Single-pixel imaging techniques enable to capture a scene without a direct line of sight to the object, but high-quality imaging has been proven challenging especially in the presence of noisy environmental illumination. Here we present a single-pixel imaging technique that can achieve high-quality images by acquiring their Fourier spectrum. We use phase-shifting sinusoid structured illumination for the spectrum acquisition. Applying inverse Fourier transform to the obtained spectrum yields the desired image. The proposed technique is capable of capturing a scene without a direct view of it. Thus, it enables a feasible placement of detectors, only if the detectors can collect the light signals from the scene. The technique is also a compressive sampling like approach, so it can reconstruct an image from sub-Nyquist measurements. We experimentally obtain clear images by utilizing a detector not placed in direct view of the imaged scene even with noise introduced by environmental illuminations.

Single-pixel imaging which employs active illumination to acquire spatial information is an innovative imaging scheme and has received increasing attentions in recent years. It is applicable to imaging at non-visible wavelengths and imaging under low light conditions. However, single-pixel imaging has once encountered problems of low reconstruction quality and long data-acquisition time. Hadamard single-pixel imaging (HSI) and Fourier single-pixel imaging (FSI) are two representative deterministic model based techniques. Both techniques are able to achieve high-quality and efficient imaging, remarkably improving the applicability of single-pixel imaging scheme. In this paper, we compare the performances of HSI and FSI with theoretical analysis and experiments. The results show that FSI is more efficient than HSI while HSI is more noise-robust than FSI. Our work may provide a guideline for researchers to choose suitable single-pixel imaging technique for their applications.

Single-pixel imaging can capture images using a detector without spatial resolution, which enables imaging in various situations that are challenging or impossible with conventional pixelated detectors. Here we report a compressive single-pixel imaging approach that can simultaneously encode and recover spatial, spectral, and 3D information of the object. In this approach, we modulate and condense the object information in the Fourier space and detect the light signals using a single-pixel detector. The data-compressing operation is similar to conventional compression algorithms that selectively store the largest coefficients of a transform domain. In our implementation, we selectively sample the largest Fourier coefficients, and no iterative optimization process is needed in the recovery process. We demonstrate an 88% compression ratio for producing a high-quality full-color 3D image. The reported approach provides a solution for information multiplexing in single-pixel imaging settings. It may also generate new insights for developing multi-modality computational imaging systems.

Typical single-pixel imaging techniques inherently consume a large number of measurements to reconstruct a high-quality and high-resolution image. Three-dimensional (3-D) single-pixel imaging with both high sampling efficiency and high depth accuracy remains a challenge. We implement fringe projection virtually by exploiting Helmholtz reciprocity. Depth information is modulated into a deformed fringe pattern whose Fourier spectrum is sampled by using sinusoidal intensity pattern illumination and single-pixel detection. The fringe pattern has a highly focused first-order component in its Fourier spectrum, which allows us to efficiently acquire the depth information from measurements far fewer than illumination pattern pixels. The 3-D information is retrieved through Fourier analysis. We experimentally obtained a 3-D reconstruction of a complex object with $599\times 599$ effective pixels, achieving a measurement-to-pixel ratio of 5.78%. The depth accuracy is evaluated at sub-millimetric level by using a test object.

Object classification generally relies on image acquisition and subsequent analysis. Real-time classification of fast-moving objects is a challenging task. Here we propose an approach for real-time classification of fast-moving objects without image acquisition. The key to the approach is to use structured illumination and single-pixel detection to acquire the object features directly. A convolutional neural network (CNN) is trained to learn the object features. The “learned” object features are then used as structured patterns for structured illumination. Object classification can be achieved by picking up the resulting light signals by a single-pixel detector and feeding the single-pixel measurements to the trained CNN. In our experiments, we show that accurate and real-time classification of fast-moving objects can be achieved. Potential applications of the proposed approach include rapid classification of flowing cells, assembly-line inspection, and aircraft classification in defense applications. Benefiting from the use of a single-pixel detector, the approach might be applicable for hidden moving object classification.

Active single-pixel imaging (also known as illumination-modulated single-pixel imaging) employs a spatial light modulator to illuminate a scene with structured patterns. The scheme of active single-pixel imaging is similar to a wireless broadcast system, allowing that multiple receivers use a single-pixel detector to capture an image simultaneously from a different place. The use of basis patterns allows for high-quality reconstructions and an efficient sampling process, but the public knowledge of the basis patterns is not a favorable feature for security applications. In order to develop a secured broadcast single-pixel imaging system, we propose to employ block-permutated Hadamard basis patterns for illumination. The randomness in permutation operations introduces strong security characteristics for the system. Both simulation and experimental results demonstrate our proposed scheme has satisfactory imaging quality and efficiency. This work generates a new insight for the application of single-pixel imaging and provides a solution for developing a secured imaging system for non-visible wavebands.