Attenuative materials are widespread used in the industry (power generation, aeronautics, etc.) so that ultrasonic imaging in attenuative media is of first interest in Non-Destructive Testing. Similar issues appear in medical imaging of human tissues, which can show strong attenuative properties. In such media, the amplitude of waves decreases as the propagation distance increases, and this effect increases as a function of the frequency. This forces operators to use low-frequency probes in order to have sufficiently high signal-to-noise ratio in the received signals, despite the loss of resolution. Moreover, the shape of the acoustic waves is distorted during the propagation by frequency-dependent attenuation, which further limits the resolution of state-of-the-art imaging techniques such as the Total Focusing Method. Recently, it has been shown that the image quality can be greatly improved by considering an acoustical model of the recorded data within an inverse problem approach. From this inversion strategy, highly resolved ultrasonic images have been obtained in non-attenuative materials. The contribution of the present work is to model more accurately the data acquisition process in the case of attenuative materials. The proposed method accounts for an attenuation model based on a frequency power law and computes the corresponding dispersion model based on the Kramers-Kronig relations. This is done in order to predict more accurately the shape of the ultrasonic echoes as a function of the propagation distance. The inversion strategy also considers amplitude attenuation, and therefore enhances the weakest amplitudes located far from the ultrasonic probe. Synthetic results are presented in order to check the validity of the model. Then, the proposed method is evaluated on an attenuative medical phantom that contains closely spaced scatterers and on a Polymethyl methacrylate (PMMA) sample.