Could be a number of things causing that noise. Assuming that the basics are checked out already - check for leaky fuel injectors, worn or fouled spark plugs, dying coil on plug igniter, lazy AFR sensor, dirty MAF/IAT, gummed up throttlebody, etc. If all of those are fine, then the most likely culprit left for this particular engine generation would be some component in the VVTi system. In particular the OCV (Oil Control Valve) and the associated OCV filter. Generally not touched under normal maintenance, the filter especially, can get gummed up with particulates. When this happens, the OCV is starved for oil pressure and the VVTi system cannot accurately set the timing. This can cause all sorts of noises - pinging from detonation, wrong valve overlap causing poor performance, and generally hurt fuel economy overall.
The 1ZZ-FE engine is pretty noisy to begin with, so it can be tough to pinpoint. The video clip will be helpful, as if it is the VVTi issue - it has a very distinct sound to it. Also would be helpful to know a little more about the vehicle history, especially in terms of maintenance or lack of maintenance; driving conditions, how it is driven, etc.