The relationship between graph Fourier transform (GFT) and discrete cosine transform (DCT) for 1D signal and 2D image

Yu, Lu; Xie, Jun; Zheng, Xiang Yuan

doi:10.1007/s11760-022-02249-5

Cited by 6 publications

(1 citation statement)

References 21 publications

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“…Recently, X. Zhou et al have applied deep belief network (DBN) to learn striation-based sonar fringe images and proposed shared latent sparse feature (SLS) to represent the interference fringe [7]. The two-dimensional Fourier transform decomposes an image into the sum of several complex plane waves [8][9][10]. When the intensity of complex plane wave component forming the fringe pattern to be measured is small, the fringe pattern will be submerged in the noise.…”

Section: Introductionmentioning

confidence: 99%

Two-Dimensional Lock-in Amplifier Algorithm in Spatial Domain

Zhang

2023

Preprint

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An algorithm based on a two-dimensional lock-in amplifier method has been proposed for extracting complex plane components in images. Traditional one-dimensional time-frequency lock-in amplifier estimates the amplitude and phase of a periodic signal at a frequency determined by a reference signal that may be submerged by noise. In the field of digital image processing, it is necessary to analyze the information in the spatial domain. In this paper, a mathematical model has been established to describe the complex plane component in the image, and a two-dimensional lock-in amplifier algorithm has been developed. Compared with traditional lock-in amplifier algorithms, the proposed algorithm can be used to process signals with higher dimensions. Simulation and experimental results show that the proposed algorithm can effectively extract the complex plane components polluted by noise at given frequencies. This two-dimensional lock-in amplifier algorithm can be applied to the extraction and reconstruction of fringe patterns in images submerged by noise. The limitation of the proposed algorithm has been discussed.

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