Conclusions

Using the terahertz reflected waveforms, we were able to measure the projections and reconstruct the original image. This process was completed in two steps. In the first, inverse and Wiener filtering were used to deconvolve the data from the reference pulse to obtain the actual projections of the test object. In the second, the Filtered Backprojection Algorithm featuring the Fourier Slice Theorem was used to filter the projections using a ramp filter and backproject the result over the image plane, thus reconstructing the image of the object.

As far as the deconvolution part of the project concerns, the regularized inverse filter gives better results than Wiener filtering, as already pointed out. Care should be exercised when picking the regularized parameter γ, so as not to increase the noise level of the resulting signal. Usually, this is a case-dependent procedure that takes numerical experimentation. It should be noted that the original data at hand were of very good quality with low noise level. Thus the results of Wiener filtering were worse than those obtained by inverse filtering.

For the reconstruction part, it was found that the number of projection angles used was vital to the clarity of the final image. We were able to greatly downsample the data and still maintain image quality to a certain point. Due to the size of the data, the algorithms ran for minutes.

Future Work

Much potential for future improvement and implementation is possible using this method of computerized tomography. Advanced deconvolution methods featuring wavelets for efficient noise reduction can be used for isolating the projections out of the measured waveforms. Furthermore, it seems reasonable to cut-off the first part of each measured waveform since it only contains noise and no useful information for the image reconstruction. This can be accomplished by appropriately windowing the raw measurements before any other manipulations takes place. Due to the linear nature of the process, different algorithm code could have been written to start reconstructing the image immediately after the first projection had been calculated. This and other efficiency tools could be implemented to greatly increase the speed of the overall reconstruction, making the process applicable for real-time use.

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