## 1 Introduction  
In extensive cancers of the larynx or hypopharynx (T3 and T4 tumors), total laryngectomy remains the procedure of choice and the most reliable surgery for advanced laryngeal cancers. After this surgery, the vocal cords are completely removed and the respiratory tract is separated from the digestive tract. It is therefore essential to train laryngectomee patients to speak with an alternate voice without the vocal cords. Several techniques [1,2] exist that allow vocal rehabilitation through the acquisition of a substitute voice that is learned with the help of a speech therapist or in a specialized rehabilitation center. Among the well-known and widely used mechanisms, the esophageal voice remains the ideal replacement for the laryngeal voice according to [3]. The principle of the esophageal speech (ES) is based on the use of a pharyngo-oesophageal digestive segment as a neovibrator. To produce this voice, it is necessary to introduce oral air into the top of the esophagus and release it under control. Thus, as mentioned above, ES is the ideal substitute for the laryngeal voice. However, and as expected, the quality and intelligibility of ES are influenced by the change in the mechanism of speech production. This change of course affects the acoustic features of the esophageal voice, which are very different from those of the laryngeal voice. Compared to normal speech, esophageal is characterized by poor intelligibility and poor quality due to chaotic fundamental frequency, specific noises that resemble belching, and low intensity. All of these instabilities in the acoustic characteristics produce poor-quality sounds that are difficult to understand. Due to the extensive use of the esophageal voice by laryngectomees, this type of voice has been the subject of numerous studies in the last few years. To our knowledge, the existing approaches for ES quality improvements can be summarized into three categories: approaches based on the transformation of acoustic features, such as formant synthesis [4], comb filtering [5], and smoothing of acoustic parameters [6]; approaches based on statistical techniques, where [7; 8; 9] have been carried out, and approaches based on the VC technique, which allows for the transformation of the voice of a source speaker (laryngectomee) into that of a target speaker (laryngeal) [10; 11; 12; 13; 14; 15; 16]. Although these approaches have of course improved the estimation of the acoustic characteristics to reconstruct a converted signal with better quality, the improvements in intelligibility and naturalness are still insufficient. First, most previous studies deal primarily with transforming the spectral envelope and F0 trajectories by simply adjusting them linearly in the logarithm field [5; 6; 7]. In addition, since the acoustic models were constructed frame by frame, the duration of the converted sequences was kept the same as that of the source sequences. However, the production of human speech is a highly dynamic process, and the frame-by-frame assumption makes the modeling ability of the conversion functions limited [17]. Moreover, temporal alignment is another problem when converting esophageal to laryngeal speech. As feature alignment is necessary for VC systems, the Dynamic Time Warping (DTW) algorithm [18] is most frequently used by researchers. This algorithm makes it possible to align the characteristics using a dynamic programming algorithm where the acoustic features are not taken into account, which may cause problems, especially for pathological alignments [19]. These aligned features are subsequently used in the learning stage, to train the model, which may result in poor quality and intelligibility of the converted speech. Thus, the results of the VCC2018 [20] and the VCC2020 [13] proved that there is still much research to be done to improve the quality and naturalness of the converted speech.