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.
Fourier single-pixel imaging (FSI) employs Fourier basis patterns for encoding spatial information and is capable of reconstructing high-quality two-dimensional and three-dimensional images. Fourier-domain sparsity in natural scenes allows FSI to recover sharp images from undersampled data. The original FSI demonstration, however, requires grayscale Fourier basis patterns for illumination. This requirement imposes a limitation on the imaging speed as digital micro-mirror devices (DMDs) generate grayscale patterns at a low refreshing rate. In this paper, we report a new strategy to increase the speed of FSI by two orders of magnitude. In this strategy, we binarize the Fourier basis patterns based on upsampling and error diffusion dithering. We demonstrate a 20,000 Hz projection rate using a DMD and capture 256-by-256-pixel dynamic scenes at a speed of 10 frames per second. The reported technique substantially accelerates image acquisition speed of FSI. It may find broad imaging applications at wavebands that are not accessible using conventional two-dimensional image sensors.
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 599×599 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.
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