Abstract: The paper is a comparative study of two classical vari-ants of parallel projection methods for solving the convex feasibility problem with their equivalents that involve variable weights in the construction of the solutions. We used a graphical representation of these methods for inpainting a convex area of an image in order to investigate their effectiveness in image reconstruction applications. We also presented a numerical analysis of the convergence of these four algorithms in terms of the average number of steps and execution time, in classical CPU and, alternativaly, in parallel GPU implementation.
Abstract: Dimensionality reduction and feature extraction are of
crucial importance for achieving high efficiency in manipulating
the high dimensional data. Two-dimensional discriminant locality
preserving projection (2D-DLPP) and two-dimensional discriminant
supervised LPP (2D-DSLPP) are two effective two-dimensional
projection methods for dimensionality reduction and feature
extraction of face image matrices. Since 2D-DLPP and 2D-DSLPP
preserve the local structure information of the original data and
exploit the discriminant information, they usually have good
recognition performance. However, 2D-DLPP and 2D-DSLPP
only employ single-sided projection, and thus the generated low
dimensional data matrices have still many features. In this paper,
by combining the discriminant supervised LPP with the bidirectional
projection, we propose the bidirectional discriminant supervised LPP
(BDSLPP). The left and right projection matrices for BDSLPP can
be computed iteratively. Experimental results show that the proposed
BDSLPP achieves higher recognition accuracy than 2D-DLPP,
2D-DSLPP, and bidirectional discriminant LPP (BDLPP).
Abstract: The photoacoustic images are obtained from a custom developed linear array photoacoustic tomography system. The biological specimens are imitated by conducting phantom tests in order to retrieve a fully functional photoacoustic image. The acquired image undergoes the active region based contour filtering to remove the noise and accurately segment the object area for further processing. The universal back projection method is used as the image reconstruction algorithm. The active contour filtering is analyzed by evaluating the signal to noise ratio and comparing it with the other filtering methods.
Abstract: Group decision making with multiple attribute has
attracted intensive concern in the decision analysis area. This paper
assumes that the contributions of all the decision makers (DMs) are not
equal to the decision process based on different knowledge and
experience in group setting. The aim of this paper is to develop a novel
approach to determine weights of DMs in the group decision making
problems. In this paper, the weights of DMs are determined in the
group decision environment via angle cosine and projection method.
First of all, the average decision of all individual decisions is defined
as the ideal decision. After that, we define the weight of each decision
maker (DM) by aggregating the angle cosine and projection between
individual decision and ideal decision with associated direction
indicator μ. By using the weights of DMs, all individual decisions are
aggregated into a collective decision. Further, the preference order of
alternatives is ranked in accordance with the overall row value of
collective decision. Finally, an example in a chemical company is
provided to illustrate the developed approach.
Abstract: In this paper we study numerical methods for solving Sylvester matrix equations of the form AX +XBT +CDT = 0. A new projection method is proposed. The union of Krylov subspaces in A and its inverse and the union of Krylov subspaces in B and its inverse are used as the right and left projection subspaces, respectively. The Arnoldi-like process for constructing the orthonormal basis of the projection subspaces is outlined. We show that the approximate solution is an exact solution of a perturbed Sylvester matrix equation. Moreover, exact expression for the norm of residual is derived and results on finite termination and convergence are presented. Some numerical examples are presented to illustrate the effectiveness of the proposed method.
Abstract: In this paper, we propose a new seed projection method for solving shifted systems with multiple right-hand sides. This seed projection method uses a seed selection strategy. Numerical experiments are presented to show the efficiency of the newly method.
Abstract: In the present work, we propose a new projection method for solving the matrix equation AXB = F. For implementing our new method, generalized forms of block Krylov subspace and global Arnoldi process are presented. The new method can be considered as an extended form of the well-known global generalized minimum residual (Gl-GMRES) method for solving multiple linear systems and it will be called as the extended Gl-GMRES (EGl- GMRES). Some new theoretical results have been established for proposed method by employing Schur complement. Finally, some numerical results are given to illustrate the efficiency of our new method.
Abstract: The design problem of Infinite Impulse Response (IIR)
digital filters is usually expressed as the minimization problem of
the complex magnitude error that includes both the magnitude and
phase information. However, the group delay of the filter obtained
by solving such design problem may be far from the desired group
delay. In this paper, we propose a design method of stable IIR digital
filters with prespecified maximum group delay errors. In the proposed
method, the approximation problems of the magnitude-phase and
group delay are separately defined, and these two approximation
problems are alternately solved using successive projections. As a
result, the proposed method can design the IIR filters that satisfy the
prespecified allowable errors for not only the complex magnitude but
also the group delay by alternately executing the coefficient update
for the magnitude-phase and the group delay approximation. The
usefulness of the proposed method is verified through some examples.
Abstract: In this paper, a new descent-projection method with a
new search direction for monotone structured variational inequalities
is proposed. The method is simple, which needs only projections
and some function evaluations, so its computational load is very tiny.
Under mild conditions on the problem-s data, the method is proved to
converges globally. Some preliminary computational results are also
reported to illustrate the efficiency of the method.
Abstract: The projection methods, usually viewed as the methods
for computing eigenvalues, can also be used to estimate pseudospectra.
This paper proposes a kind of projection methods for computing
the pseudospectra of large scale matrices, including orthogonalization
projection method and oblique projection method respectively. This
possibility may be of practical importance in applications involving
large scale highly nonnormal matrices. Numerical algorithms are
given and some numerical experiments illustrate the efficiency of
the new algorithms.
Abstract: In this paper, we introduce a novel algorithm for object tracking in video sequence. In order to represent the object to be tracked, we propose a spatial color histogram model which encodes both the color distribution and spatial information. The object tracking from frame to frame is accomplished via center voting and back projection method. The center voting method has every pixel in the new frame to cast a vote on whereabouts the object center is. The back projection method segments the object from the background. The segmented foreground provides information on object size and orientation, omitting the need to estimate them separately. We do not put any assumption on camera motion; the proposed algorithm works equally well for object tracking in both static and moving camera videos.
Abstract: An unstructured finite volume numerical model is
presented here for simulating shallow-water flows with wetting and
drying fronts. The model is based on the Green-s theorem in
combination with Chorin-s projection method. A 2nd-order upwind
scheme coupled with a Least Square technique is used to handle
convection terms. An Wetting and drying treatment is used in the
present model to ensures the total mass conservation. To test it-s
capacity and reliability, the present model is used to solve the
Parabolic Bowl problem. We compare our numerical solutions with
the corresponding analytical and existing standard numerical results.
Excellent agreements are found in all the cases.