  A tomographic method is considered that forms images from sets of spatially
randomized source signals and receiver sensitivities. The method is designed to
allow image reconstruction for an extended number of transmitters and receivers
in the presence noise and without plane wave approximation or otherwise
approximation on the size or regularity of source and receiver functions. An
overdetermined set of functions are formed from the Hadamard product between a
Gaussian function and a uniformly distributed random number set. It is shown
that this particular type of randomization tends to produce well-conditioned
matrices whose pseudoinverses may be determined without implementing relaxation
methods. When the inverted sets are applied to simulated first-order scattering
from a Shepp-Logan phantom, successful image reconstructions are achieved for
signal-to-noise ratios (SNR) as low as 1. Evaluation of the randomization
approach is conducted by comparing condition numbers with other forms of signal
randomization. Image quality resulting from tomographic reconstructions is then
compared with an idealized synthetic aperture approach, which is subjected to a
comparable SNR. By root-mean-square-difference comparisons it is concluded that
- provided a sufficient level of oversampling - the dynamic transmit and
dynamic receive approach produces superior images, particularly in the presence
of low SNR.

Medical Physics;Numerical Analysis