Hybrid sensitivity-correlation regularisation matrix for electrical impedance tomography

In electrical impedance tomography, the primary task of image reconstruction process is to solve a discrete ill-posed inverse problem. The estimated solution is commonly obtained under a regularisation framework so that the noise amplified solution, which occurs during the matrix inversion process, can be avoided. The regularisation framework aims at balancing the model-data fitness while simultaneously constraining the solution space with additional prior (commonly prescribed through the regularisation matrix and solution-norm). In this study, a relationship between two robust regularisation matrices namely Newton one-step error reconstruction and fidelity-embedded regularisation is explicitly highlighted in both spatial and singular value decomposition domains. A hybrid regularisation matrix which encompasses the two prior knowledge, non-uniform sensitivity distribution and array response correlation, is then proposed as an alternative prior. Experimental results along with several evaluated performance parameters highlight the ability of the proposed prior to achieve a well-balanced and robust performance.