A trampoline or double dip recovery, would involve a premature recovery, followed by a second decline in output. The argument is that confidence may return because of very low interest rates and the high level of fiscal injection into the economy. This may lead to a temporary recovery. However, this recovery may be short lived because the fundamental problems have not been addressed. In particular, banks are still showing signs of reluctance to lend. Until the balance sheets of banks improve the economic recovery will be limited by lack of funds for investment.
A saxophone recovery, would involve a sharp recovery that runs out of steam. This could occur if spending rises due to very low interest rates we currently have. However, this sharp recovery may cause interest rates to rise. This rise in interest rates to more normal levels would then quickly sniff out the recovery as the temporary boost of low interest rates evaporates. Another factor which may cause the recovery to falter is the pressure on the government to reduce its ballooning budget deficit. Currently, the government is running a huge budget deficit, to help stimulate the economy. Economic recovery may necessitate higher taxes and spending cuts. This could then plunge the economy back into recession. (see: weak economic recovery)
The third option is a nike shaped recovery, where once the economy gets going it creates a virtuous circle of rising confidence, rising house prices, and rising investment. As spending and confidence picks up, the banks may return to normal lending this enables investment to keep increasing. I haven't seen many people predict this kind of recovery. It happened after the last recession. But, that was because the recession was caused by high interest rates, so when interest rates were cut, and the pound devalued, there was a strong boost to the economy.