The tomography based on post-processing of phased array signals is of great potential for ultrasonic testing to accurately size the detected flaws. The use of matrix phased arrays in ultrasound tomography can provide three-dimensional data both at one measuring position and during scanning. However, application of these transducers implies processing of a large amount of data, which affects the data processing time. In this study, the post-processing frequency-domain algorithm based on the application of non-uniform fast Fourier transform was experimentally verified. This algorithm is allowed to restore correct results when approaches of optimised set of signals acquisition (sparse and non-uniform phased arrays) are applied. The experimental verification showed that the developed algorithm yields high-resolution results with a high signal-to-noise ratio.