A Fast Barzilai-Borwein Gradient Projection for Sparse Reconstruction Algorithm Based on 3D Modeling: Application to ERT Imaging

Abstract

Image reconstruction for electrical resistance tomography (ERT) is an ill-posed inverse problem. L1 regularization is used to solve the inverse problem. An effective method of Barzilai-Borwein gradient projection for sparse reconstruction (GPSR-BB) can resolve the inverse problem into bound-constrained quadratic programming and achieve a gradient projection with line search. However, it is computationally expensive to solve the problem when the data dimension is substantial. Hence, a projection method is employed and combined with the GPSR-BB algorithm to improve the real-time performance. The problem can be mainly solved in the Krylov subspace. For comparison, another L1 regularization GPSR-BB method based on the truncated singular value decomposition is also conducted. Both simulation (with 3D modeling) and experimental results demonstrate the new method’s effectiveness in reducing the computational time and improving the image quality.

Keywords

• Electrical resistance tomography
• projection method
• L₁ regularization method
• gradient projection for sparse reconstruction