Single-pixel imaging with sampling distributed over simplex vertices

Single pixel imaging at high pixel resolutions

The usually reported pixel resolution of single pixel imaging (SPI) varies between 32 × 32 and 256 × 256 pixels falling far below imaging standards with classical methods. Low resolution results from the trade-off between the acceptable compression ratio, the limited DMD modulation frequency, and reasonable reconstruction time, and has not improved significantly during the decade of intensive research on SPI. In this paper we show that image measurement at the full resolution of the DMD, which lasts only a fraction of a second, is possible for sparse images or in a situation when the field of view is limited but is a priori unknown. We propose the sampling and reconstruction strategies that enable us to reconstruct sparse images at the resolution of 1024 × 768 within the time of 0.3s. Non-sparse images are reconstructed with less details. The compression ratio is on the order of 0.4% which corresponds to an acquisition frequency of 7Hz. Sampling is differential, binary, and non-adaptive, and includes information on multiple partitioning of the image which later allows us to determine the actual field of view. Reconstruction is based on the differential Fourier domain regularized inversion (D-FDRI). The proposed SPI framework is an alternative to both adaptive SPI, which is challenging to implement in real time, and to classical compressive sensing image recovery methods, which are very slow at high resolutions.

Differential real-time single-pixel imaging with Fourier domain regularization: applications to VIS-IR imaging and polarization imaging

The speed and quality of single-pixel imaging (SPI) are fundamentally limited by image modulation frequency and by the levels of optical noise and compression noise. In an approach to come close to these limits, we introduce a SPI technique, which is inherently differential, and comprises a novel way of measuring the zeroth spatial frequency of images and makes use of varied thresholding of sampling patterns. With the proposed sampling, the entropy of the detection signal is increased in comparison to standard SPI protocols. Image reconstruction is obtained with a single matrix-vector product so the cost of the reconstruction method scales proportionally with the number of measured samples. A differential operator is included in the reconstruction and following the method is based on finding the generalized inversion of the modified measurement matrix with regularization in the Fourier domain. We demonstrate 256 × 256 SPI at up to 17 Hz at visible and near-infrared wavelength ranges using 2 polarization or spectral channels. A low bit-resolution data acquisition device with alternating-current-coupling can be used in the measurement indicating that the proposed method combines improved noise robustness with a differential removal of the direct current component of the signal.

Fractional Fourier single-pixel imaging

Single-pixel imaging technology has a number of advantages over conventional imaging approaches, such as wide operation wavelength region, compressive sampling, low light radiation dose and insensitivity to distortion. Here, we report on a novel single-pixel imaging based on fractional Fourier transform (FRFT), which captures images by acquiring the fractional-domain information of targets. With the use of structured illumination of two-dimensional FRFT base patterns, FRFT coefficients of the object could be measured by single-pixel detection. Then, the object image is achieved by performing inverse FRFT on the measurements. Furthermore, the proposed method can reconstruct the object image from sub-Nyquist measurements because of the sparsity of image data in fractional domain. In comparison with traditional single-pixel imaging, it provides a new degree of freedom, namely fractional order, and therefore has more flexibility and new features for practical applications. In experiments, the proposed method has been applied for edge detection of object, with an adjustable parameter as a new degree of freedom.

High-resolution fast mid-wave infrared compressive imaging

In the mid-wave infrared (MIR) band, large detector arrays are extremely costly and technically difficult to be manufactured. Thus, it is difficult to obtain high-resolution images for a conventional MIR camera. Spatial compressive imaging can improve resolution. However, system errors due to misalignment or optical aberrations degrade reconstruction quality significantly. Another common issue for compressive imaging is the slow imaging speed, which is caused by slow measurement collection and reconstruction processes. To deal with the two issues, we use an imaging calibration method to improve reconstruction quality and a sliding window measurement collection strategy plus a reconstruction algorithm accelerated by parallel computing to fasten the speed. We build a prototype of a compressive imaging camera with an angular resolution 1.17 lp/mrad. A four-bar target is used as an object. We reconstruct a moving scene of size $1280 \times 1024$ with a frame rate 20 frames per second.

Noise Suppression in Compressive Single-Pixel Imaging

Compressive single-pixel imaging (CSPI) is a novel imaging scheme that retrieves images with nonpixelated detection. It has been studied intensively for its minimum requirement of detector resolution and capacity to reconstruct image with underdetermined acquisition. In practice, CSPI is inevitably involved with noise. It is thus essential to understand how noise affects its imaging process, and more importantly, to develop effective strategies for noise compression. In this work, two ypes of noise classified as multiplicative and additive noises are discussed. A normalized compressive reconstruction scheme is firstly proposed to counteract multiplicative noise. For additive noise, two types of compressive algorithms are studied. We find that pseudo-inverse operation could render worse reconstructions with more samplings in compressive sensing. This problem is then solved by introducing zero-mean inverse measurement matrix. Both experiment and simulation results show that our proposed algorithms significantly surpass traditional methods. Our study is believed to be helpful in not only CSPI but also other denoising works when compressive sensing is applied.

Stray light correction for medium wave infrared focal plane array-based compressive imaging

With focal plane array-based (FPA) compressive imaging (CI), high-resolution medium wave infrared (MWIR) images can be reconstructed by a low-resolution FPA sensor. However, in MWIR FPA CI system, the stray light is inevitable, which reduces the image contrast and increases the blocky structural artifacts of the reconstructed images. In this work, we focus on the stray light in MWIR FPA CI system. This paper investigates the sources of stray light in MWIR FPA CI system and modifies the systematic radiation model. According to the systematic computation model, we illustrate that stray light impedes the accurate sampling of compressive measurements in the MWIR FPA CI system, which may increase the blocky structural artifacts in the reconstructed high-resolution images. With the help of digital micro-mirror device modulation, we propose an operational method to substantially correct the effect of the stray light in MWIR FPA CI system, which can improve the image contrast and reduce the blocky structural artifacts of the reconstructed images, while not significantly increasing the cost of image acquisition and computation. Based on the experimental results obtained from the actual MWIR FPA CI system, we have verified the effectiveness and practicability of the proposed stray light correction method.

Efficient full-color single-pixel imaging based on the human vision property-"giving in to the blues"

Single-pixel imaging is a novel, to the best of our knowledge, computational imaging scheme, but a large number of measurements are typically required in data acquisition. Full-color single-pixel imaging takes many more measurements than does monochromatic single-pixel imaging. Utilizing the fact that human eyes have a poorer spatial resolution to blues than reds and greens, we propose to sample the blue component of color images with an ultra-low sampling ratio so as to reduce the number of measurements. We demonstrate our method with simulations and experiments, concluding that 95% of the measurements can be reduced in the acquisition of the blue component of natural color images in the size of 256×256 pixels, and the resulting images are without remarkable visual loss. Moreover, utilizing the sparsity of natural images, the sampling ratios of the red and green components can be reduced to 15% and 50%, respectively. This Letter may generate a new insight of how to optimize the imaging efficiency by utilizing human vision properties. The proposed method can be adopted by other full-color computational imaging techniques.

Pseudo-thermal imaging by using sequential-deviations for real-time image reconstruction

Ghost imaging technologies acquire images through intensity correlation of reference patterns and bucket values. Among them, an interesting method named correspondence imaging can generate positive-negative images by only conditionally averaging reference patterns, but still requires full/over sampling to treat the ensemble average of bucket values as a selection criteria, causing a long acquisition time. Here, we propose a sequential-deviation ghost imaging approach, which can realize real-time reconstructions of positive-negative images with a high image quality close to that of differential ghost imaging. Since it is no longer necessary to compare with the ensemble average, this method can improve the real-time performance. An explanation of its essence is also given here. Both simulation and experimental results have demonstrated the feasibility of this technique. This work may complement the theory of ghost imaging.

Optical machine learning with incoherent light and a single-pixel detector

An optical diffractive neural network (DNN) can be implemented with a cascaded phase mask architecture. Like an optical computer, the system can perform machine learning tasks such as number digit recognition in an all-optical manner. However, the system can work only under coherent light illumination, and the precision requirement in practical experiments is quite high. This Letter proposes an optical machine learning framework based on single-pixel imaging (MLSPI). The MLSPI system can perform the same linear pattern recognition task as DNN. Furthermore, it can work under incoherent lighting conditions, has lower experimental complexity, and can be easily programmable.