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The iterative Born method is an inverse technique that has been used successfully in ultrasound imaging. However, the calculation cost of the standard iterative Born method is high, and parallel computation is limited to the forward problem. In this work, two methods are introduced to increase the rate of convergence of the iterative Born algorithm. These methods are tested on three different objects. The results are promising, with both algorithms giving accurate results at lower computational cost. The first method, referred to as the coarse resolution initial value (CRIV) method, uses the iterative Born algorithm for a coarse grid to quickly estimate the initial value of the object to be reconstructed. From this initial value, the final image is obtained for a finer grid with additional iterations. The cost of this method is 40% less than that of the iterative Born technique. The second method, the quadriphase source (QS) method, simultaneously uses four single sources, and object reconstruction for each is performed in parallel; the reconstruction results for all four sources then are averaged to obtain the final image. The cost of this method is 20% less than that of the standard iterative Born method. When the object to be reconstructed is of low contrast and/or has a small phase shift, the QS method is very promising because parallel computation can be used to solve both the forward and inverse problems. However, the QS method fails for high contrast objects.