中文摘要：

根据傅立叶衍射投影定理,不同频率超声波得到的投影数据的傅立叶变换分布在复平面为不同半径的圆弧,提出了多频率超声衍射层析成像思想,并进行了实验研究,重建的时间比单频率法短约70%.由于多频率投影数据傅立叶变换比单频率法在复平面上分布更加不均匀,故重建的噪声也更大,整体变分法将图像恢复的数学模型转化为带有整体变分正则化项的能量泛函问题,采用变分原理将其中的最小化问题转为偏微分方程的求解.降噪后的多频率超声图像的误差比降噪前的图像小约50%.

英文摘要：

According to the Fourier diffraction projection theory, the Fourier transform of projection data from multi-band frequency ultrasonic is distributed over complex plane in form of different radius arcs. The idea of multi-band ultrasound diffraction tomography is proposed, and the simulation of algorithm for image reconstruction shows its time shortens about 70% compared with that of single frequency method. Because the Fourier transform of projection data of multi-band diffraction ultrasound tomography spreads much more non-uniform on complex plane than that of single frequency, higher noises are produced in image reconstruction. The principle of total variation translates math model of image restoration into the problem of energy function with TV regularization, and the minimum problem is changed by the principle of variation into the solution of Partial Differential Equations. The reconstruction error of multi-band images with TV is reduced about 50%.