Reconstrução de imagens em tomografia de capacitância elétrica por representações esparsas

Abstract

Process Tomography is an important tool for many sectors of industry. Such importance comes from the necessity of obtaining knowledge of physical properties from hard reaching places, as the interior of a solid object or pipe. Tomography is a very versatile tool, it can be adapted for investigating different physical properties. Among the many tomographic modalities is the electrical, know as Electrical Impedance Tomography (EIT). The EIT can also be divided in two: Electrical Resistance Tomography (ERT) and Electrical Capacitance Tomography (ECT). While the ERT is capable of distinguishing conducting materials from non-conducting ones, the ECT is capable of distinguishing two non-conducting materials by their electrical permittivity. The electrical modality has advantages such as: low acquisition time, low cost and non-radioactive. The main challenges of electrical tomography are: dependency of the trajectory of the field in the medium (effect know as soft-field) and the low number of electrodes available for measurement due to their sizes. As a result of the soft-field effect, the sum of individual contributions of small discrete segments in a given region is different from the contribution of the entire region as one. In other words, the relation between the electrical property and the electrical measurements are non-linear. Due to the small number of measuring electrodes, commonly 8 or 12, reconstructing images with practical resolution is an ill-posed problem. In order to overcome these obstacles, many methods were proposed and the majority are based on the resolution of an inverse problem of a linear model. This work proposes a method of image reconstruction with sparse inducing regularization that seeks to obtain an image representation with only few elements of a redundant basis. The elements of this basis are obtained from training images and used as input of an ECT simulation. The output capacitances of the model make up the columns of a redundant sensitivity matrix. Such matrix can be viewed as a piecewise linearization of the direct problem. For validation purposes, experimental tests were conducted on two-phase flows (air-water). The training signals were obtained from an experiment with a capacitive wire-mesh sensor along with an ECT sensor. The results obtained show that the proposed method is capable of reconstructing images from a set of only 8 capacitance measurements. The reconstructed images show better results, according to different metrics, when compared to other methods that also use sparse representations.