I turned back but I didn't see anyone, so I thought that I had imagined it.

imagined 是动词 imagine 的过去分词形式。imagine 由词根 image（图像、形象）和后缀 -ine（表示"使成为"）组成，本义是"在脑海中形成图像"，引申为"想象、幻想"。在这里表示"以为是自己想象出来的东西"。