Parametric Image Reconstruction Using the Discrete Cosine Transform for Optical Tomography

It is well known that the inverse problem in optical tomography is highly ill-posed. The image reconstruction process is often unstable and nonunique, because the number of the boundary measurements data is far fewer than the number of the unknown parameters to be reconstructed. To overcome this problem, one can either increase the number of measurement data (e.g., multispectral or multifrequency methods), or reduce the number of unknowns (e.g., using prior structural information from other imaging modalities). We introduce a novel approach for reducing the unknown parameters in the reconstruction process. The discrete cosine transform (DCT), which has long been used in image compression, is here employed to parameterize the reconstructed image. In general, only a few DCT coefficients are needed to describe the main features in an optical tomographic image. Thus, the number of unknowns in the image reconstruction process can be drastically reduced. We show numerical and experimental examples that illustrate the performance of the new algorithm as compared to a standard model-based iterative image reconstructions scheme. We especially focus on the influence of initial guesses and noise levels on the reconstruction results.