Analysis of data adequacy in transmission-mode ultrasound computed tomography using rank and condition number

In order to optimize the data acquisition plan design and estimate the final error ranges of reconstruction images, a data adequacy analysis method of transmission-mode ultrasound computed tomography (TUCT) using rank and condition number is proposed. By analyzing the principle of TUCT, measurement equations are presented by linear equations set, which transforms the reconstruction problem of TUCT into the problem of solving linear equations set. The rank and condition number which indicate solvability and stability of the linear equations set are used to analysis the data adequacy, and estimates the error range of reconstruction images. Theoretical analysis and experiment show that the reconstruction problem is solvable if and only if the linear equations set is full rank and the final error ranges of reconstruction images are approximatively proportional to the condition numbers of the coefficient matrixes if measurement error and medium nonhomogeneity are identical. Thus the rank and condition number can be used to analysis the data adequacy of the collected data and evaluate the final errors, which would help optimizing equipment design.