1. A method for linearizing attenuation measurements obtained by means of a direct conversion spectrometer comprising a radiation source and a detector for detecting said radiation after it has passed through an object, an attenuation measurement being represented by a vector M d giving the attenuation of the radiation in a plurality N k of energy channels of the detector, the actual attenuation of the material constituting the object being resolved according to a characteristic base of the attenuation in this material, μ n , n=1,. .. , N with N≧2; said spectrometer being characterized by a response matrix Ψ giving, for a plurality N k of energy channels of the detector, the probability that a photon emitted in an energy bin h=1,. .. , N h is detected in an energy channel, said method being characterized in that it estimates a vector M lin , called an equivalent linear attenuation vector, giving for each energy channel an attenuation linearly depending on the thickness of material through which the radiation passes, said method comprising an initialization step ( 510 , 610 ) wherein M lin is estimated by the attenuation measurement M d and a succession of iterations, each iteration j providing an estimate {circumflex over (M)} lin (j) and comprising: (a) a step ( 520 , 620 ) of projecting the estimate {circumflex over (M)} lin (j−1) of M lin obtained at the previous iteration onto an image base Ψμ n , n=1,. .. , N, image by said response matrix Ψ of said characteristic base of the attenuation of the material; (b) a step of determining an energy non linear deformation, T, ( 530 , 631 - 633 ) of the components of the estimate {circumflex over (M)} lin (j−1) for obtaining a corresponding attenuation M r d (j) in said different energy channels, in accordance with a non linear model of the spectrometer; (c) a step ( 540 , 640 ) of reverse deformation of the components of M d to provide a new estimate {circumflex over (M)} lin (j) of the equivalent linear attenuation M lin of said attenuation measurement, or of the components ĉ 1 ,. .. , ĉ N of said equivalent linear attenuation M lin in said image base.