Design Question: 20 MS/s data acquisition
A microcontroller is not appropriate for what you are trying to do.  The data is coming too fast for a micro to be able to do anything useful with it.

Let's say you get a micro that runs at 100 MIPs.  That's really fast for a micro.  New data words are coming in at 16 MHz rate.  That leaves only 6&frac14; instructions per sample, which is probably not even enough to grab it from some input port and send it on somewhere else.

From your description, I think you're right in that software processing the stream of samples can allow for video reconstruction.  However, realistically, that's not going to happen in real time.  All you can hope to do in real time is store the total data, then process it into good video, or frames, or whatever you want, in a batch process later.  That can afford to run as long as it takes to produce the cleaned result.

Modern disk drives you can get off the shelf for PCs can handle both the data rate and the data volume.  32 Mbytes/s and 230 Gbytes aren't pushing any limits.  A USB 3.0 port on a modern PC can handle that data rate.

Your problem is therefore how to get a stream of 16 bit words at 16 MHz rate into a USB 3.0 port.  I'd look around for off the shelf chips that can do this.  I'd start by looking at what FTDI has to offer, but would also check out TI and others.  You may need to use a small FPGA to clock the A/D, grab the data, present it as two bytes to the USB chip, etc.  That's a fairly straight forward, but high speed, process well suited to a small FPGA.