  Computational ultrasound imaging has become a well-established methodology in
the ultrasound community. Simulations of ultrasound sequences and images allow
the study of innovative techniques in terms of emission strategy, beamforming
and probe design. There is a wide spectrum of software dedicated to ultrasound
imaging, each having its specificities in its applications and in the numerical
method. I describe in this two-part paper a new ultrasound simulator (SIMUS)
for Matlab, which belongs to the Matlab UltraSound Toolbox (MUST). The SIMUS
software is based on far-field and paraxial approximations. It simulates
acoustic pressure fields and radiofrequency RF signals for uniform linear or
convex probes. SIMUS is an open-source software whose features are 1) rapidity,
2) ease of use, 3) frequency domain, 4) pedagogy. The main goal was to offer a
comprehensive turnkey tool, along with a detailed theory for pedagogical and
research purposes. This first part of the paper describes in detail the
underlying linear theory of SIMUS and provides examples of simulated acoustic
fields and ultrasound images. The second part is devoted to the comparison of
SIMUS with popular software: Field II, k-Wave, and the Verasonics simulator.
The Matlab open codes for the simulator SIMUS are distributed under the terms
of the GNU Lesser General Public License, and can be downloaded from
https://www.biomecardio.com/MUST.
