Image reconstruction based on a single-pixel camera and left optimization

Cheng T., Li D.G. Реконструкция изображения на основе однопикселной камеры и левосторонней оптимизации. Image reconstruction based on a single-pixel camera and left optimization  [на англ. яз.] // Оптический журнал. 2022. Т. 89. № 5. С. 31–40. http://doi.org/10.17586/1023-5086-2022-89-05-31-40

Cheng T., Li D.G. Реконструкция изображения на основе однопикселной камеры и левосторонней оптимизации. Image reconstruction based on a single-pixel camera and left optimization [in English] // Opticheskii Zhurnal. 2022. V. 89. № 5. P. 31–40. http://doi.org/10.17586/1023-5086-2022-89-05-31-40

Tao Cheng and Degao Li, "Image reconstruction based on a single-pixel camera and left optimization," Journal of Optical Technology. 89(5), 269-276 (2022). https://doi.org/10.1364/JOT.89.000269

Subject of study. A set of schemes that can make the single-pixel camera use the prior information of the image to improve the image reconstruction effect is proposed. Method. After the measurement data of the single-pixel camera is processed by standardization or left optimization, the energy and direction information of the signal can be reflected by the processed data. According to the energy and direction information characteristics of the reconstructed image by orthogonal matching pursuit, the use of total variation minimization algorithms in specific area can improve the image reconstruction effect. Main Results. Based on the [0-1] random matrix and the [0-1] circulant matrix, the measurement data of the single-pixel camera cannot effectively reflect the energy and direction information of the signal. After the measurement data of a single-pixel camera are processed by standardization, the energy information of the signal can be more clearly reflected. Although the direction information is also reflected, it is not very obvious. After the measurement data of the single-pixel camera are processed by left optimization, both the energy and direction information of the signal can be well reflected. Therefore, the energy and direction information of the measurement data of the singlepixel camera after left optimization can be used as criteria for evaluating the quality of the signal reconstruction. Experimental results show that based on such criteria, using orthogonal matching pursuit and total variation minimization algorithms in different columns of the measurement data can greatly improve the image reconstruction. Even if the measurement data contains noise, signal-to-noise ratio can be improved by more than 16 dB. Practical significance. In real compressed sensing engineering applications, the measurement data and measurement matrix are the only known factors. Because the real image is unknown, the quality of the reconstruction can only be evaluated based on long-term work experience. Or logical reasoning is on basis of the results of simulation experiments. Based on the energy and direction information of the measurement data of the single-pixel camera after left optimization, the result of image reconstruction can be evaluated objectively.

The work is supported by the National Natural Science Foundation of China under Grants 41461082 and 81660296 and the China Postdoctoral Science  Foundation under Grant 2016M592525.