## 5 Discussions
### Pulse-Mode USCT versus WCE-Mode USCT  
One of the objectives of this work was to compare USCT in pulse mode and in WCE mode. The study of the contrast-to-noise ratio (CNR) showed that the WCE-mode USCT was advantageous. Indeed, the gain provided by the WCE-mode method was high. It was more significant at 500 kHz; >2500% for USCT of the newborn arm, and 600% for the chicken drumstick (Table 6). At 1 MHz and 2.25 MHz, the WCE-mode USCT improved the CNR markedly, but this improvement was different from object to object. For the newborn arm phantom, the gain at 2.25 MHz was higher than that at 1 MHz. On average, the multifrequency modality did not provide any improvement in CNR. The study of the transducers and their acoustic fields, discussed below, will provide an explanation of this point. The analysis of the acoustic signals could be of some help in understanding the relevance of the WCE-mode method. Figure 15 shows three signals selected at 5\({}^{\circ}\), 90\({}^{\circ}\), and 336\({}^{\circ}\) on the 1 MHz sinograms, respectively in pulse-mode (solid line) and WCE-mode (dotted line), obtained for the chicken drumstick. Four main areas could be observed, for which the WCE-mode method improved resolution (AA), improved amplitude and resolution (BB), improved amplitude without affecting resolution (CC) or, conversely, reduced amplitude while maintaining resolution (DD). These examples illustrated the relevance of the WCE-mode method, which allowed weak echoes to be amplified, and resolution, and thus the CNR of USCT, to be improved. The pseudo-wavelets were not similar to the theoretical analyzing wavelets. This had an influence on the pulse duration and on the axial resolution. At 2.25 MHz for example, the axial resolution was lower in WCE mode (832 um, Table 4) than in pulse mode (1.5 mm, Table 2). At this frequency, small details were visible in WCE-mode USCT, and hardly or not at all in pulse-mode USCT. The small structures in the fibrous areas of the chicken drumstick were better resolved. On the newborn arm phantom, this effect was less remarkable, since the detection of blood vessels of low acoustic impedance contrast was not better at this frequency. At 1 MHz, the axial resolution was of the same order of magnitude for both methods, and equal to 1.8 mm. The comparison of the images in pulse mode and in WCE mode showed that the different organs were visible, and that the contrast increased between the two modes. At 500 kHz, the axial resolution was worse in WCE-mode (3.2 mm, Table 4) than in pulse-mode (2.5 mm, Table 2). Consequently, the images obtained in WCE-mode were less well resolved than those obtained in pulse-mode, and the explanation of the benefit between the two modes was not related to the axial resolution for this frequency. This poor resolution at 500 kHz also influenced the multifrequency USCT. If the theoretical analyzing wavelets had been modeled correctly, the axial resolution would have been further improved at high frequencies, but not at low frequencies (Table 3). The error in the construction of the pseudo-wavelets therefore limited the axial resolution. The analysis of the bandwidths was related. The wider the bandwidth, the more energy was transmitted at low frequencies of the spectrum, and the better the resolution at high frequencies of the spectrum. The moduli of the pseudo-wavelet spectra were more consistent with the equivalent moduli of the theoretical analyzing wavelet spectra, and the bandwidths of the pseudo-wavelet and the theoretical analyzing wavelet were almost the same. At 500 kHz, the bandwidth in pulse-mode (591 kHz, Table 2) was higher than that in WCE-mode (458 kHz, Table 4) (Figure 6). If the theoretical analyzing wavelet had been well numerized, the improvement would still not have been sufficient; the bandwidth would have been the same, and the lowest significant frequency at \(-6\) dB would still have been higher than in pulse-mode (267 kHz in WCE-mode against 229 kHz in pulse-mode), and the highest significant frequency lower (725 kHz against 820 kHz).