Single-pixel imaging is a developing family of techniques
which offer several advantages over conventional imaging with a segmented detector.
These include higher speed, improved availability and quality
of detectors at long wavelengths.
Examples include laser-scanning microscopy,
frequency-domain techniques, ghost imaging,
and methods employing an orthogonal mask sequence such as Hadamard masks.
We analyze this class of imaging techniques in terms of Frame theory,
which concerns sets of vectors that span a given vector space
but are not linearly independent as in the case of a basis.
The use of frames (rather than bases) allows for redundant measurements,
which can improve the signal-to-noise ratio (SNR) of the reconstructed image.
Current single-pixel techniques
admit an intuitive, physically-motivated reconstruction scheme,
but the reconstruction method is not always obvious.
The analysis provides a prescription
for reconstruction with any single-pixel imaging scheme.
For example, illumination with speckle-like patterns
which lack the statistical properties associated with speckle
does not allow accurate reconstruction with conventional methods,
but frame theory-inspired analysis allows
production of high-contrast, diffraction-limited images.
Even for schemes where reconstruction methods exist,
the theory can improve contrast, accuracy and resolution.
Frame theory-motivated reconstruction from simulated ghost imaging data
results in markedly improved contrast,
This analysis makes viable new single-pixel techniques
which lack intuitive reconstruction strategies,
and tuning of imaging properties such as noise for specific applications.