TV transmission needs more bandwidth if we transmit double sideband then double of the bandwidth required is wasted thus vestigial sideband finds the compromise between this and improve low frequency response by adding this with full single side band and lower portion of the other sideband.
Actually Double Side band transmission is not wasting any data while traonsmission. But the problem with DSB is its bandwidth required is more. SSB requires less bandwidth. But there is no practical device exactly cut the sidebands and low frequency part contains important information. Therefore VSB ( Vestigeal Side Band) transmisson is preferred
SSB is suitable for Audio transmission where low frequency components are neglible towards overall signal reception. For video transmission where low frequency components are not negligible SSB fails to clearly seperate the upper and lower side bands. This is due to the traces of the frequencies close to the carrier frequency which cannot be totally transmitted in a single side band. Traces of them remain and contribute to loss of signal. In order to avoid this a trace ( called Vestige ) of the unwanted side band near the carrier frequency is transmitted in addition to the single Side Band like in SSB. This is hence called Vestigial SSB modulation and is suited for video transmission
