Balanced single-pixel camera with noiselet sampling

Single-pixel cameras (SPC) are image capturing devices, which use only a single detector to collect information about the entire image, by making use of its spatial modulation. Although a single detector is enough to obtain images of good quality in idealistic conditions, in practice the SPC systems are prone to all sorts of noise, including variations of light intensity over time, ambient illumination and signal oscillations induced by electronic components. We address this problem by studying a modification of a SPC set-up, in which two detectors are used to simultaneously measure the modulation of the image with the sensing patterns and their negations. We choose discrete noiselets for the sampling patterns and we apply the theory of compressive sensing to reduce the number of samples taken by the balanced SPC. Low mutual coherence of the noiselet functions and wavelets, as well as other properties such as fast calculation algorithm and possibility of transforming discrete noiselets into binary patterns (ready to display with binary SLM) makes them a solid choice for compressive image acquisition. We show that the combination of noiselet-based sampling with balanced SPC set-up leads to much better signal-to-noise ratio of the recovered image than it is possible in other configurations with the same equipment and measurement conditions.