## 1. Introduction

[2] Tomographic imaging of the electron density has evolved during the past decade to become an important ionospheric diagnostic. Efforts have been directed by a number of research groups [*Raymund*, 1995; *Raymund et al.*, 1993, 1990; *Austen et al.*, 1988; *Sutton and Na*, 1996] to verify and establish the technique as a tool that can be readily used for many purposes like routine monitoring of the ionosphere, correcting the ionospheric delay experienced by the Global Positioning System (GPS) signals, geophysical studies of the plasma etc. It is important to establish an algorithm that will produce reliable reconstruction of the whole range of possible ionospheric density distribution. The ray tomography technique involves use of one-dimensional information to reconstruct a two-dimensional image. The data consists of measurements of the line integral of electron density in the ionosphere for many different paths. The line integral paths can be considered as many unique rays traversing the plane of the reconstruction region. Region of interest can be gridded into small areas or pixels. It is assumed that the electron density will remain constant in each pixel. The line integral of electron density over some path is the total electron content (TEC). Mathematically it can be expressed as below:

where, *N*_{e}(*l*) is the variable electron density along the signal path “*l*,” and the line integration is along the signal path from the satellite *S* to the receiver *R* [*Klobuchar*, 1996].

[3] Ray tomography includes two-dimensional as well as three-dimensional tomography. An alternative approach extends the tomographic idea into imaging the entire ionospheric region by considering full three-dimensional voxel based (i.e., volume pixel based) tomography. *Meggs et al.* [2002, 2004], developed an inversion program called the MultiInstrument Data Analysis System (MIDAS), for determining the electron density distribution and consequently the TEC values in each voxel. Their main conclusion was that on an hour by hour basis, imaging the ionospheric TEC (or determining delay) using a full inversion is more reliable than using a thin shell model. In two-dimensional tomography a chain of stations receive the signals from the visible GPS satellites, and the geometry can be created in such a way that the TEC measurements can be used to reconstruct a vertical slice or vertical cross section of the ionospheric electron density in a vertical plane between the satellite and the ground stations [*Mitchell et al.*, 1997].

[4] To reconstruct the ionosphere, the TEC can be used with the tomography technique for the two-dimensional imaging of electron density distribution in the ionosphere. The estimated TEC for a chain of receivers are inverted to obtain the electron density distribution as a function of latitude and altitude over a given longitude. Inversion, by nature being an ill-posed mathematical problem which may not have a unique set of solution. As a result, various mathematical algorithms are used for this inversion [*Pryse et al.*, 1998; *Raymund*, 1995]. When these algorithms are used in ionospheric tomography to reconstruct the electron density profiles, almost all of them suffer from the basic inability to correctly estimate the vertical profiles of these distributions. This problem to a large extent is also due to the geometry of the whole system, as one cannot have the TEC information from large projection angles from a ground based receiver. Also the completeness of the data is limited, as the receivers do not lock onto a satellite until it is at least a few degrees above the horizon.

[5] The accuracy of the reconstructed image generally depends on many factors like satellite receiver configuration, the raypath modeling, grid intersections and finally the reconstruction algorithm. There is a direct relationship between the information contained in the measured TEC data and the accuracy of the reconstructed image. Thus the proper choice of receiving stations which could optimize the information contend in a given longitudinal plane is one of the key factors for obtaining accurate images from any ionospheric tomography network [*Thampi et al.*, 2004].

[6] In this paper, a novel approach to the tomography model is adopted which will produce the path length matrix (PLM) required in the reconstruction technique and some iterative approaches such as, Algebraic Reconstruction Technique (ART) and Multiplicative Algebraic Reconstruction Technique (MART), for the reconstruction of electron density and the TEC.

[7] The whole organization of the paper is as follows: In section 2, a short view on ray tomography is given. The ionospheric model, the reconstruction technique with the algorithms of ART and MART and a new method for determining the initial guess are discussed in section 3. In section 4, the validation methodology is presented. Analysis and results using ART and MART have been provided in section 5. Conclusion is provided in section 6.