Development of Novel Reconstruction Methods Based on l1--Minimization for Near Infrared Diffuse Optical Tomography

Abstract

Diffuse optical tomography uses near infrared (NIR) light as the probing media to recover the distributions of tissue optical properties. It has a potential to become an adjunct imaging modality for breast and brain imaging, that is capable of providing functional information of the tissue under investigation. As NIR light propagation in the tissue is dominated by scattering, the image reconstruction problem (inverse problem) tends to be non-linear and ill-posed, requiring usage of advanced computational methods to compensate this. Traditional image reconstruction methods in diffuse optical tomography employ l2 –norm based regularization, which is known to remove high frequency noises in the re-constructed images and make them appear smooth. The recovered contrast in the reconstructed image in these type of methods are typically dependent on the iterative nature of the method employed, in which the non-linear iterative technique is known to perform better in comparison to linear techniques. The usage of non-linear iterative techniques in the real-time, especially in dynamical imaging, becomes prohibitive due to the computational complexity associated with them. In the rapid dynamic diffuse optical imaging, assumption of a linear dependency in the solutions between successive frames results in a linear inverse problem. This new frame work along with the l1–norm based regularization can provide better robustness to noise and results in a better contrast recovery compared to conventional l2 –based techniques. Moreover, it is shown that the proposed l1-based technique is computationally efficient compared to its counterpart(l2 –based one). The proposed framework requires a reasonably close estimate of the actual solution for the initial frame and any suboptimal estimate leads to erroneous reconstruction results for the subsequent frames. Modern diffuse optical imaging systems are multi-modal in nature, where diffuse optical imaging is combined with traditional imaging modalities such as MRI, CT, and Ultrasound. A novel approach that can more effectively use the structural information provided by the traditional imaging modalities in these scenarios is introduced, which is based on prior image constrained- l1 minimization scheme. This method has been motivated by the recent progress in the sparse image reconstruction techniques. It is shown that the- l1 based frame work is more effective in terms of localizing the tumor region and recovering the optical property values both in numerical and gelatin phantom cases compared to the traditional methods that use structural information.