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 performing the algorithm comprises using the following equation to determine the attenuation map: μ ⁡ ( x , y ) = ∫ θ θ + π ⁢ ∫ - ∞ + ∞ ⁢ ⁡ [ ∂ g ⁡ ( s , θ ) ∂ s ] ⁡ [ 1 2 ⁢ π ⁢ ( - ⅈsgnω ) ] ⁢ ⅇ 2 ⁢ πⅈω ⁡ ( xsinθ + ysinθ ) ⁢ ⅆ θ , where is the Fourier transform, g(θ,s) is the Radon transform, and μ(x,y) is the attenuation map.