## 1 Introduction
The computational cost issue tends to be less limiting nowadays thanks to the continuous increase in the power of computers and high-performance computing systems, so that USCT could become, in the medium term, an interesting modality for complete organ imaging. Nevertheless, convergence issues still limit iterative approaches when the organ, for example a limb, contains bones. For a more simplified and faster application, the reflection mode can be preferred. In reflection mode with a single transducer or single array, USCT can be viewed as a combination of B-mode ultrasound for the physical acoustic propagation, and X-ray tomography for the image construction process [19]. It is a linearized inversion of the inverse acoustic scattering problem corresponding to imaging perturbations of a known reference medium. Acquisition and processing times are respectively reduced to a few seconds (<2 s with a 128-element multiplexed antenna) and a few minutes (<1 min with a desktop computer). The processing of sinograms (sets of signals depending on the angle of incidence) is based on the well-known algorithm of reconstruction by summation of filtered backprojections or backpropagation (FBP). The image is morphological and remains qualitative. Quantitative parametric approaches have been proposed by several groups, but the pre- and postprocessing times are increased [20; 21]. Recently, [PERSON] et al. [15; 16] proposed a compound (reflection/transmission) high-frequency (3 MHz), high-energy quantitative USCT, and the results on a complete knee organ, including the skin, the muscle and the bone, were very convincing. The choice of the center frequency of the transducers or the array is very relevant. Clinical B-mode ultrasound and USCT of soft tissues offer essentially the same resolutions, up to 100 \(\upmu\)m for shallow tissue depths (<5 cm) and for frequencies above 2 MHz. When imaging an organ containing bones and fibrous muscles that attenuate the ultrasonic waves, the use of lower frequencies (<2 MHz) would make it possible to avoid multiple scattering phenomena, while gaining depth of penetration to allow in-depth analysis and/or imagingof the interdiaphyseal area. But the spatiotemporal resolution of the image is reduced. The \"lost\" resolution can be enhanced using efficient signal processing methods, such as signal deconvolution [22; 23] or pulse compression [24; 25]. Our group has developed a procedure for multiscale wavelet decomposition of the signals allowing all available wave packets to be processed in terms of frequency and time [26]. This method, called \"wavelet-based coded excitation\" (WCE), can be used to determine, independently, the velocity of the ultrasonic wave and the path of the wave through the thickness of the cortical zone of a bone, geometrically assimilated to a succession of contiguous parallelepiped plates [20]. The method can also be adapted to the measurement of the apparent density of the bone mass [25; 27]. When adapted to a circular antenna and to canonical targets, the method improves the contrast by at least 11% [28]. The clinical use of B-mode ultrasound requires the control of potentially induced biological effects, particularly when the generated power is increased to improve propagation distances. The mechanical index (MI) and the thermal index (TI), two adequate predictors of these effects, are controlled, varying from one device to another, and from one examination configuration to another; in general lower than 1.9 for MI, and 1.4 for TI for an average power of 100 mW/cm\({}^{2}\). When these limit values are respected, the effects are considered negligible [29]. Therefore, the intensity of the transmitted waves must be taken into account. It depends on the distance from the transmitter, the duration of the signals, and the repetition periods.