Mohsen Rabbani and Khosrow Maleknejad
The purpose of this paper is to use Alpert wavelet basis and modify the integrand function approximation coefficients to solve Fredholm‐Hammerstein integral equations.
Abstract
Purpose
The purpose of this paper is to use Alpert wavelet basis and modify the integrand function approximation coefficients to solve Fredholm‐Hammerstein integral equations.
Design/methodology/approach
L2[0, 1] was considered as solution space and the solution was projected to the subspaces of L2[0, 1] with finite dimension so that basis elements of these subspaces were orthonormal.
Findings
In this process, solution of Fredholm‐Hammerstein integral equation is found by solving the generated system of nonlinear equations.
Originality/value
Comparing the method with others shows that this system has less computation. In fact, decreasing of computations result from the modification.
Details
Keywords
Khosrow Maleknejad, Saeed Sohrabi and Yasser Rostami
The purpose of this paper, with reference to compression of different images' portions with various qualities, is to obtain a high‐compression coefficient.
Abstract
Purpose
The purpose of this paper, with reference to compression of different images' portions with various qualities, is to obtain a high‐compression coefficient.
Design/methodology/approach
Usually, not all parts of a medical image have equal significance. Also, an image's background can be combined with noise. This method separates a part of the video which is moving from a part that is stationary.
Findings
This process results in the high‐quality compression of medical frames.
Originality/value
Separating parts of a frame using 2D and 3D wavelet transform makes a valuable contribution to biocybernetics.
Details
Keywords
Mohsen Rabbani and Khosrow Maleknejad
The purpose of this paper is to explain the choice of Alpert multi‐wavelet as basis functions to discrete Fredholm integral equation of the second kind by using Petrov‐Galerkin…
Abstract
Purpose
The purpose of this paper is to explain the choice of Alpert multi‐wavelet as basis functions to discrete Fredholm integral equation of the second kind by using Petrov‐Galerkin method.
Design/methodology/approach
In this process, two kinds of matrices are obtained from inner product between basis of test space and trial space; some of them are diagonal with positive elements and some others are invertible. These matrices depend on type of selection of test and trial space basis.
Findings
In this process, solution of Fredholm integral equation of the second kind is found by solving the generated system of linear equations.
Originality/value
In previous work, convergence of Petrov‐Galerkin method has been discussed with some restrictions on degrees of chosen polynomial basis, but in this paper convergence is obtained for every degree. In point of computation, because of appearance of diagonal and invertible matrices, a small dimension system with a more accurate solution is obtained. The numerical examples illustrate these facts.