Transmission tomography for high contrast media based on sparse data

2013-08-05Transmission tomography is a powerful tool to image the interior structure based on measured data on the boundary. It provides a "non-destructive" imaging and widely used in different areas. However, the reconstructed image quality degrades when lower number of data is available. In this work, we consider tomography problems involving detection of high contrast structures with limited amount of data, and propose a sparse representation for the images of our interest. The sparse model is useful to reduce the unknown variables for the tomographic reconstruction. In the first part, we propose an object-based model for high velocity structure in travel time tomography. We focus on how to speed up the path tracking procedure on high velocity object assumption. To estimate the object parameters, we use probabilistic approach to define the appearance probability of different models, and estimate the probability distribution by accelerated random walk. The result can be viewed as a "probability map", which represent the appearance of the high velocity structure in different regions. Compared to the conventional grid-based model, our approach provides stable results and superior reconstruction quality. As an application, we use the high contrast tomography to detect fractures in a low permeability reservoir under water-flooding. In particular, we (i) propose to use the injected water as a probe signal, where we are able to measure the travel time without shutting down the usual operation, and (ii) formulate the fracture as high velocity objects and do tomographic reconstruction. The results from commercial simulator show our method can successfully identify the location of fractures, and the field experiment is consistent with the conclusion from experts in the field engineering team. In the second part, we study the X-ray transmission tomography where the object is assumed to be made from few distinct materials. This problem is called discrete tomography (DT). Such images arise in tomography problems where very high contrast is expected, e.g., in angiography medical imaging or electron tomography. We assume the image of interest can be segmented as several smooth boundary, constant intensity regions. Moreover, we design transform which can represent each region with sparse coefficients, and formulate the tomographic reconstruction as a sparse recovery. A common assumption for DT is that the set of possible intensity levels is known in advance. However, determining the prescribed intensity levels is a difficult problem, coupled with measurement calibration and the prior knowledge of image. We introduce an unsupervised DT algorithm that jointly reconstructs the image and estimates the unknown intensity levels. Our algorithm alternates between (i) an L₁ sparse recovery step with a reweighed cost function that search the sparse representation which fits the measurements, and (ii) an estimation step for the most likely intensity levels. We experimentally demonstrate that the proposed algorithm successfully estimates the unknown levels and leads to high quality reconstruction of phantom images