Learning Sparsifying Transforms for Image Reconstruction in Electrical Impedance Tomography

Electrical Impedance Tomography (EIT) is a fast and non-invasive imaging technology that reconstructs the internal electrical properties of a subject. However, its functionality is limited by low spatial resolution arising from an ill-posed and ill-conditioned inverse problem. Several sparsity-promoting regularization methods have been applied to improve the quality of EIT image reconstruction, including various ℓ
0
and ℓ
1
-based analytical models (TV, TwIST, etc.), and a patch-based sparse representation via a learned dictionary (using the K-SVD algorithm), dubbed CS-EIT. To further exploit the potential of compressed sensing in Electrical Impedance Tomography, this paper incorporates the recent novel method of transform learning for EIT image reconstruction. We propose a blind compressed sensing algorithm, dubbed TL-EIT, which simultaneously optimizes the sparsifying transform and updates the reconstructed image. We demonstrate using both synthetic and in vivo data that the proposed TL-EIT is more effective than other sparsity-based algorithms for reconstructing high-quality EIT images. In addition, TL-EIT also accelerates the reconstruction process in comparison to other learning-based algorithms like CS-EIT.