Bayesian Image Reconstruction Using Weighted Laplace Prior for Lung Respiratory Monitoring With Electrical Impedance Tomography

Abstract

The poor spatial resolution of electrical impedance tomography (EIT) limits its use in medical devices because of its highly nonlinear and ill-posed nature. A novel hierarchical block sparse Bayesian learning (BSBL) method is designed for lung respiratory monitoring with EIT. It is its excellent modeling capability and noise robustness that allows BSBL to adaptively explore and exploit the internal conductivity distribution, e.g., block sparsity and intra-block correlation. First, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> -nearest neighbor (KNN) strategy is employed to automatically group each block based on the clustering property and incorporated to constrain the intra-block correlation matrix based on the spatial distance. Second, a three-layer hierarchical BSBL model using weighted Laplace (WL) prior is considered to enhance the recovery performance. Finally, an efficient bound optimization (BO) method is performed for Bayesian inference, avoiding the tedious parameter adjustment. This leads to improvements in recovery performance, algorithm robustness, and computational efficiency. Moreover, root mean square error (RMSE), image correlation coefficient (ICC), and relative size coverage ratio (RCR) are applied for quantitative comparisons of image quality. Numerical simulations and in vivo lung respiratory experiments showed that the proposed KNN-BSBL-WL method outperforms existing referenced methods in terms of reconstruction accuracy and computational time. On average, KNN-BSBL-WL obtains the RMSE <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$= 0.07\,\,\pm \,\,0.02$ </tex-math></inline-formula> , ICC <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$= 0.96\,\,\pm \,\,0.01$ </tex-math></inline-formula> , and RCR <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$= 0.98\,\,\pm \,\,0.05$ </tex-math></inline-formula> , which are closest to the true values of the recorded snapshots obtained in the experiments. Meanwhile, the average time of KNN-BSBL-WL is 0.16 s, achieving an acceleration ratio close to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\sim 3$ </tex-math></inline-formula> compared with the referenced KNN-BSBL method. Therefore, the proposed method is an efficient and robust means of imaging reconstruction, which further improves the feasibility of EIT in respiratory clinical applications.