A method of producing a tomogram, the method comprising the steps of: providing an x-ray detector panel comprising a plurality of pixels; providing an x-ray emitter panel spaced from the x-ray detector panel, the emitter panel comprising a plurality of x-ray emitters (m); identifying relative locations of the emitters (m) and pixels relative to each other; emitting a respective cone of x-ray radiation from each emitter (m) toward the detector panel; producing respective attenuation images ( f̌ m) at the detector panel in response to each respective cone of x-ray radiation impinging the detector panel; and reconstructing a density function indicative of attenuation of the x-ray radiation by: selecting a reconstruction slice corresponding to a plane located between the detector and emitter panels; providing an array of grid cells on the reconstruction slice; in response to selecting the reconstruction slice: for each respective attenuation image, back-projecting each pixel in the respective attenuation image back towards the respective emitter for that attenuation image onto the reconstruction slice and determining a proportion of overlap of that back-projected pixel with each grid cell to obtain a plurality of weighting factors comprising a respective weighting factor for each grid cell for that back-projected pixel; characterised by using the plurality of weighting factors for each back-projected pixel in each attenuation image to calculate an average back-projected intensity (〈 ǧ 〉) for each grid cell in the selected reconstruction slice to produce an average intensity image for the selected reconstruction slice; and convolving the average intensity image with a ramp filter to obtain the density function within the selected reconstruction slice. providing an x-ray detector panel comprising a plurality of pixels; providing an x-ray emitter panel spaced from the x-ray detector panel, the emitter panel comprising a plurality of x-ray emitters (m); identifying relative locations of the emitters (m) and pixels relative to each other; emitting a respective cone of x-ray radiation from each emitter (m) toward the detector panel; producing respective attenuation images ( f̌ m) at the detector panel in response to each respective cone of x-ray radiation impinging the detector panel; and reconstructing a density function indicative of attenuation of the x-ray radiation by: selecting a reconstruction slice corresponding to a plane located between the detector and emitter panels; providing an array of grid cells on the reconstruction slice; in response to selecting the reconstruction slice: for each respective attenuation image, back-projecting each pixel in the respective attenuation image back towards the respective emitter for that attenuation image onto the reconstruction slice and determining a proportion of overlap of that back-projected pixel with each grid cell to obtain a plurality of weighting factors comprising a respective weighting factor for each grid cell for that back-projected pixel; characterised by using the plurality of weighting factors for each back-projected pixel in each attenuation image to calculate an average back-projected intensity (〈 ǧ 〉) for each grid cell in the selected reconstruction slice to produce an average intensity image for the selected reconstruction slice; and convolving the average intensity image with a ramp filter to obtain the density function within the selected reconstruction slice. selecting a reconstruction slice corresponding to a plane located between the detector and emitter panels; providing an array of grid cells on the reconstruction slice; in response to selecting the reconstruction slice: for each respective attenuation image, back-projecting each pixel in the respective attenuation image back towards the respective emitter for that attenuation image onto the reconstruction slice and determining a proportion of overlap of that back-projected pixel with each grid cell to obtain a plurality of weighting factors comprising a respective weighting factor for each grid cell for that back-projected pixel; characterised by using the plurality of weighting factors for each back-projected pixel in each attenuation image to calculate an average back-projected intensity (〈 ǧ 〉) for each grid cell in the selected reconstruction slice to produce an average intensity image for the selected reconstruction slice; and convolving the average intensity image with a ramp filter to obtain the density function within the selected reconstruction slice.