New sampling scheme for region-of-interest tomography

The wavelet localization technique was recently applied to the study of region-of-interest (ROI) tomography. It achieves a significant saving in the required projections if only a small region of a tomographic image is of interest. In this paper, we first show that with the same sampling scheme, a simple interpolation applied to the samples can give a result at least as good as that using the original wavelet localization approach. It implies that the use of the wavelet transform is not the key to the reduction of the sampling requirement. In fact, the quality of the reconstructed ROI is largely determined by the structure of the sampling scheme. Rather than directly reducing the projection number, the use of the wavelet theory permits a clear understanding of how to achieve a good sampling pattern. Based on an error analysis using the wavelet theory, we further suggest a new sampling scheme such that the number of required projections in each angle is reduced in a multiresolution form. A new multiresolution interpolation algorithm is then used to interpolate the missing samples to obtain the full projections. As a result, more than 84% of projections are saved, as compared with the traditional approach, in reconstructing an ROI of 32×32 pixels in an image of 256×256 pixels. A series of simulations was performed to reconstruct different sizes of the ROI. All results show that the signal-to-error ratios of the reconstructed ROI are comparable with that using full projection data set.