The adaptive integration (ADI) method for two-dimensional (2-D) phase unwrapping is presented. The method uses an algorithm for noise robust estimation of partial derivatives, followed by a noise robust adaptive integration process. The ADI method can easily unwrap phase images with moderate noise levels, and the resulting images are congruent modulo 2pi with the observed, wrapped, input images. In a quantitative evaluation, both the ADI and the BLS methods (Strand et al.) were better than the least-squares methods of Ghiglia and Romero (GR), and of Marroquin and Rivera (MRM). In a qualitative evaluation, the ADI, the BLS, and a conjugate gradient version of the MRM method (MRMCG), were all compared using a synthetic image with shear, using 115 magnetic resonance images, and using 22 fiber-optic interferometry images. For the synthetic image and the interferometry images, the ADI method gave consistently visually better results than the other methods. For the MR images, the MRMCG method was best, and the ADI method second best. The ADI method was less sensitive to the mask definition and the block size than the BLS method, and successfully unwrapped images with shears that were not marked in the masks. The computational requirements of the ADI method for images of nonrectangular objects were comparable to only two iterations of many least-squares-based methods (e.g., GR). We believe the ADI method provides a powerful addition to the ensemble of tools available for 2-D phase unwrapping.

We present a block least-squares (BLS) method for two-dimensional (2-D) phase unwrapping. The method works by tessellating the input image into small square blocks with only one phase wrap. These blocks are unwrapped using a simple procedure, and the unwrapped blocks are merged together using one of two proposed block merging algorithms. By specifying a suitable mask, the method can easily handle objects of any shape. This approach is compared with the Ghiglia-Romero method and the Marroquin-Rivera method. On synthetic images with different noise levels, the BLS method is shown to be superior, both with respect to the resulting gray values in the unwrapped image as well as visual inspection. The method is also shown to successfully unwrap synthetic and real images with shears, fiber-optic interferometry images, and medical magnetic resonance images. We believe the new method has the potential to improve the present quality of phase unwrapped images of several different image modalities.

Starts by giving the medical imaging modalities that are in practical use and lists several of the new medical imaging modalities under development. The remainder of the paper is concentrated on progress in MR imaging, ultrasound imaging and X-ray CT imaging. These modalities are major radiological imaging tools, which will have growing significance in the next decade. They are surpassed only by ordinary X-ray projection imaging, which is much more static in its development. Particular attention is given to applications where image processing and image analysis tasks are needed.