Abstract

Fourier single-pixel imaging (FSI) is a branch of single-pixel imaging techniques. It allows any image to be reconstructed by acquiring its Fourier spectrum by using a single-pixel detector. FSI uses Fourier basis patterns for structured illumination or structured detection to acquire the Fourier spectrum of image. However, the spatial resolution of the reconstructed image mainly depends on the number of Fourier coefficients sampled. The reconstruction of a high-resolution image typically requires a number of Fourier coefficients to be sampled. Consequently, a large number of single-pixel measurements lead to a long data acquisition time, resulting in imaging of a dynamic scene challenging. Here we propose a new sampling strategy for FSI. It allows FSI to reconstruct a clear and sharp image with a reduced number of measurements. The key to the proposed sampling strategy is to perform a density-varying sampling in the Fourier space and, more importantly, the density with respect to the importance of Fourier coefficients is subject to a one-dimensional Gaussian function. The final image is reconstructed from the undersampled Fourier spectrum through compressive sensing. We experimentally demonstrate the proposed method is able to reconstruct a sharp and clear image of 256 × 256 pixels with a sampling ratio of 10%. The proposed method enables fast single-pixel imaging and provides a new approach for efficient spatial information acquisition.

Highlights

  • Single-pixel imaging [1,2,3,4,5,6,7,8] is a computational imaging technique that allows images to be acquired by using a spatially unresolvable detector, namely, single-pixel detector

  • Spatial light modulation allows the spatial information of the target object to be encoded into a 1-D light signal sequence, which is suitable for single-pixel detection

  • The desired object image can be retrieved by decoding the spatial information from the resulting single-pixel measurements through the image reconstruction algorithm corresponding to the spatial light modulation strategy

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Summary

Introduction

Single-pixel imaging [1,2,3,4,5,6,7,8] is a computational imaging technique that allows images to be acquired by using a spatially unresolvable detector, namely, single-pixel detector (such as, photodiode, solar cell, and photomultiplier tube). Single-pixel imaging has been considered as a potential solution for imaging at special wavebands and attracted a lot of attention in the last decade [9,10,11,12,13,14,15,16]. The key to single-pixel imaging is spatial light modulation. Spatial light modulation allows the spatial information of the target object to be encoded into a 1-D light signal sequence, which is suitable for single-pixel detection. The desired object image can be retrieved by decoding the spatial information from the resulting single-pixel measurements through the image reconstruction algorithm corresponding to the spatial light modulation strategy

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