2D Ultrasound Sparse Arrays Multi-Depth Radiation Optimization Using Simulated Annealing and Spiral-Array Inspired Energy Functions

Full matrix arrays are excellent tools for 3D ultrasound imaging, but the required number of active elements is too high to be individually controlled by an equal number of scanner channels. The number of active elements is significantly reduced by the sparse array techniques, but the position of the remaining elements must be carefully optimized. This issue is here faced by introducing novel energy functions in the simulated annealing algorithm. At each iteration step of the optimization process, one element is freely translated and the associated radiated pattern is simulated. To control the pressure field behavior at multiple depths, three energy functions inspired by the pressure field radiated by a Blackman-tapered spiral array are introduced. Such energy functions aim at limiting the main lobe width while lowering the side lobe and grating lobe levels at multiple depths. Numerical optimization results illustrate the influence of the number of iterations, pressure measurement points and depths as well as the influence of the energy function definition on the optimized layout. It is also shown that performance close to- or even better than the one provided by a spiral array, here assumed as reference, may be obtained. The finite-time convergence properties of simulated annealing allow the duration of the optimization process to be set in advance.