Wavelet-Based Image Reconstruction for Hard-Field Tomography With Severely Limited Data

We introduce a new wavelet-based hard-field image reconstruction method that is well suited for data inversion of limited path-integral data obtained from a geometrically sparse sensor array. It is applied to a chemical species tomography system based on near-IR spectroscopic absorption measurements along an irregular array of only 27 paths. This system can be classified as producing severely limited data, where both the number of viewing angles and the number of measurements are small. As shown in our previous work, the Landweber iteration method allows stable solution of this tomography problem by incorporating suitable a priori information. In the new method, a 2-D discrete wavelet transform has been used as a smoothing function. We present a method of designing the optimal wavelet-based smoothing function, depending on a priori knowledge of the subject. The significance of the particular wavelet filter selected is considered in terms of the accuracy of reconstruction of the spatial location and shape of the gas distribution. Results are presented for simulated phantoms using different sensor arrays and for experiments with propane plumes, showing excellent spatial localization and quantification. The computational time of the iterative algorithm is significantly reduced by applying the wavelet transform method. Some of our conclusions are applicable to other hard-field tomographic modalities in applications where similar constraints may be encountered.