Real-time single-pixel video imaging with Fourier domain regularization

Abstract

We present a closed-form image reconstruction method for single-pixel imaging based on the generalized inverse of the measurement matrix. Its numerical cost scales proportionally with the number of measured samples. Regularization of the inverse problem is obtained by minimizing the norms of the convolution between the reconstructed image and a set of spatial filters. The final reconstruction formula can be expressed in terms of matrix pseudoinverse. At high compression, this approach is an interesting alternative to the methods of compressive sensing based on l1-norm optimization, which are too slow for real-time applications. For instance, we demonstrate experimental single-pixel detection with real-time reconstruction obtained in parallel with measurement at a frame rate of 11 Hz for highly compressive measurements with a resolution of 256 × 256. To this end, we preselect the sampling functions to match the average spectrum obtained with an image database. The sampling functions are selected from the Walsh-Hadamard basis, from the discrete cosine basis, or from a subset of Morlet wavelets convolved with white noise. We show that by incorporating the quadratic criterion into the closed-form reconstruction formula, we can use binary rather than continuous sampling and reach similar reconstruction quality as is obtained by minimizing the total variation. This makes it possible to use cosine- or Morlet-based sampling with digital micromirror devices without advanced binarization methods.

Instant ghost imaging: algorithm and on-chip implementation

“…Assuming that reconstructing an image with the size of 400 × 280 requires 10,000 measurements, this on-chip hardware system needs 20 s to obtain one image. We noted that there are some high-speed schemes in the field of computational GI and single-pixel imaging [42], for example, Xu et al displayed a single-pixel imaging at a speed of 1,000 frames per second with the size of 32 × 32 [44]. However, the limiting factor of our imaging speed is the CMOS (PYTHON300, whose operating frequency is 500 measurements per second), not the speed of FPGA.…”

Instant ghost imaging: improving robustness for ghost imaging subject to optical background noise

“…Ghost imaging (GI) is an imaging technique that generates the image of an object by calculating the second-order correlation function between two light beams [1][2][3][4][5][6]. Ghost imaging has been widely researched in recent years [7][8][9][10][11][12][13][14][15][16]; it has important applications in many fields such as cryptography [17,18], lidar [19,20], medical imaging [21,22], micro object imaging [23,24], three-dimensional imaging [25][26][27][28] and single-pixel imaging [29][30][31][32][33]. In many practical scenes, GI is subject to interference from the transmission medium and from optical background noise.…”

Image watermarking and fusion based on Fourier single-pixel imaging with weighed light source

“…In 2014, Zhang et al presented a novel Fourier single-pixel imaging (FSPI) technique, in which the phase-shifting sinusoid structured illumination and the inverse Fast Fourier transform (IFFT) were employed to obtain the high-quanlity images [18]. Subsequently, a series of improved expansion schemes based on FSPI were reported [19][20][21][22].…”