A method of non-destructive testing of a part by transmission radiography, comprising the following steps, executed by a calculator: acquiring of N projections ( P ( n)) of the part using a transmission radiography device from N different and predetermined angles (ANG (n)) of view of the part, where N is a given natural integer, generating of N computed images ( P̂ ( n)) of the part from a reference model (MODP) of the part corresponding to the N angles (ANG (n)) of view and from a vector p of parameters ( p i) characterizing a projection geometry of acquisition for the N angles (ANG (n)) of view at each of several successive iterations, estimating (E3a, E3b, E3c), by the successive iterations, of the vector p from an initial vector p = p ini and of at least one of a vector c of parameters from an initial vector c = c ini and of a vector α of parameters from an initial vector α = α ini, where the vector c of the parameters ( c k) accounts for beam hardening of radiation in the part and the vector α of the parameters ( α j) characterizes Compton scattering of the radiation in the part, by minimizing the sum of the squared norms of the differences between the N projections ( P ( n)) having been acquired and the N computed images ( P̂ ( n)), processing of the N projections ( P ( n)) and/or of the N computed images ( P̂ ( n)) comprising a first processing and/or a second processing, the first processing comprising a correction of the beam hardening over the N projections ( P ( n)) from the vector c having been estimated or a generation of the beam hardening over the N computed images ( P̂ ( n)) from the vector c having been estimated, the second processing comprising a correction of the Compton scattering over the N projections ( P ( n)) from the vector α having been estimated or a generation of the Compton scattering over the N computed images ( P̂ ( n)) from the vector α having been estimated, identifying of defects of the part by comparison of the N projections ( P ( n)) having been processed with the N computed images ( P̂ ( n)) having been processed. acquiring of N projections ( P ( n)) of the part using a transmission radiography device from N different and predetermined angles (ANG (n)) of view of the part, where N is a given natural integer, generating of N computed images ( P̂ ( n)) of the part from a reference model (MODP) of the part corresponding to the N angles (ANG (n)) of view and from a vector p of parameters ( p i) characterizing a projection geometry of acquisition for the N angles (ANG (n)) of view at each of several successive iterations, estimating (E3a, E3b, E3c), by the successive iterations, of the vector p from an initial vector p = p ini and of at least one of a vector c of parameters from an initial vector c = c ini and of a vector α of parameters from an initial vector α = α ini, where the vector c of the parameters ( c k) accounts for beam hardening of radiation in the part and the vector α of the parameters ( α j) characterizes Compton scattering of the radiation in the part, by minimizing the sum of the squared norms of the differences between the N projections ( P ( n)) having been acquired and the N computed images ( P̂ ( n)), processing of the N projections ( P ( n)) and/or of the N computed images ( P̂ ( n)) comprising a first processing and/or a second processing, the first processing comprising a correction of the beam hardening over the N projections ( P ( n)) from the vector c having been estimated or a generation of the beam hardening over the N computed images ( P̂ ( n)) from the vector c having been estimated, the second processing comprising a correction of the Compton scattering over the N projections ( P ( n)) from the vector α having been estimated or a generation of the Compton scattering over the N computed images ( P̂ ( n)) from the vector α having been estimated, the first processing comprising a correction of the beam hardening over the N projections ( P ( n)) from the vector c having been estimated or a generation of the beam hardening over the N computed images ( P̂ ( n)) from the vector c having been estimated, the second processing comprising a correction of the Compton scattering over the N projections ( P ( n)) from the vector α having been estimated or a generation of the Compton scattering over the N computed images ( P̂ ( n)) from the vector α having been estimated, identifying of defects of the part by comparison of the N projections ( P ( n)) having been processed with the N computed images ( P̂ ( n)) having been processed.