Incorporating a Spatial Prior into Nonlinear D-Bar EIT Imaging for Complex Admittivities

Abstract

Electrical Impedance Tomography (EIT) aims to recover the internal conductivity and permittivity distributions of a body from electrical measurements taken on electrodes on the surface of the body. The reconstruction task is a severely ill-posed nonlinear inverse problem that is highly sensitive to measurement noise and modeling errors. Regularized D-bar methods have shown great promise in producing noise-robust algorithms by employing a low-pass filterin of nonlinear (nonphysical) Fourier transform data specifi to the EIT problem. Including prior data with the approximate locations of major organ boundaries in the scattering transform provides a means of extending the radius of the low-pass filte to include higher frequency components in the reconstruction, in particular, features that are known with high confidence This information is additionally included in the system of D-bar equations with an independent regularization parameter from that of the extended scattering transform. In this paper, this approach is used in the 2-D D-bar method for admittivity (conductivity as well as permittivity) EIT imaging. Noise-robust reconstructions are presented for simulated EIT data on chest-shaped phantoms with a simulated pneumothorax and pleural effusion. No assumption of the pathology is used in the construction of the prior, yet the method still produces significant enhancements of the underlying pathology (pneumothorax or pleural effusion) even in the presence of strong noise.

Use of an optimized spatial prior in D-bar reconstructions of EIT tank data

“…The inclusion of a priori estimates into iterative reconstruction methods has been demonstrated to provide improved spatial resolution in EIT images (see, for example, [4,5,7,10,11,14,15,21,35,36]). More recently, a method for including a priori information into direct D-bar reconstruction methods was proposed in [2] and extended in [17] and [1]. These methods, which have been demonstrated to provide improved spatial resolution in reconstructions of simulated EIT data, begin with an estimated prior conductivity distribution.…”

“…When the true conductivity distribution is unknown, determining useful conductivity values for the prior poses a significant challenge. Various methods have been suggested in [2,17,1], which use either "blind" estimates for conductivity values, or use regional average, max, or min values extracted directly from preliminary D-bar reconstructions. The novel approach proposed here is motivated by our observation that when the scattering prior t pr is a poor match for t, artifacts tend to develop in the resulting reconstructions, as illustrated in Fig.…”

“…We then form a scattering prior t pr from (9). As in [2,17,1], this information is inserted into the D-bar algorithm in two distinct ways, which are described as follows.…”

“…In [17,1], the computation (12) was accomplished with a slight refinement, in which a thresholding parameter was used to detect blow-up in t(k) for |k| ≤ R 1 , and this unstable scattering data t(k) was further truncated and replaced with values t pr (k).…”

“…This will be discussed in further detail within this section. In our method, as in [2,17,1], we may control the influence of the prior by adjusting R 2 .…”