Which Byzantine emperor retook Constantinople from the Latin Empire in 1261?

The Byzantine emperor who retook Constantinople from the Latin Empire in 1261 was Michael VIII Palaiologos.

The Fourth Crusade captured and sacked Constantinople in 1204, establishing the Latin Empire and forcing the Byzantine ruling family into successor states. Michael VIII was emperor of the Empire of Nicaea, the strongest of these Byzantine successor states, and made recovering Constantinople his central political goal.

On 25 July 1261, the Nicaean general Alexios Strategopoulos entered the city with a small force after learning that its Latin garrison and Venetian fleet were away. The operation succeeded with limited fighting. Michael was not personally leading the troops at the moment of capture, but the victory occurred under his imperial authority.

Michael entered Constantinople in triumph on 15 August 1261 and was crowned at Hagia Sophia. The restoration launched the long Palaiologan era of Byzantine rule. A common confusion is to name Strategopoulos as the emperor: he led the military operation, while Michael VIII was the ruler who recovered the capital and re-established the Byzantine Empire.