Single-pixel imaging by hadamard, fourier and discrete cosine transform - Sha, Fangyuan (2018)
Single pixel imaging is a new system that has received increasing attention in recent days.Within single-pixel imaging, the Fourier transform contains three steps, followed by four steps of active illumination, meaning that in this method, there are four times as many measurements are involved, causing the problem of long data-acquisition time. Applying the Hadamard transform can solve the problem of long data-acquisition time, but this method shows a lower clarity among all the transforms when objects have multiple grey levels. In this report, we apply the discrete cosine transform (DCT) for the purpose of single-pixel imaging, which not only saves data storage but also achieves a better clarity than the Hadamard transform does. I addition, fewer calculations are required during the process of pattern generation for illumination. Next, the report discusses the characteristics of the three transforms in terms of the sampling ratio, window shape, noise level of patterns, noise level of measurements, the quantization level of patterns and the quantization level of measurements. Last, the report uses the structural similarity (SSIM) index and mean square of the error (MSE) to express the clarity of reconstructed images. The result shows that single-pixel imaging using DCT patterns is better for clarity, whereas the Hadamard patterns provide better stability when the sensitivity of the light detector is relatively low. It is also remarkable that white noise can negatively affect the performance of DCT, and this should be a direction for further research.