Total-body positron emission tomography (PET) is a useful diagnostic tool for evaluating malignant disease. However, tumour detection is limited by image artefacts due to the lack of attenuation correction and noise. Attenuation correction may be possible using transmission data acquired after or simultaneously with emission data. Despite the elimination of attenuation artefacts, however, tumour detection is still hampered by noise, which is amplified during image reconstruction by filtered backprojection (FBP). We have investigated, as an alternative to FBP, an accelerated expectation maximization (EM) algorithm for its potential to improve tumour detectability in total-body PET. Signal to noise ratio (SNR), calculated for a tumour with respect to the surrounding background, is used as a figure of merit. A software tumour phantom, with conditions typical of those encountered in a total-body PET study using simultaneous acquisition, is used to optimize and compare various reconstruction approaches. Accelerated EM reconstruction followed by two-dimensional filtering is shown to yield significantly higher SNR than FBP for a range of tumour sizes, concentrations and counting statistics (deltaSNR = 6.3 +/- 3.9, p < 0.001). The methods developed are illustrated by examples derived from physical phantom and patient data.