Noise on power rail from motor controller

I have emailed Jeremy, and he suggested posting my problem here;

I designed an antenna pointer that uses the MC33926 Motor Driver
Carrier, controlled by a Arduino mini-pro. The controller drives a
small brushed motor, and outputs a video from an onboard receiver. I am getting horizontal lines in the video when the motor is getting power, I have tried all the motor brush filter caps and wire twisting suggestions with no success. I have substituted the motor with a 10 ohm resistor and still get the lines. The system is 12 volt Li-Poly powered, the max current when in operation is 1.2 amps. All components, Arduino, motor controller, motor, receiver, and video monitor, share the same battery. I have separated the video monitor power, only feeding it the analog video and still have the lines.

I am using a 7805 regulating 5 volts to the VIN of the motor controller. The motor controller logic shares the 5 volts regulated on the arduino. For a test I ran a second battery to the input of the 7805 , with the ground of this second battery common to the primary battery and the rest of the circuit. By doing this all the noise went away. This project needs to be powered from a single battery so I have to find a simple solution.

One solution I came up with was putting (4) IN4007 diodes in series from the primary battery B+ to the input of the 7805, and a 2200uf capacitor on the input of the 7805 to ground. The video looks clean but there is a small ripple on the scope. Is there a better solution?