The paper presents an overview of theoretical aspects of ultrasound image reconstruction techniques based on the circular Radon transform inversion. Their potential application in ultrasonography in a similar way as it was successfully done in the x-ray computer tomography is demonstrated. The methods employing Radon transform were previously extensively explored in the synthetic aperture radars, geophysics, and medical imaging using x-ray computer tomography. In this paper the main attention is paid to the ultrasound imaging employing monostatic transmit-receive configuration. Specifically, a single transmit and receive omnidirectional source placed at the same spatial location is used for generation of a wide-band ultrasound pulse and detection of back-scattered waves. The paper presents derivation of the closed-form solution of the CRT inversion algorithms by two different approaches: the range-migration algorithm (RMA) and the deconvolution algorithm (DA). Experimentally determined data of ultrasound phantom obtained using a 32-element 5 MHz linear transducer array with 0.48 mm element pitch and 0.36 mm element width and 5 mm height, excited by a 2 sine cycles burst pulse are used for comparison of images reconstructed by the RMA, DA, and conventional synthetic aperture focusing technique (SAFT). It is demonstrated that both the RMA and SAFT allow better lateral resolution and visualization depth to be achieved as compared to the DA approach. Comparison of the results obtained by the RMA method and the SAFT indicates slight improvement of the lateral resolution for the SAFT of approximately 1.5 and 1.6% at the depth of 12 and 32 mm, respectively. Concurrently, however, the visualization depth increase for the RMA is shown in comparison with the SAFT. Specifically, the scattered echo amplitude increase by the factor of 1.36 and 1.12 at the depth of 22 and 32 mm is demonstrated. It is also shown that the RMA runs about 30% faster than the SAFT and about 12% faster than the DA method.

The purpose of this work is to present a theoretical analysis of top orthogonal to bottom arrays of conducting electrodes of infinitesimal thickness (conducting strips) residing on the opposite surfaces of piezoelectric slab. The components of electric field are expanded into double periodic Bloch series with corresponding amplitudes represented by Legendre polynomials, in the proposed semi-analytical model of the considered two-dimensional (2D) array of strips. The boundary and edge conditions are satisfied directly by field representation, as a result. The method results in a small system of linear equations for unknown expansion coefficients to be solved numerically. A simple numerical example is given to illustrate the method. Also a test transducer was designed and a pilot experiment was carried out to illustrate the acoustic-wave generating capabilities of the proposed arrangement of top orthogonal to bottom arrays of conducting strips.