Fast Delay-Multiply-and-Sum Beamformer: Application to Confocal Microwave Imaging

Confocal microwave imaging is a promising medical imaging method in which the quality and the speed of imaging depend on the used beamformer. The delay-multiply-and-sum (DMAS) is a potential alternative to the golden standard method delay-and-sum (DAS). The advantages of DMAS over DAS and some other common beamformers, e.g., finer resolution and higher contrast, have been demonstrated through many papers, and the main disadvantage of this method is its high computational complexity. This letter introduces fast DMAS (FDMAS) method, which offers the same linear computational complexity as DAS while maintaining the output similar to DMAS. FDMAS computes the output of DMAS using the first and the second moments of the observations. This letter mathematically proves the equality between the proposed method and DMAS, and also demonstrates the equality of these methods’ results using real random values and experimental complex data. Moreover, the lower computational load order of the proposed method in comparison to the DMAS is shown. As a conclusion, the FDMAS technique provides the advantages of DMAS without encountering the computational complexity issue. It is noteworthy that the FDMAS is an iterative method and thereby can update the results by adding new observations without carrying out any unnecessary computations.