In such incomplete projection data situation, fast reconstruction algorithms based on the Radon inversion formula, such as the Convolution Back projection (CBP) algorithm and the Fourier Inversion (FI) algorithm produce degraded images. Recently, a linear prediction modeling approach was suggested by Srinivasa et al. [5] for estimating the missing projections and then use the CBP algorithm for image reconstruction. In this paper a multiresolution modeling approach in the Radon space is proposed for projection completion in the hollow projection data problem. The multiresolution modeling [1-4] has been a topic of recent origin. The modeling, estimation and analysis has been motivated by the theory of multiscale representation and wavelet transforms.

The multi resolution modeling offers the flexibility of modeling the localized frequency components of different bands separately. A priori information about the missing data can be also conveniently incorporated along with the estimation procedure.

A new algorithm is proposed in this paper for projection completion based on multiresolution modeling approach in hollow, limited angle and truncated data situations. There are many instances encountered in practice having this type of missing data. For example, the presence of X-ray opaque objects, such as artificial joint, bullet, metallic pins, present within the cross section obscure the rays passing through them. The algorithm consists of the following steps. First, the wavelet coefficients of the projection data available is obtained. A priori information from the data available is incorporated in the missing region. A simple linear interpolation can be used for this purpose. AR model parameters are then computed for each scale or scales of interest from the wavelet transformed projection data. The wavelet coefficients corresponding to the missing region can then be estimated using the linear prediction models developed. By inverse transforming the wavelet coefficients obtained after prediction, the completed projection are obtained. The effectiveness of the proposed algorithm has been studied and compared with the direct LP modeling in the Radon space.

The proposed modeling approach for projection completion is superior to the direct LP modeling. This is because an apriori information about the missing data is incorporated along with the modeling approach. Incorporating apriori information and the estimation of localised high frequency components in the missing region based on the proposed modeling approach significantly improves the reconstructed image. Various distortion measures computed to study the quality of reconstructed images clearly indicated the superiority of the proposed algorithm. REFERENCES

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3. S. C. Clippingdale and R. G. Wilson, "Least-Squares Estimation on a multiresolution Pyramid" ICASSP 89 Intl. Conf. on Acoust. Speech Signal Processing, vol. 3, pp. 1409-1412, Glasgow, England, May 23-26, 1989
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