Single-pixel compressive imaging based on the transformation of discrete orthogonal Krawtchouk moments

Efficient and noise-resistant single-pixel imaging based on Pseudo-Zernike moments

An efficient and noise-resistant single-pixel imaging (SPI) technique based on Pseudo-Zernike moments (PZ-SPI) is proposed. In this technique, the illumination light fields are modulated to satisfy the Pseudo-Zernike polynomials. Then the modulated light fields are projected onto the object. And the single-pixel detector is used to measure the reflected light intensities to calculate the Pseudo-Zernike moments. Finally, the object image is reconstructed by iterative summation of the product of the Pseudo-Zernike polynomials and the Pseudo-Zernike moments. Through the numerical simulation and experimental demonstration, PZ-SPI can effectively reconstruct image at low sampling ratios. Besides, comparing with the Fourier-SPI and Zernike-SPI, PZ-SPI has good robustness to background noise in SPI system. These advantages expand the application of PZ-SPI in complex environments.

Comparison of Common Algorithms for Single-Pixel Imaging via Compressed Sensing

Single-pixel imaging (SPI) uses a single-pixel detector instead of a detector array with a lot of pixels in traditional imaging techniques to realize two-dimensional or even multi-dimensional imaging. For SPI using compressed sensing, the target to be imaged is illuminated by a series of patterns with spatial resolution, and then the reflected or transmitted intensity is compressively sampled by the single-pixel detector to reconstruct the target image while breaking the limitation of the Nyquist sampling theorem. Recently, in the area of signal processing using compressed sensing, many measurement matrices as well as reconstruction algorithms have been proposed. It is necessary to explore the application of these methods in SPI. Therefore, this paper reviews the concept of compressive sensing SPI and summarizes the main measurement matrices and reconstruction algorithms in compressive sensing. Further, the performance of their applications in SPI through simulations and experiments is explored in detail, and then their advantages and disadvantages are summarized. Finally, the prospect of compressive sensing with SPI is discussed.

Single-pixel imaging using discrete Zernike moments

A novel single-pixel imaging (SPI) technique based on discrete orthogonal Zernike moments is proposed. In this technique, the target object is illuminated by two sets of Zernike basis patterns which satisfy the Zernike polynomials. The Zernike moments of object image are obtained by measuring the reflected light intensities through a single-pixel detector. And the object image is reconstructed by summing the product of Zernike polynomials and detected intensities iteratively. By theoretical and experimental demonstrations, an image with high quality is retrieved under compressive sampling. Moreover, the Zernike illuminating patterns are used for object classification due to the rotation invariant of Zernike moments. By measuring the amplitudes of a few specific Zernike moments through the SPI system, the rotated images with different angles and the same content are classified into the same class on experiment. This classification technique has the advantages of high efficiency and high accuracy due to the high modulation speed and high sensitivity of SPI system.

Stable Calculation of Krawtchouk Functions from Triplet Relations

Deployment of the recurrence relation or difference equation to generate discrete classical orthogonal polynomials is vulnerable to error propagation. This issue is addressed for the case of Krawtchouk functions, i.e., the orthonormal basis derived from the Krawtchouk polynomials. An algorithm is proposed for stable determination of these functions. This is achieved by defining proper initial points for the start of the recursions, balancing the order of the direction in which recursions are executed and adaptively restricting the range over which equations are applied. The adaptation is controlled by a user-specified deviation from unit norm. The theoretical background is given, the algorithmic concept is explained and the effect of controlled accuracy is demonstrated by examples.

DQN based single-pixel imaging

For an orthogonal transform based single-pixel imaging (OT-SPI), to accelerate its speed while degrading as little as possible of its imaging quality, the normal way is to artificially plan the sampling path for optimizing the sampling strategy based on the characteristic of the orthogonal transform. Here, we propose an optimized sampling method using a Deep Q-learning Network (DQN), which considers the sampling process as decision-making, and the improvement of the reconstructed image as feedback, to obtain a relatively optimal sampling strategy for an OT-SPI. We verify the effectiveness of the method through simulations and experiments. Thanks to the DQN, the proposed single-pixel imaging technique is capable of obtaining an optimal sampling strategy directly, and therefore it requires no artificial planning of the sampling path there, which eliminates the influence of the imperfect sampling path planning on the imaging performance.