What happened
The FAA’s narrative, in sentence case. The FAA writes it in capitals and removes private details.
Narrative: the aircraft was level at FL350 encountering light icing and occasional light to moderate turbulence. Requested and was cleared to FL390. After level-off, the crew noticed airspeed slowly increase from mach .63 to .70 and power was reduced and airspeed continued to increase to mach .74 and power was further reduced. The aircraft was still encountering light to moderate turbulence. The copilot noticed discrepancy between the left and right airspeed indicators. As the discrepancy was being discussed, both engines lost power and an emergency was declared. As the aircraft descended, it was noted that the left engine had approximately 10 percent. The right engine was restarted at approximately 16,000 feet mean sea level and the left engine was brought up to operating power. A diversion was successfully made to New Orleans, Louisiana. It was later determined that residue found in the pilot's pitot system may have caused the inaccurate airspeed indication. The slow actual speed combined with the turbulence may have caused interrupted airflow to the engines, causing the loss of power.
As the FAA filed it
NARRATIVE: THE AIRCRAFT WAS LEVEL AT FL350 ENCOUNTERING LIGHT ICING AND OCCASIONAL LIGHT TO MODERATE TURBULENCE. REQUESTED AND WAS CLEARED TO FL390. AFTER LEVEL-OFF, THE CREW NOTICED AIRSPEED SLOWLY INCREASE FROM MACH .63 TO .70 AND POWER WAS REDUCED AND AIRSPEED CONTINUED TO INCREASE TO MACH .74 AND POWER WAS FURTHER REDUCED. THE AIRCRAFT WAS STILL ENCOUNTERING LIGHT TO MODERATE TURBULENCE. THE COPILOT NOTICED DISCREPANCY BETWEEN THE LEFT AND RIGHT AIRSPEED INDICATORS. AS THE DISCREPANCY WAS BEING DISCUSSED, BOTH ENGINES LOST POWER AND AN EMERGENCY WAS DECLARED. AS THE AIRCRAFT DESCENDED, IT WAS NOTED THAT THE LEFT ENGINE HAD APPROXIMATELY 10 PERCENT. THE RIGHT ENGINE WAS RESTARTED AT APPROXIMATELY 16,000 FEET MEAN SEA LEVEL AND THE LEFT ENGINE WAS BROUGHT UP TO OPERATING POWER. A DIVERSION WAS SUCCESSFULLY MADE TO NEW ORLEANS, LOUISIANA. IT WAS LATER DETERMINED THAT RESIDUE FOUND IN THE PILOT'S PITOT SYSTEM MAY HAVE CAUSED THE INACCURATE AIRSPEED INDICATION. THE SLOW ACTUAL SPEED COMBINED WITH THE TURBULENCE MAY HAVE CAUSED INTERRUPTED AIRFLOW TO THE ENGINES, CAUSING THE LOSS OF POWER.