1. A method for reconstructing an attenuation map for a positron emission tomography (PET) image, the method comprising: obtaining time-of-flight (TOF) PET data of the PET image; estimating the gradient of an attenuation sinogram; and determining, by a processor, the attenuation map using the estimated gradient of the attenuation sinogram by performing an algorithm, wherein no sub-region in the attenuation map is known prior to performing the method.