Abstract
Single-pixel imaging via compressed sensing can reconstruct high-quality images from a few linear random measurements of an object known a priori to be sparse or compressive, by using a point/bucket detector without spatial resolution. Nevertheless, random measurements still have blindness, limiting the sampling ratios and leading to a harsh trade-off between the acquisition time and the spatial resolution. Here, we present a new compressive imaging approach by using a strategy we call cake-cutting, which can optimally reorder the deterministic Hadamard basis. The proposed method is capable of recovering images of large pixel-size with dramatically reduced sampling ratios, realizing super sub-Nyquist sampling and significantly decreasing the acquisition time. Furthermore, such kind of sorting strategy can be easily combined with the structured characteristic of the Hadamard matrix to accelerate the computational process and to simultaneously reduce the memory consumption of the matrix storage. With the help of differential modulation/measurement technology, we demonstrate this method with a single-photon single-pixel camera under the ulta-weak light condition and retrieve clear images through partially obscuring scenes. Thus, this method complements the present single-pixel imaging approaches and can be applied to many fields.
Highlights
Techniques for capturing two-dimensional (2D) image information are significant for many applications, such as astronomical observation [1], phase retrieval [2], and fluorescence microscopy [3].Single-pixel imaging (SPI), as one of these imaging techniques, offers many benefits especially for the scenarios where pixelated array detectors are too expensive and not well developed, having drawn more and more attention
Since the optical experiments generally have no original image as a reference, the experimental results in Figure 9 are directly normalized to a range of 0 ∼ 1
We propose a single-pixel compressive imaging method based on “cake-cutting” Hadamard basis ordering, which is capable of precisely reconstructing images of large resolution from super sub-Nyquist measurements
Summary
Techniques for capturing two-dimensional (2D) image information are significant for many applications, such as astronomical observation [1], phase retrieval [2], and fluorescence microscopy [3]. Single-pixel imaging (SPI), as one of these imaging techniques, offers many benefits especially for the scenarios where pixelated array detectors are too expensive and not well developed, having drawn more and more attention. SPI might trace back to early raster scanning modalities, such as the flying-spot camera in 1884 and optical coherence tomography [4] in 1991. The existing mature array detectors mostly apply this point scanning technology. As an alternative of SPI, it records the total light intensities during each modulation, and calculates the intensity correlation between modulation patterns and detected bucket signals to acquire a 2D image.
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