Comparison of Regularisation Methods in Image Reconstruction for Micro-Bioimpedance Tomography Nadira Jamil, Yunjie Yang, Andreas Tsiamis, Jiabin Jia and Stewart Smith School of Engineering The University of Edinburgh Edinburgh, United Kingdom. n.jamil@ed.ac.uk Abstract—Electrical impedance tomography (EIT) is an imaging technique that reconstructs the conductivity distribution of an inhomogeneous medium and is capable of monitoring physiological changes in biological materials. This paper focuses on comparison of state-of-the-art regularisation methods in solving the image reconstruction problem in micro-scale EIT for biomedical applications. Since the quality of image reproduction is weak for micro-scale phantoms, it is vital to study the image reconstruction algorithm. Hence, we present three regularisation methods in this paper - Tikhonov, Gaussian-Laplace and L1 - for the image reconstruction of 700 µm diameter test samples. We verified our method using 500 µm × 250 µm rectangular Pt electrodes and compared the performance of these regularisation methods. The results suggest that Gaussian-Laplace regularisation provides better image reconstruction than L1 and Tikhonov algorithms. Keywords— Tomography; image reconstruction; conductivity; microelectrodes; regularisation method I. INTRODUCTION Live-cell imaging is an important analytical tool in biomedical research and pharmaceutical laboratories. Live-cell microscopy involves a compromise between obtaining a good image quality and ensuring the cells are in a good condition. Hence, the spatial and temporal resolutions in an experiment are often limited to avoid exposing the cells to a high illumination intensity over a long period of time. Electrical Impedance Tomography (EIT) is a promising technique for non-invasive, radiation-free, and conductivity- related process monitoring. It is widely relevant and safe for the patient, allowing real-time, continuous monitoring of electrical properties of organs or tissue over extended periods of time. EIT is a non-invasive imaging technique aiming to estimate conductivity distribution based on the calculated boundary voltages [1]. Tomography is an imaging technique performed by sectioning, through the use of any kind of penetrating wave. This technique is being applied in the field of biological [2] and physical sciences [3]. In most cases, the production of these images is based on mathematical tomographic reconstruction. Fundamentally, EIT involves the solving of two problems: the forward problem and the inverse problem. The forward problem determines the electrical voltage distribution on the outermost surface of the phantom arising from the applied current pattern injection and conductivity distribution [4]. The inverse problem on the other hand is the image reconstructing step for EIT. The purpose of the reconstruction algorithm is to define conductivity distribution obtained from the electrical voltage measurement and sensitivity matrix [5]. There are a number of popular image reconstruction algorithms, including linear back-projection (LBP) [6], Landweber iteration [7], linear regularised Gauss-Newton method [8] and non-linear regularised Gauss-Newton method [8]. LBP is a simple and fast algorithm of image reconstruction, besides being one of the most common techniques used in electrical tomography [9]. It is regularly implemented for its high speed, however, it results in a low quality of reconstructed image. Therefore, to attain high-quality image reconstructions, iterative image reconstruction algorithms are applied and Landweber iteration is one of the examples [1]. It is based on the linearization of a normalised form of the problem. In this paper, three regularisation methods in EIT image reconstruction are presented and compared for cell spheroid imaging using microelectrodes. The EIT system presented has the ability to produce high temporal resolution two-dimensional (2D) or three-dimensional (3D) images [10]. This extends the range of available live-cell imaging techniques, which are essential tools in biomedical research. II. REGULARISATION METHOD Theoretically, EIT defines the relationship between conductivity change, δσ, and the potential difference, δV, within a detecting domain. This relationship can be written as: = ܄ߜ۸ߜ࣌ (1) where J is the Jacobian (sensitivity) matrix of EIT. The image reconstruction for EIT encompasses the calculation of conductivity distribution when the current introduced is known and voltage readings are recorded. Due to the intrinsic ill-posedness and ill-conditioned characteristic of the EIT-image-reconstruction problem, the solution can be formulated as the following optimization problem based on regularisation techniques: ߜ࣌ ఒ = arg min ఙ ‖۸δ࣌ − ‖܄ߜ ଶ + ߣ(ߜ࣌) (2) where λ represents the positive scalar regularisation parameter and f is the regularisation function encoding prior constraint information. The implementation of the various regularisation functions in (2) will be clarified in the next sub-sections. We would also like to acknowledge the financial support of EPSRC (EP/K034510/1) IMPACT programme grant, People's Trust Council (Majlis Amanah Rakyat, Malaysia) and 2015 IEEE Instrumentation & Measurement Society Graduate Fellowship Award.