The potentiality of passive thermoacoustic tomography (PTT) is considered t
heoretically. The problem is formulated to reconstruct the distribution of
the thermodynamic temperature at a depth from the acoustic radiation genera
ted by thermal noise and measured by a set of piezotransducers on the body
surface. The 2-D inverse problem has been studied. Three mathematical metho
ds of reconstruction were investigated: (I) the least squares method; (2) T
ikhonov's regularization method; and (3) the method of elimination of non-p
hysical solutions. The reconstruction in square as well as in rectangular a
reas was studied. If one uses the least squares method the square area can
be separated into 5 x 5 subareas, the typical dimension of every one is 0.5
-2cm for measurements conducted in the frequency range 2-0.5 MHz. The preci
sion ST in temperature reconstruction in different layers is about 0.1-0.2
K for smooth distributions of the thermodynamic temperature and 0.1-0.4K fo
r abrupt distributions, if the number of different scans is about 10(2) and
the time of data collecting is about 1 min.