Abstract: Diffuse Optical Tomography (DOT) is a non-invasive imaging modality used in clinical diagnosis for earlier detection of carcinoma cells in brain tissue. It is a form of optical tomography which produces gives the reconstructed image of a human soft tissue with by using near-infra-red light. It comprises of two steps called forward model and inverse model. The forward model provides the light propagation in a biological medium. The inverse model uses the scattered light to collect the optical parameters of human tissue. DOT suffers from severe ill-posedness due to its incomplete measurement data. So the accurate analysis of this modality is very complicated. To overcome this problem, optical properties of the soft tissue such as absorption coefficient, scattering coefficient, optical flux are processed by the standard regularization technique called Levenberg - Marquardt regularization. The reconstruction algorithms such as Split Bregman and Gradient projection for sparse reconstruction (GPSR) methods are used to reconstruct the image of a human soft tissue for tumour detection. Among these algorithms, Split Bregman method provides better performance than GPSR algorithm. The parameters such as signal to noise ratio (SNR), contrast to noise ratio (CNR), relative error (RE) and CPU time for reconstructing images are analyzed to get a better performance.
Abstract: The numerical analytic continuation of a function f(z) = f(x + iy) on a strip is discussed in this paper. The data are only given approximately on the real axis. The periodicity of given data is assumed. A truncated Fourier spectral method has been introduced to deal with the ill-posedness of the problem. The theoretic results show that the discrepancy principle can work well for this problem. Some numerical results are also given to show the efficiency of the method.
Abstract: We study the problem of reconstructing a three dimensional binary matrices whose interiors are only accessible through few projections. Such question is prominently motivated by the demand in material science for developing tool for reconstruction of crystalline structures from their images obtained by high-resolution transmission electron microscopy. Various approaches have been suggested to reconstruct 3D-object (crystalline structure) by reconstructing slice of the 3D-object. To handle the ill-posedness of the problem, a priori information such as convexity, connectivity and periodicity are used to limit the number of possible solutions. Formally, 3Dobject (crystalline structure) having a priory information is modeled by a class of 3D-binary matrices satisfying a priori information. We consider 3D-binary matrices with periodicity constraints, and we propose a polynomial time algorithm to reconstruct 3D-binary matrices with periodicity constraints from two orthogonal projections.
Abstract: Nondestructive testing in engineering is an inverse
Cauchy problem for Laplace equation. In this paper the problem
of nondestructive testing is expressed by a Laplace-s equation with
third-kind boundary conditions. In order to find unknown values on
the boundary, the method of fundamental solution is introduced and
realized. Because of the ill-posedness of studied problems, the TSVD
regularization technique in combination with L-curve criteria and
Generalized Cross Validation criteria is employed. Numerical results
are shown that the TSVD method combined with L-curve criteria is
more efficient than the TSVD method combined with GCV criteria.
The abstract goes here.
Abstract: The electromagnetic imaging of inhomogeneous
dielectric cylinders buried in a slab medium by transverse electric
(TE) wave illumination is investigated. Dielectric cylinders of
unknown permittivities are buried in second space and scattered a
group of unrelated waves incident from first space where the scattered
field is recorded. By proper arrangement of the various unrelated
incident fields, the difficulties of ill-posedness and nonlinearity are
circumvented, and the permittivity distribution can be reconstructed
through simple matrix operations. The algorithm is based on the
moment method and the unrelated illumination method. Numerical
results are given to demonstrate the capability of the inverse
algorithm. Good reconstruction is obtained even in the presence of
additive Gaussian random noise in measured data. In addition, the
effect of noise on the reconstruction result is also investigated.