Sparse sampling in frequency domain and laser imaging

Abstract

The monochromaticity of the laser and the characteristics of the natural image’s spectrum, including sparsity and concentrating in the low frequency range, make it possible to sample the image spectrum sparsely. Based on small-scale laser detectors and the introduced laser reference signals, a method of laser imaging with sparse sampling in frequency domain is proposed in this paper. The principle of frequency sparse sampling laser imaging and the imaging system structure are introduced. The simulation results of spectrum and complex images reconstructed are given. Both the effects of the signals’ parameters, such as the ratio of the reference laser signal amplitude to the laser echo spectrum amplitude and the initial phase of the laser reference signal, on reconstruction results are investigated. The reconstruction results are evaluated by correlation coefficient, mean square error (MSE), and structural similarity index (SSIM). For the strong correlation between phase and amplitude of the laser echo complex image, the amplitude image and the phase image are both set to be 256 × 256 diagram. The sparse laser detector plane array consists of 5 64 × 64 frequency domain laser detector arrays, which form a cross and make a sparsity rate of 31.25%(5/16). The simulation results show that the correlation coefficient, MSE and SSIM of the spectrum reconstructed are 0.96, 22.14, 1.00 and those of the complex image reconstructed are 0.96, 1857.25 and 0.67 respectively. The simulation results indicate that the method proposed is effective. However, the method requires the laser reference signal amplitude to be about 30 times the mean value of the laser echo spectrum amplitude, which reduces the dynamic range of the detectors. The initial phase of the laser reference signal has no obvious effect on the reconstruction results.