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Dimension reduction plays an essential role when decreasing the complexity of solving large-scale problems. The well-known Johnson-Lindenstrauss (JL) Lemma and Restricted Isometry Property (RIP) admit the use of random projection to reduce the dimension while keeping the Euclidean distance, which leads to the boom of sparsity related signal processing. Recently, successful applications of sparse models...
Universal compressed sensing algorithms recover a “structured” signal from its under-sampled linear measurements, without knowing its distribution. The recently developed minimum entropy pursuit (MEP) optimization suggests a framework for developing universal compressed sensing algorithms. In the noiseless setting, among all signals that satisfy the measurement constraints, MEP seeks the “simplest”...
It often happens that we are interested in reconstructing an unknown signal from partial measurements. Also, it is typically assumed that the location (temporal or spatial) of each sample is known and that the only distortion present in the observations is due to additive measurement noise. However, there are some applications where such location information is lost. In this paper, we consider the...
A linear-time algorithm termed SPARse Truncated Amplitude flow (SPARTA) is developed for the phase retrieval (PR) of sparse signals. Upon formulating the sparse PR as a non-convex empirical loss minimization task, SPARTA emerges as an iterative solver consisting of two components: s1) a sparse orthogonality-promoting initialization leveraging support recovery and principal component analysis; and,...
Random sinusoidal features are a popular approach for speeding up kernel-based inference in large datasets. Prior to the inference stage, the approach suggests performing dimensionality reduction by first multiplying each data vector by a random Gaussian matrix, and then computing an element-wise sinusoid. Theoretical analysis shows that collecting a sufficient number of such features can be reliably...
In this paper, we propose a new approach for robust compressive sensing (CS) using memristor crossbars that are constructed by recently invented memristor devices. The exciting features of a memristor crossbar, such as high density, low power and great scalability, make it a promising candidate to perform large-scale matrix operations. To apply memristor crossbars to solve a robust CS problem, the...
Outlier detection algorithms are often computationally intensive because of their need to score each point in the data. Even simple distance-based algorithms have quadratic complexity. High-dimensional outlier detection algorithms such as subspace methods are often even more computationally intensive because of their need to explore different subspaces of the data. In this paper, we propose an exceedingly...
It is generally well known that the overall performance of the most widely used types of unsupervised change detection methods, based on the luminance pixel-wise difference, is mainly relied on the quality of the so-called difference image and the accuracy of the classification method. In order to address these two issues, this work proposes to first estimate, a new and robust similarity feature map,...
We are interested in solving the problem of locating a subset of facilities in the case of uncertainties and variations in the system parameters. Dealing with this problem using scenarios based approach needs an important computational effort. The two phases proposed method in this paper combines both exact and heuristic approaches to minimize the maximum regret of the model. We proposed and compared...
Obstacle detection and tracking is essential module for autonomous driving. Vision based obstacle detection and tracking faces huge challenges due to factors like cluttered background, partial occlusion, inconsistent illumination, etc. In this paper, we propose a robust and low complexity stereo-vision based obstacle detection and tracking framework. Low complexity techniques are employed to detect...
The Census transform is very useful in stereo matching algorithms. But the traditional Census transform cost too much computation, and its accuracy and robustness are not satisfying. In this paper, a modified semi-global matching (SGM) algorithm based on the fast Census transform is proposed to improve the quality of the range map and decrease the computation. In addition, we modify the disparity...
This paper presents a semi-incremental recognition method for online handwritten mathematical expressions (MEs). The method reduces the waiting time after an ME is written until the result of recognition is output. Our method has two main processes, one is to process the latest stroke, the other is to find and correct wrong recognitions in the strokes up to the latest stroke. In the first process,...
The mathematical framework of networks is well suited to describe several systems consisting of a large number of entities interacting with each others. Every entity is represented by a network node and each interaction by a link between two nodes. It is therefore possible to model these networks as graphs. In this paper, we present a reliability study for chain topologies based on spanning tree in...
Web resources protection is one of the most difficult problems on network. Many solutions relevant have been put forward and some protecting systems have come out until now. However, almost all solutions are based on the method that compares with files' digital signature firstly and judges files have been tampered with or not secondly [1]. And all these solutions are useless for resolving misusing...
We study the problem of estimating an unknown vector from noisy underdetermined observations, with recovery guarantees. In such context, a regularity model on the unknown is needed to obtain recovery guarantees. We show that we can guarantee the recovery of generic models (cones) with the minimization of an arbitrary regularizer subject to a data-fit constraint (generalized robust basis pursuit) under...
Parametric motion models are commonly used in image sequence analysis for different tasks. A robust estimation framework is usually required to reliably compute the motion model. The choice of the right model is also important. However, dealing simultaneously with both issues remains an open question. We propose a robust motion model selection method with two variants, which relies on the Fisher test...
Improving the execution time and the numerical complexity of the well-known kurtosis-based maximization method, the RobustICA, is investigated in this paper. A Newton-based scheme is proposed and compared to the conventional RobustICA method. A new implementation using the nonlinear Conjugate Gradient one is investigated also. Regarding the Newton approach, an exact computation of the Hessian of the...
Multivariate multiscale entropy (mvMSE) has been proposed as a combination of the coarse-graining process and multivariate sample entropy (mvSE) to quantify the irregularity of multivariate signals. However, both the coarse-graining process and mvSE may not be reliable for short signals. Although the coarse-graining process can be replaced with multivariate empirical mode decomposition (MEMD), the...
The fast multipole algorithm (FMA) has been thought of as one of top ten algorithms in science and engineering in the 20th century and its multilevel variant (MLFMA) was first proposed in electromagnetics. The memory usage and CPU time for solving a dense matrix equation iteratively are of O(N2) complexity, where N is the number of unknowns, and this cost usually prevents one from solving large-scale...
Decision-Aid Methods (DAMs) such as the Cost-Benefit Analysis (CBA) and the Analytical Hierarchy Process (AHP) help decision-makers to rank alternatives or to choose the best one among several potential ones. The new Belief Function based Technique for Order Preference by Similarity to Ideal Solution (BF-TOPSIS) methods have been recently developed for Multi-Criteria Decision-Making problems. In this...
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