1. Introduction

Spatial light modulator (SLM) assisted single-pixel imaging [1–32] is a novel imaging scheme. SLMs enable embedding two-dimensional (2-D) even three-dimensional (3-D) spatial information of a scene into one-dimensional (1-D) light signals. As such, one is able to use a single-pixel detector, instead of a pixelated detector, to pick up the information-embedded light signals, extract the spatial information from the signals, and reconstruct the desired image. For some invisible wavebands, pixelated detectors are expensive or even unavailable. On the contrary, single-pixel imaging technique allows one to use a single-pixel detector for imaging, which is potentially able to tackle the difficulty of imaging at invisible wavebands. Thus, single-pixel imaging has attracted considerable attention in recent years.

Single-pixel imaging techniques generally use a digital micromirror device (DMD) [2–27], a light emitted diode (LED) matrix [28,29], or a liquid crystal on silicon (LCoS) [30,31] as a spatial light modulator for structured illumination. Nowadays, DMD is the most popular choice, as it can achieve not only a high resolution (1920$\times$1080 pixels or higher), but also high refreshing rate for binary patterns (22 kHz or higher). DMDs are based on light reflection and therefore have to use a light source for side illumination. Thus, DMD-based single-pixel imaging commonly employs a lens system for light coupling as well as a projection lens system for pattern projection. The use of projection lens might introduce aberration to the resultant images. LED matrix assisted single-pixel imaging techniques are most recently reported. Although the achievable resolution of LED matrices is lower than that of DMDs, the refreshing rate of LED matrices is higher. Therefore, LED matrix assisted single-pixel imaging techniques are suitable for imaging fast events. DMDs and LED matrices are commonly used for intensity modulation while LCoSs for phase modulation. In order to modulate intensity, an LCoS chip has to be sandwiched in between two linear polarizers. To our best knowledge, existent single-pixel imaging techniques require at least a lens system, which makes small-size and aberration-free single-pixel imaging systems impossible.

Here, we propose to use a cell phone liquid crystal display (LCD) for spatial light modulation, as it is low-cost. Additionally, the pixel size of a cell phone LCD is smaller than that of computer LCD monitors. Smaller pixels enable higher spatial resolution. Compared with LCoSs which only consist of a liquid crystal layer, LCDs are composed by a liquid crystal layer, an LED-based back illumination, a color filter, and a linear polarizer. Therefore, LCDs need no extra illumination sources. Even an LCD alone is capable of structured intensity modulation, both in grayscale mode and true-color mode. Consequently, a compact and lensless single-pixel configuration can be achieved by using an LCD for structured illumination together with a flexible solar cell for light signals detection. Lensless single-pixel imaging can not only reduce the configuration size, but also effectively avoid aberration. We believe the technique can find application in various fields. In this paper, we report a compact and multi-functional scanner as an instance of lensless single-pixel imaging. The reported scanner requires no mechanical motion and therefore enables noiseless scanning which is a challenge for typical scanners.

The first model of typical scanners may be dated back to 1984 by Microtek. Initially, the scanners can only perform grayscale scanning. The first true-color scanner was announced in 1989. Although scanners have been developed over 30 years, the principle does not change a lot. As Fig. 1(a) shows, a typical scanner consists of a line CCD (also known as 1-D CCD), a stepping motor, imaging lenses, a light source, an image processor, an analog-to-digital (A/D) convertor, and some sockets interface for data transfer.

 

Fig. 1 Comparison of typical scanner (a) and proposed single-pixel scanner (b). The solar cell in (b) is rendered to be semi-transparent to make the document in the middle visible.

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Scanning is essentially a 2-D image acquisition process. However, for the sake of cost, scanners are typically equipped with a line CCD rather than a 2-D image sensor. The line CCD is driven by the stepping motor so that the CCD can sweep across the document. The image processor collects the streaming data from the CCD and reconstructs a 2-D image. Generally, some post-processing image enhancements (such as brightness or contrast adjustments) are applied to the image. Additionally, the raw image will be compressed by an algorithm (such as, JPEG, PNG or TIFF) and sent out through some socket.

Document cameras are an alternative scanner which uses a 2-D pixelated camera with a camera lens to capture the image of a document. The advantage of the document cameras is instant scanning, as it uses a 2-D pixelated camera for image acquisition. However, the 2-D pixelated camera should cooperate with a corresponding camera lens to capture an image. In order to obtain a large enough field-of-view and keep the lens within in the working distance, it is difficult to fabricate a small-size document camera. Moreover, as camera lens might introduce aberration, post-processing calibration is generally employed.

Scanners have found wide and important applications in many fields. Nowadays, scanners are generally able to offer some features such as region-of-interest scanning (ROI), tunable scanning resolution, optical characters recognition (OCR), etc. However, scanners also have some disadvantages, such as large size, heavy weight, and noise due to mechanical motion.

In this paper, we report a lensless single-pixel imaging technique, based on which a motionless, small-size, portable, and multi-functional scanner is fabricated. The scanner utilizes a liquid crystal display (LCD) and a flexible solar cell for spatial information acquisition. Using an LCD to generate structured illumination, the scanner can achieve multiple tasks. It can not only achieve grayscale scanning and true-color scanning, but also reconstruct clear enough text document image from under-sampled data for an accurate OCR result, on-the-fly encryption, and genuine document identification. The reported scanner is much thinner than typical scanners. The reported scanner also enables noiseless scanning, as it has no mechanical motion. As demonstrated by the single-pixel scanner, the proposed lensless single-pixel imaging technique might find other applications in various fields.

2. Principle of single-pixel scanner

Images are typically considered as 2-D spatial signals in real space. Typical scanners perform raster scan to acquire the spatial inforamtion. As Fig. 1(a) shows, a typical scanner uses a line CCD to record a column of the image. To record the rest columns, the line CCD needs to be moved throughout the document by the motor.

Different from that of typical scanners, the principle of single-pixel scanner is based on the representation of images in some transformation domain (Hadamard domain in our case). In other words, any image is essentially a superposition of a complete set of weighted orthogonal basis patterns. The size of the basis patterns is identical to that of the image. The number of a complete set of basis patterns is equivalent to the number of image pixels. Any image can be decomposed into as many weighted basis patterns as pixel count. Therefore, image acquisition is referred to a process of weight of basis pattern acquisition. Mathematically, the weights are the inner product between the object image and the corresponding basis pattern. Thus, a weight can be obtained by illuminating the object with the corresponding basis patterns and recording the resultant light intensity. According to this concept, we design a single-pixel scanner, as Fig. 1(b) shows.

The document to be scanned is sandwiched in an LCD and a flexible solar cell (single-pixel detector). The LCD is used to display basis patterns and the flexible solar cell collects the transmitted light through the document. As Fig. 2 shows, the printed side of the document to be scanned faces the LCD. Consequently, the printed side of the document is under structured illumination by the LCD. According to the principle of single-pixel imaging, the spatial information of the document will be encoded into a sequence of temporal signals by the structured illumination. The intensity of the resultant light carries the spatial information. As illustrated by Fig. 2, the thickness of the document will lead to the change of direct light to scattered light ratio. However, direct light, scattered light, or both can be used for image reconstruction. Thus, as long as the transmitted light can be detected by the detector, the spatial information can be acquired. Additionally, the sandwich structure not only enables the single-pixel detector to collect all the direct light and the indirect light, but also prevents the detector from collecting ambient light. This feature allows the signal-to-noise ratio to significantly improve. As a result, high-quality image reconstruction can be achieved.

 

Fig. 2 Illustration of light transmitted through a document. (a) Light transmitted through a thin document contains strong direct light and weak scattering light. (b) Light transmitted through a thick document contains weak direct light and strong scattering light. Both components are effective for imaging as they carry the spatial information of the document.

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More importantly, the proposed single-pixel scanner is based on transmission imaging while the typical scanners are based on reflection imaging. Such distinctiveness enables the proposed single-pixel scanner to achieve genuine document identification by utilizing the unique ‘paperprint’ of any paper document, which will be discussed in Section 2.5. Moreover, the scanner requires no mechanical motion and therefore can scan documents silently.

2.1 Grayscale scanning

Here we propose to use Hadamard basis patterns to perform single-pixel scanning. As the utilized LCD may have gamma (nonlinear) distortion, using binary Hadamard basis patterns can avoid the influence of gamma distortion [20].

To reconstruct an $M\times N$-pixel object image, we can acquire its 2-D Hadamard spectrum and apply an inverse 2-D transform to the spectrum. Specifically, the 2-D Hadamard spectrum of an image is a matrix consisted of $M\times N$ real-valued Hadamard coefficients. Each coefficient is characterized by its ‘sequency pair’ (that is, the coordinate in the Hadamard domain). To derive the Hadamard coefficient corresponding to sequency pair $\left(u,v\right)$, we can use the Hadamard basis pattern, whose sequency pair is $\left(u,v\right)$, for illumination. The basis pattern can be obtained by generating the Hadamard spectrum of the basis pattern first and then applying a 2-D inverse Hadamard transform to the spectrum. The spectrum of basis pattern is simple. It consists of a Dirac (delta) function located at $\left(u_0,v_0\right)$ in Hadamard domain. In mathematical terms, the spectrum of the Hadamard basis pattern is a full-zeros matrix with a non-zero element at $\left(u_0,v_0\right)$. For normalization, the magnitude of the non-zero element is assigned to be $M\times N$. In order to improve signal-to-noise ratio in data acquisition, we employ differential method of measurement, by illuminating a basis pattern followed by its inverse [4,5]. The Hadamard coefficient is the subtraction of the two corresponding measurements.

Sampling the complete spectrum takes as many measurements as image pixels. If differential measurement is employed, the number of measurements will be doubled. In other words, the number of measurements is proportional to the image pixels. The larger size of the document image is, the greater number of measurements will be required. The sparsity of document image allows us to perform under sampling to reduce the number of measurements. The sparsity is referred to that the energy of image concentrates on the top-left corner (the origin) of the Hadamard spectrum (ordered in Walsh-ordering). Thus, one can exploit the sparsity to reduce the number of measurements by sampling the coefficients at the top-left corner and discarding the rest. Previously, we have investigated how different sampling path affects reconstruction quality of under-sampled data [20] and found ‘zig-zag’ path is the optimal. Thus, we propose to sample the Hadamard spectrum along a ‘zig-zag’ path.

One can reconstruct the image from the Hadamard spectrum acquired by applying an inversed 2-D Hadamard transform. The generation of Hadamard patterns, the sampling strategy, and the image reconstruction process are detailed in Reference [20].

2.2 True-color scanning

Inspired by the principle of colored CCD/CMOS cameras, we exploit Helmholtz reciprocity [33] to perform true-color scanning. For conventional imaging, colored CCD/CMOS cameras are designed to mount a Bayer’s filter on the mono-chromatic CCD/CMOS chip to achieve color-coded detection. By applying proper interpolation to the color encoding image, the color information can be decoded and a true-color image can be reconstructed. Here, we exploit the reciprocity to implement chromatic illumination for true-color scanning. To do so, we generate colored basis pattern in accordance with the Bayer’s mask, as Fig. 3 shows. Each originally grayscale basis pattern is multiplied by the Bayer’s mask. The size of mask is the same as that of the patterns. Finally, the colored basis pattern is displayed on the LCD. The data acquisition and image reconstruction processes are identical to those in grayscale scanning, except that a demosaic algorithm [34] will be applied to the raw reconstruction to convert the image from mono-chromatic to chromatic.

 

Fig. 3 Generation of color coded Hadamard basis pattern (8$\times$8 pixels) with Bayer’s mask.

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The color-coded illumination in single-pixel imaging is equivalent to the color-coded detection in conventional imaging, which can be interpreted by the Helmholtz reciprocity [33]. As the proposed scanner is based on active single-pixel imaging, the reciprocity allows that the role of the illumination and that of the detection devices are interchanged with each other. Specifically, the perspective is determined by the illumination part while the shading profile is determined by the detection part. Therefore, the LCD is equivalent to a CCD/CMOS chip and the flexible solar cell is equivalent to a planar light source. Images acquired by the proposed configuration would be identical to those by a reciprocal configuration.

2.3 On-the-fly encryption scanning

Typically, to scan and encrypt a confidential document consists of two steps, as Fig. 4(a) shows. The first step is to digitalize the document with a scanner and the resultant image file is stored on a computer. The second step is image encryption. A certain encryption is applied to the stored image data and converts the plaintext to a ciphertext. The ciphertext is protected by a key so that only authorized audiences who own the key can decrypt it. However, if the computer used for image storage or encryption is hacked, the scanned confidential documents are at a high risk of information leakage.

 

Fig. 4 Comparison of two-step document scanning and encryption by typical scanner (a) and single-step document scanning and encryption by proposed single-pixel scanner (b).

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On the contrary, the proposed scanner enables single-step scanning and encryption, as Fig. 4(b) shows. The one-step strategy implies scanning and encryption can be done at the same time with on-the-fly encryption. On-the-fly encryption avoids plaintext from being stored and even existing on the computer and therefore reduces the risk of information leakage. By exploiting the relativity between the illumination pattern and the object image, we can perform information encryption by encrypting the illumination pattern [26]. Here we employ permutated illumination patterns for encryption. All illumination patterns are permutated on pixel level. Permutation refers to reordering the position of pixels. The permutation law is actually the key that protects the document. Figure 5 shows an example of two pairs of original-encrypted Hadamard basis pattern. The decryption process is referred to permutation of the reconstructed image according to the key. Please note that the key needs not to be stored on the computer that is used in scanning, because the encrypted illumination patterns can be pre-generated. As demonstrated in Ref [26], the strength of the key ensures that anyone cannot retrieve the key from encrypted patterns.

 

Fig. 5 Example of original-encrypted Hadamard basis pattern pairs. (a) and (c) are original Hadamard basis patterns with a different sequency pair. (b) and (d) are encrypted patterns corresponding to (a) and (c), respectively.

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2.4 OCR from under-sampled data

OCR is a common method of digitalizing printed texts so that they can be electronically edited, searched, stored more compactly, displayed on-line, and used in machine processes. Nowadays, commercial scanners generally provide the functionality of OCR. For typical scanners, OCR is a two-step process. The first step is to scan the whole document, after which OCR is applied to the scanned document image. Instead, for the proposed single-pixel scanner, OCR can be done during the document image acquisition. As the energy of document image concentrates at and around the origin of some transformation domain (such as, Fourier, Hadamard, discrete cosine transform), we can reconstruct a clear enough document image for accurate OCR even when the image is under-sampled. In other words, fully sampling the image is not necessary. Specifically, we propose to conduct a third-party algorithm (in our case, Google Tesseract) to a document image reconstructed from under-sampled data for OCR. We note that OCR from under-sampled data is impossible for typical scanners. It is because typical scanners are based on raster scanning in the spatial domain and undersampling will result in an incomplete scanning result.

2.5 Genuine document identification

As the proposed single-pixel scanner is based on transmission imaging, the transmitted light that passes through the paper will be modulated by the printed contents and the texture of the paper itself. Thus, not only the printed contents, but also the texture of the paper itself can be reconstructed in the final image. We term the texture of paper ‘paperprint’. Note that paperprint can hardly be recorded by typical scanners, because typical scanners are based on reflection imaging. Such distinctiveness enables the proposed single-pixel scanner to achieve genuine document identification. To our best knowledge, paperprint is nature-made, highly random, unique, and irreproducible. The uniqueness of paperprint enables one to identify whether a certain document is genuine by obtaining the paperprint by the proposed scanner and comparing the paperprint of the document with the paperprint kept in database. More importantly, the irreproducibility of paperprint prevents one from faking a document. The proposed single-pixel scanner uses transmitted light for imaging. As the incident light passes through the paper, the light will be modulated by the paperprint. Thus, together with the printed content, the paperprint will be reconstructed in the final image. Therefore, the proposed scanner enables genuine document identification.

3. Experiments

As Fig. 6 shows, we use a 5.5-inch cell phone LCD (LS055R1SX01) to generate structured illumination. The pixel size of the LCD is 47.25 microns. Thus, the achievable scanning resolution is ~537.6 dots per inch (dpi) in theory. We use a flexible solar cell (Nesolar SPDA-6.0) as a single-pixel detector. The document to be scanned is sandwiched in between the LCD and the solar cell. The solar cell collects the transmitted light through the document and the resultant photoelectric signals are collected by a data acquisition board (National Instruments USB-6343). The imaging system is compact, as thin as 2.48 millimeters (from the bottom of the LCD to the top of the solar cell).

 

Fig. 6 Flexible solar cell and LCD used in experiments.

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3.1 Grayscale text document scanning and OCR

In the first experiment, we perform grayscale scanning by using the proposed single-pixel scanner. Considering the proposed scanner is based on transmission imaging, the document to be scanned is prepared by using an ink jet printer to print the texts on a transparent film paper. In order to test the scanner under a crucial condition, the font size of the text is set to be 6 which is much smaller than regular size (9~12).

We generate a complete set of 256$\times$256-pixel Hadamard basis patterns for illumination. We employ 4$\times$4 binning in order to obtain a larger field-of-view. As a result, each illumination pattern occupies 1024$\times$1024 pixels of the LCD. To perform Hadamard single-pixel imaging, we acquire the 2-D Hadamard transform of the document along a ‘zigzag’ path [20]. We also employ differential method of measurement in order to improve the signal-to-noise ratio in data acquisition. The number of measurements is 131,072. Please note that measurement in the context is referred to switching one Hadamard basis pattern and recording one resultant voltage output by the solar cell. As the Hadamard spectrum of a 256$\times$256-pixel image has 256$\times$256 coefficients and differential measurement takes two measurements for each coefficient, fully sampling the Hadamard spectrum of a 256$\times$256-pixel image consumes 131,072 ( = 256$\times$256$\times$2) measurements.

The LCD used in our experiments is able to switch 120 patterns per second. However, the LCD controller provides no input or output synchronization ports (hardware triggers). We have to use software synchronization to control the switch of illumination patterns. Therefore, after a pattern is sent out to the LCD for displaying, the program has to pause for 0.1 seconds to ensure the pattern has been displayed completely. As a result, we can only display 9 patterns per second. As fully sampling a 256 $\times$256-pixel image takes 131,072 measurements (illumination patterns), the time for fully-sampling a 256 $\times$ 256-pixel image is ~4.05 hours.

The scanning results of the text document for different sampling ratios are presented in Fig. 7. As the figure shows, the reconstruction quality improves as the sampling ratio increases. Ringing artifact (see the partial enlargements given in Fig. 7) caused by undersampling suppresses the image contrast, which can also be evidenced by that reconstructions with a lower sampling ratio have a darker background than those with a higher sampling ratio do. In order to quantitatively assess the reconstruction, we apply OCR to the reconstructed text document images by using Google Tesseract 4.0. The document contains 603 characters in total. When the sampling ratio is 20%, the OCR engine fails in recognizing any characters, resulting in OCR accuracy = 0%. When the sampling ratio is doubled ( = 40%), 596 of 603 characters are accurately recognized. The OCR accuracy dramatically improves to 98.84%. As the sampling ratio further increases, the OCR accuracy is around 99%. Finally, when the document is fully sampled, only 1 of 603 characters is wrong in OCR, resulting in an OCR accuracy of 99.83%. This experiment demonstrates accurate OCR needs not fully-sampling and the proposed single-pixel scanner allows for accurate OCR for under-sampled text document images.

 

Fig. 7 Grayscale text document scanning results for different sampling ratios. The first row in panel (a) is the Hadamard spectrum for sampling ratio = 20%, the second row is the reconstructed image from the spectrum, the third row is a partial enlargement of the reconstruction. (b)-(e) are counterparts of (a) for sampling ratio = 40%, 60%, 80%, and 100%, respectively.

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3.2 Grayscale text encryption scanning

In the second experiment, we use the same document as that in the previous experiment for encryption scanning. The experiment is to demonstrate on-the-fly encryption ability provided by the proposed scanner. The key used for pixel permutation is generated by a pseudo-random number generator. As Fig. 8 shows, the reconstructed images without decryption appear noisy, which stands true for different sampling ratios. The contents in the images before decryption are unable to be recognized. Please note that the plaintext never exists or be stored in the computer from the very beginning to the stage before image decryption. Instead, the plaintext is temporally stored in the computer during image encryption for any conventional encryption scanning approach. Thus, we state that the proposed technique can well protect the confidential information. Interestingly, as the third row in Fig. 8 shows, the text appears after the images are decrypted. For under-sampled images, the reconstructed decrypted text documents appear noisy. As the sampling ratio increases, noise fades out. Characters become marginally recognizable when the sampling ratio = 60%. The fully-sampled result is identical to that in the previous experiment. The results also demonstrate the sampling efficiency of the proposed technique in the encryption scanning mode.

 

Fig. 8 Grayscale text document encryption scanning results for different sampling ratios. The first row in panel (a) is the Hadamard spectrum for sampling ratio = 20%, the second row is the reconstructed image from the spectrum, the third row is the decrypted result from the reconstructed image, and the forth row is a partial enlargement of the decrypted result. (b)-(e) are counterparts of (a) for sampling ratio = 40%, 60%, 80%, and 100%, respectively.

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3.3 Colored image scanning

In the third experiment, we use a colored image as the target object for scanning. First of all, we perform a simple color balance (also known as white balance) process to correct colors due to the unknown spectral response of the utilized solar cell. The color balance process refers to the acquisition of the calibration factors $k_{\text{R}}$, $k_{\text{G}}$, and $k_{\text{B}}$ for red, green, and blue primitive colors, respectively.

The color balance is implemented by using the color scanning strategy described Section 2.2 and using a null object, which is believed to be a white object, for scanning. As the number of unknowns is 3 only, it is not necessary to reconstruct a high-resolution image for the null object. Thus, we use 8$\times$8-pixel binning to obtain a 32$\times$32-pixel null object image. The reconstructed image is denoted by $I$. The three calibration factors are obtained by averaging the red ($I_{\text{R}}$), green ($I_{\text{G}}$), and blue ($I_{\text{B}}$) channel of the reconstructed image, respectively. As a result, the derived calibration factors are $k_{\text{R}}={\overline{I}}_{\text{R}}=0.5511$, $k_{\text{G}}={\overline{I}}_{\text{G}}=0.7077$, and $k_{\text{B}}={\overline{I}}_{\text{B}}=0.4118$. Please note that the calibration factors are applicable for all the reconstructions using the same devices.

With the imaging system calibrated, we carry out colored scanning for two test image documents –‘the gate’ and ‘the flowers’. Similarly, we use a complete set of 256$\times$256-pixel color-coded Hadamard basis patterns for illumination. We also employ 4$\times$4 binning in order to obtain a larger field-of-view. As a result, each illumination pattern occupies 1024$\times$1024 pixels of the LCD. As the results shown in Fig. 9, the test objects are finely reconstructed. The initial reconstructions (Figs. 9(a) and 9(e)) have some mosaic alike features which are actually subject to the Bayer’s mask. The features carry the color information of the object. To reconstruct the color from the mosaic features, we apply the linearly interpolation demosaic algorithm [34] to the initial reconstructions. The resultant color reconstructions are shown in Figs. 9(c) and 9(g). As the figures show, the color reconstructions have color distortion and appear too green. We further apply color balance the images (the red, green, and blue channels of images divided by the calibration factors, respectively). The results shown in Figs. 9(d) and 9(h) look much more realistic than previous. The experiment demonstrates the proposed scanner can reproduce high-quality true-color scanning results.

 

Fig. 9 Colored image scanning results. Results for ‘the gate’: (a) initial reconstruction and (b) partial enlargement showing the color information embedded mosaic features. (c) true-color reconstruction without color calibration. (d) true-color reconstruction with color calibration. (e)-(h) are the counterpart of (a)-(d) for ‘the flowers’.

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3.4 Genuine document identification

We simulate a genuine document and 2 faked documents by printing 3 identical patterns, ‘JNU’, onto a piece A4 paper. Our goal is to distinguish the genuine from the faked. Without loss of generality, the 3 patterns are printed on the same piece paper, as Fig. 10(a) shows. The image shown in Fig. 10(a) is obtained by using a typical scanner (Canon PIXMA MP-288). However, the 3 documents look almost the same and one can hardly distinguish with naked eyes. We assume that top-right document in Fig. 10(a) is genuine and the rest are faked. We first scan the top-right document shown in Fig. 10(a) with the proposed single-pixel scanner and the image derived is shown in Fig. 10(b). In order to demonstrate the paperprint is able to help identify the genuine document, we further scan the 3 documents in turn using the single-pixel scanner, including the top-left document. In other words, the genuine document is scanned twice. Please note that we deliberately apply a lateral shift and rotation to the genuine document before scanning so as to test the robustness of the technique. The derived images are shown in Figs. 10(c)-10(e). Figure 10(c) corresponds to the top-left pattern in Fig. 10(a), Fig. 10(d) the top-right, and Fig. 10(e) the bottom. As the results show, the patterns are finely reconstructed and the paperprint can be seen clearly. We propose to perform quantitative identification according to image correlation. We calculate the 2-D correlation coefficient between the genuine document image (Fig. 10(b)) and the test images (Fig. 10(c)-10(e)), respectively. The derived coefficients are 0.8003, 0.5172, and 0.6250, respectively. The large correlation coefficient implies the document is genuine. One can identify the genuine by careful observation. We marked some characteristic bright spots of the paperprint with black arrows in Figs. 10(b) and 10(c). The experiment demonstrates the propose scanner is able to distinguish the genuine document from the faked ones by utilizing paperprint.

 

Fig. 10 Genuine document identification results. (a) image of test object scanned by a typical scanner. (b) image of genuine document scanned by proposed scanner. (c)-(e) test documents scanned by proposed scanner, among which (c) is image of genuine document and (d) and (e) are images of faked documents. Black arrows in (b) and (d) indicate the characteristic bright spots of the paperprint.

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Besides, artificial watermarks have been widely used on postage stamps, currency, and other government documents to discourage counterfeiting. Watermarks are identifying images or patterns in paper that appears as various shades of lightness/darkness when viewed by transmitted light. Thus, watermarks are invisible when the document is scanned by a typical scanner which uses reflection light for imaging. On the contrary, the proposed scanner, which utilizes transmitted light, is able to acquire the watermarks. To demonstrate this point, we scan a 100 Hong Kong dollar banknote by using a typical scanner and the proposed single-pixel scanner, respectively. As Fig. 11 shows, the watermark does not appear in the image [Fig. 11(a) and a partial enlargement Fig. 11(b)] acquired by the typical scanner. Instead, the watermark (the pattern of Hong Kong orchid flower and ‘100’) can be clearly seen in the image reconstructed by the proposed single-pixel scanner [Fig. 11(c)]. The results demonstrate the proposed scanner is also suitable for watermark-based genuine document identification.

 

Fig. 11 Watermark scanning results. (a) image scanned by a typical scanner (Canon PIXMA MP-288). (b) is a partial enlargement of (a). (c) image scanned by the proposed single-pixel scanner.

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3.5 Effect of paper thickness on reconstruction quality

We investigate how the thickness of A4 paper affects the reconstruction quality. The investigation is done by printing the same text (font size = 6) as used in Section 3.1 onto 4 pieces of A4 paper with a different thickness and performing OCR for reconstruction quality evaluation. The thicknesses of paper are 70 grams per square meter (gsm), 100 gsm, 120 gsm, and 250 gsm, respectively.

The reconstructed images are shown in Fig. 12. Please note that the non-uniform background of the reconstructed image is the paperprint. The thickness of paper leads to the change of direct light to scattered light ratio. Specifically, the thicker paper results in more scattered light and less direct light. As both direct and scattered light carry the desired spatial information, the change of direct and scattered light ratio will not affect the signal-to-noise ratio. However, due to the absorption by paper, the intensity of transmitted light reduces as the thickness increases. The weaker transmitted light would reduce the signal-to-noise ratio. Therefore, the degeneration of signal-to-noise ratio is mainly due to absorption instead of scattering. Our results show that, for the 70-gsm paper, 593 among 603 characters are accurately recognized resulting in an OCR accuracy = 98.3%; for the 100-gsm paper, 588 among 603 characters are correct resulting in accuracy = 97.5%; for the 120-gsm paper, 593 among 603 characters are accurately recognized resulting in an OCR accuracy = 98.3%; for the 250-gsm paper (over 3-fold thicker than the 70-gsm paper), 487 among 603 characters are accurately recognized the OCR accuracy resulting in an OCR accuracy = 80.8%. In conclusion, the increment of paper thickness reasonably degrades the image reconstruction quality, but the degeneration is acceptable. The results demonstrate that the proposed scanner can produce clear image even when the target object is a turbid medium.

 

Fig. 12 Scanning and OCR results for different paper thickness: (a) 70 gsm, (b) 100 gsm, (c) 120 gsm, and (d) 250 gsm. The OCR accuracies for (a)-(d) are 98.3%, 97.5%, 98.3%, and 80.6%, respectively.

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4. Discussion

We acknowledge that transmission imaging mode of the proposed scanner has two sides. On one hand, it is not only suitable for imaging transmittance object (such as, negative films) but also capable of genuine document identification. However, on the other side, transmission imaging limits the scanner in single-side printed documents scanning.

Another drawback of the proposed scanner is that it suffers from long imaging time, which is because the utilized LCD controller provides no input or output synchronization ports (hardware triggers). We believe this issue can be resolved by using a controller with hardware triggers. Additionally, the post-processing time of the scanner is negligible, because it only takes a 2-D inversed Hadamard transform, whose computation complexity is even lower than 2-D Fourier transform, for image reconstruction.

We choose Hadamard basis patterns for image acquisition in our experiment, because the patterns are binary and therefore robust against gamma distortion of the utilized LCD. The use of binarized Fourier basis patterns for image acquisition is also a candidate [10]. We can also use deep learning [8] to optimize illumination patterns for high-efficiency for different types of documents.

The OCR accuracy might vary with the font and the size of text as well as the performance of the utilized OCR engine. To train the OCR engine with under-sampled text images might help improve the OCR accuracy for low-sampling-ratio data.

As large-size LCD monitors and flexible solar cells are commercially available, the proposed technique might allow for large-size documents scanning. The motivation why we use a flexible solar cell for single-pixel detection is it has a large-size active area and the photoelectric response throughout the active area is uniform. Thus, a flexible solar cell, according to the reciprocity, is a uniform planar illumination source.

The reported single-pixel scanner is only an instance of the proposed lensless single-pixel imaging technique. We believe the technique could find more applications in various fields.

5. Conclusion

We put forward a lensless single-pixel imaging technique and demonstrate the technique by applying it to achieve a motionless, portable, and multi-functional scanner. The thickness of the scanner is only 2.48 millimeters. It requires no mechanical motion and therefore enables silent scanning. As is experimentally demonstrated, the single-pixel scanner can not only reproduce high-quality grayscale and true-color, but also reconstruct clear enough text document image from under-sampled data for an accurate OCR result, on-the-fly encrypted scanning, and genuine document identification. The use of an LCD for structured illumination avoids aberration and significantly reduces the size of the imaging system. The proposed lensless single-pixel imaging technique might allow for small-size imaging systems in various fields.