Inverse Problems in Science and Engineering 

About: Inverse Problems in Science and Engineering is an academic journal published by Taylor & Francis. The journal publishes majorly in the area(s): Inverse problem & Boundary value problem. It has an ISSN identifier of 1741-5977. Over the lifetime, 1295 publications have been published receiving 14145 citations. The journal is also known as: International journal on inverse problems in science and engineering & IPSE.

Deep learning for photoacoustic tomography from sparse data.

Abstract: The development of fast and accurate image reconstruction algorithms is a central aspect of computed tomography. In this paper, we investigate this issue for the sparse data problem in photoacousti...

Detection of material interfaces using a regularized level set method in piezoelectric structures

Abstract: An algorithm to solve the inverse problem of detecting inclusion interfaces in a piezoelectric structure is proposed. The material interfaces are implicitly represented by level sets which are identified by applying regularization using total variation penalty terms. The inverse problem is solved iteratively and the extended finite element method is used for the analysis of the structure in each iteration. The formulation is presented for three-dimensional structures and inclusions made of different materials are detected by using multiple level sets. The results obtained prove that the iterative procedure proposed can determine the location and approximate shape of material sub-domains in the presence of higher noise levels.

A survey of applications of the MFS to inverse problems

Abstract: The method of fundamental solutions (MFS) is a relatively new method for the numerical solution of boundary value problems and initial/boundary value problems governed by certain partial differential equations. The ease with which it can be implemented and its effectiveness have made it a very popular tool for the solution of a large variety of problems arising in science and engineering. In recent years, it has been used extensively for a particular class of such problems, namely inverse problems. In this study, in view of the growing interest in this area, we review the applications of the MFS to inverse and related problems, over the last decade.

Iterative thresholding compressed sensing MRI based on contourlet transform

Abstract: Reducing the acquisition time is important for clinical magnetic resonance imaging (MRI). Compressed sensing has recently emerged as a theoretical foundation for the reconstruction of magnetic resonance images from undersampled k-space measurements, assuming those images are sparse in a certain transform domain. However, most real-world signals are compressible rather than exactly sparse. For example, the commonly used two-dimensional wavelet for compressed sensing MRI (CS-MRI) does not sparsely represent curves and edges. In this article, we introduce a geometric image transform, the contourlet, to overcome this shortage. In addition, the improved redundancy provided by the contourlet can successfully suppress the pseudo-Gibbs phenomenon, a tiresome artefact produced by undersampling of k-space, around the singularities of images. For numerical calculation, a simple but effective iterative thresholding algorithm is employed to solve l 1 norm optimization for CS-MRI. Considering the recovered information ...

CMARS: a new contribution to nonparametric regression with multivariate adaptive regression splines supported by continuous optimization

Abstract: Regression analysis is a widely used statistical method for modelling relationships between variables. Multivariate adaptive regression splines (MARS) especially is very useful for high-dimensional problems and fitting nonlinear multivariate functions. A special advantage of MARS lies in its ability to estimate contributions of some basis functions so that both additive and interactive effects of the predictors are allowed to determine the response variable. The MARS method consists of two parts: forward and backward algorithms. Through these algorithms, it seeks to achieve two objectives: a good fit to the data, but a simple model. In this article, we use a penalized residual sum of squares for MARS as a Tikhonov regularization problem, and treat this with continuous optimization technique, in particular, the framework of conic quadratic programming. We call this new approach to MARS as CMARS, and consider it as becoming an important complementary and model-based alternative to the backward stepwise algo...