Each SPECT projection represents the sum of activity along lines through the patient at a specific angle. To reconstruct the underlying distribution, each projection must be mathematically redistributed back across the image matrix along the direction from which it was acquired.

In simple back projection, counts from each projection are smeared back across the image. When projections from multiple angles are combined, areas with high activity accumulate greater counts. However, this process introduces a characteristic star-shaped blurring artefact because each projection contributes signal across an entire line.

The blurring occurs because simple back projection over-represents low-frequency components of the image. To correct this, a mathematical filter is applied in the frequency domain before back projection. This filter enhances high-frequency components, sharpening edges and compensating for the inherent smoothing of the back projection process.

Common filters include the ramp filter (which corrects the basic blurring effect) and smoothing filters such as Butterworth filters, which reduce noise amplification.

Filtered back projection is computationally efficient and conceptually straightforward. However, it assumes ideal imaging conditions and does not explicitly model photon attenuation, scatter, or system response. For this reason, modern SPECT systems increasingly use iterative reconstruction methods, which more accurately model physical processes.