Application of Gradient Projection for Sparse Reconstruction to Compressed Sensing for Image Reconstruction of Electrical Capacitance Tomography

Abstract

The compressed sensing algorithm based on gradient projection for spare reconstruction (CS-GPSR) is applied to electrical capacitance tomography (ECT) image reconstruction in this paper. First, using the orthogonal basis of FFT transformation, the grey signals of original images can be sparse. Secondly, the observation matrix of ECT system was designed by rearranging the exciting-measuring order, and the capacitance measurements and corresponding sensitivity matrix can be obtained. Finally, the reconstructed images can be obtained using CS-GPSR algorithm. Simulation experiments were carried out and the results showed that the reconstructed images with higher quality can be obtained using the presented CS-GPSR algorithm, compared with conventional linear back projection (LBP) and Landweber iterative algorithms.

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“…In ECT applications, Xia et al [11] proposed an image reconstruction method based on CS theory called fast linearized alternating direction method of multipliers (FLADMM), and compared it with the linear back projection (LBP) algorithm, the Landweber iteration algorithm (LIA), and the conjugate gradient (CG) method. Zhang et al [12] applied the CS theory based on gradient projection for reconstruction algorithm to solve inverse-problem of ECT, and draw a conclusion that the CS-based image reconstruction algorithm can improve the image quality and reduce the time consumption.…”

“…To apply the CS theory in ECT, the gray vector g of image to be constructed is the original signal x in CS as discussed above. In this study, discrete Fourier transform (DFT) basis is used as sparse domain DFT to make g sparse for satisfying the premise of CS theory firstly, to get sparse expression g = DFT z (11) Substituting ( 11) into the linear model of ECT system c m = Sg (12) and the linear model expressed as (12) based on CS theory can be transformed into…”