Time of flight PET (TOF-PET) is an advance over traditional PET that uses the time difference in detection of the two photon events. TOF information provides better localization of the annihilation event along the line formed by each detector pair, resulting in an overall improvement in signal to noise ratio (SNR) of the reconstructed image. This technology uses a direct estimation of the sinogram only from TOF PET data. The gradient of the attenuation sinogram is estimated using the current algorithm, and an efficient analytical reconstruction method for reconstruction of the attenuation background from derivatives of the attenuation sinogram is presented. A relationship is established to link the TOF PET data and attenuation sinogram. The method can accurately and stably determine an attenuation sinogram and the attenuation correction map without any specific knowledge on it.