Gradient projection for spare reconstruction（ GPSR） algorithm based on compressed sensing（ CS）theory is applied to electrical capacitance tomography（ ECT） image reconstruction. Use orthogonal basis of discrete Fourier transformation（ DFT）

the gray signals of original images can be transformed into sparse signals.Measurement matrix of ECT system is designed by rearranging the rows of the sensitivity matrix of ECT in a random order and the measurement projection vector is designed by rearranging the rows of the capacitance value vector in the same order. The GPSR algorithm is used for image reconstruction. The simulation results show that the quality of the reconstructed images are better than the corresponding images obtained by the LBP algorithm and the Landweber algorithm. The proposed algorithm can achieve higher precision of ECT image reconstruction and provide a new method for the research of ECT image reconstruction.