia microarray gene expression data can be carried out using the robust ℓ, 2, p-norm SPARSITY-based gene selection method and classification algorithms. It can be useful to examine the expression level of the genes identified by this study to predict leukemia.