The present embodiments relate to positron emission tomography (PET).  In PET, attenuation information is used in reconstruction.  The attenuation is derived from a computed tomography (CT) or other x-ray scan.  There is a desire to limit the use of x-rays. 
A three-dimensional PET scanner acquires oblique lines of response (LORs) in addition to the direct plane LORs.  As a result, the edge axial planes of the reconstructed volume suffer from a lower sensitivity than the central axial planes because the edge axial planes are reconstructed from a smaller set of oblique LORs.  A CT scan, which is acquired first, defines the axial extent of the reconstructed volume.  Typically, the axial coverage length is chosen in such a way that a certain number of overlapping PET bed positions completely sample the reconstruction volume.  The bed overlap is designed to achieve a uniform sensitivity by summing the roughly triangular axial sensitivity profiles corresponding to each bed position.  Nevertheless, the edge planes of the last bed acquisition still have a lower sensitivity because only direct plane LORs are available.  This problem can be solved by acquiring an additional bed position, so as to make the axial sensitivity more uniform throughout the CT defined volume.  The problem is not yet solved however, because the attenuation correction factors (ACFs) for some oblique LORs are not available from the CT scan because these LORs are passing outside the CT defined volume.  As a result, the edge axial planes would still suffer from a lower sensitivity if only LORs with CT-known ACFs are used during reconstruction.  Increasing x-ray dose to increase the CT volume is not desired. 
To avoid this issue, reconstruction may be performed without x-ray based attenuation information.  In PET, simultaneous emission activity and attenuation map reconstruction in non-time of flight (TOF) PET has been a topic of investigation in order to exclude the x-ray transmission sources completely.  Both distributions are assumed to be reconstructed from a single emission data set.  A significant amount of information about attenuation is contained in the emission data.  The artifact of cross-talking between the activity and the attenuation images, when the activity image features propagate to attenuation map images and vice versa, is difficult to avoid. 
Recent theoretical investigations concluded that both activity and attenuation distributions may be determined from PET TOF data up to an activity image scaling parameter.  These advances encouraged investigation of practical applications of transmission less TOF reconstruction.  One limitation of this approach is that the attenuation information cannot be determined outside of the emission sinogram support.  In addition, the solution may not be sufficiently stable.  Therefore, the practical application might still require a priori knowledge of the attenuation.  Recent examples of simultaneous activity and attenuation reconstruction in TOF PET indeed use a significant amount of prior information.  MRI data may be used to define regions of uniform attenuation and estimate the attenuation coefficient in each region from the emission TOF data.  Derived truncated attenuation map regions have been used in the application for PET-MRI.  Another example is the use of additional external nuclear transmission sources.  This approach is difficult when using emission data alone for general cases, such as when attenuation map support is larger compared to activity image support.