On the efficiency of computational imaging with structured illumination

TL;DR

This paper analyzes the resolution and noise limits of computational imaging systems using structured illumination and single-pixel detectors, highlighting the importance of pattern orthogonality for image quality.

Contribution

It provides a theoretical framework linking illumination pattern properties to resolution and noise performance in computational imaging.

Findings

Squared resolution ratio equals image area divided by number of patterns.

Signal-to-noise ratio depends on the number of registered photons and pattern orthogonality.

Non-orthogonal patterns reduce SNR due to spatial correlations.

Abstract

A generic computational imaging setup is considered which assumes sequential illumination of a semi-transparent object by an arbitrary set of structured illumination patterns. For each incident illumination pattern, all transmitted light is collected by a photon-counting bucket (single-pixel) detector. The transmission coefficients measured in this way are then used to reconstruct the spatial distribution of the object's projected transmission. It is demonstrated that the squared spatial resolution of such a setup is usually equal to the ratio of the image area to the number of linearly independent illumination patterns. If the noise in the measured transmission coefficients is dominated by photon shot noise, then the ratio of the spatially-averaged squared mean signal to the spatially-averaged noise variance in the "flat" distribution reconstructed in the absence of the object, is equal to the average number of registered photons when the illumination patterns are orthogonal. The signal-to-noise ratio in a reconstructed transmission distribution is always lower in the case of non-orthogonal illumination patterns due to spatial correlations in the measured data. Examples of imaging methods relevant to the presented analysis include conventional imaging with a pixelated detector, computational ghost imaging, compressive sensing, super-resolution imaging and computed tomography.