# Improved Least Squares Phase Unwrapping Method Based on Chebyshev Filter
## 1 Introduction
Compared to the methods mentioned above, the third category, the minimum norm-based methods, has the fastest unwrapping speed and smoothest phase unwrapping results [15]. The least squares (LS) phase unwrapping method is one of the most commonly used methods of the minimum norm-based methods. The LS phase unwrapping method can be understood as finding the solution to the Poisson equation under Neumann boundary conditions, which can be achieved through iterative methods, discrete cosine transforms (DCT), fast Fourier transform (FFT), and an unweighted multi-level grid method, but it also produces significant unwrapping errors with large phase noise and high phase gradient [17]. In recent years, some scholars have improved the LS phase unwrapping method based on its rapidity and smoothness, making the LS phase unwrapping method suitable for high phase noise and high phase gradient. For example, [PERSON] et al. [26] proposed a phase calibration unwrapping algorithm for phase data corrupted by strong decorrelation speckle noise (PCUA). This algorithm uses the average phase gradient to replace the phase gradient that is greater than the standard deviation when solving the Poisson equation. The advantages of the LS phase unwrapping method can be exploited by reducing the phase gradient, and then the error phase is corrected by the iterative method. However, the phase unwrapping effect is unstable when the phase noise and phase gradient change. After this, to make the phase unwrapping results more stable, [PERSON] et al. [27] proposed a robust phase unwrapping algorithm for noisy and segmented phase measurements (RPUA). When solving the Poisson equation, it uses the sine function to correct the phase gradient, which further improves the phase unwrapping accuracy under high noise and high phase gradient. However, in true interference data phase unwrapping, the results obtained are also unstable. Based on the above analysis, there are certain difficulties in phase unwrapping. Using traditional category I and category II methods, phase unwrapping under high phase noise and steep phase gradient will produce large errors [24; 25]. [PERSON] et al. and [PERSON] et al. show that using iterative LS phase unwrapping can reduce the phase unwrapping error under high phase noise and steep phase gradient, but when calculating the equivalent phase gradient, it is too dependent on the overall steepness of the phase gradient to change the steep phase gradient into a sufficiently large number of flat phase gradients. However, the calculation of an equivalent flat phase gradient is too dependent on the overall steepness of the phase gradient. It is difficult to change a steep phase gradient into a sufficiently flat phase gradient. Therefore, to make the LS phase unwrapping method more stable under high phase noise and high phase gradient, this paper proposes an improved LS phase unwrapping method based on the Chebyshev filter [28] and designs its adaptive filtering threshold so that the high phase gradient is changed into flatter phase gradient as much as possible. Finally, an iterative method of unwrapping phase errors is used to eliminate errors under high phase noise and steep phase gradient. This paper is organized as follows: Section 2 describes the principle of LS phase unwrapping and the improvement method of this paper. Section 3 is the experimental results and analysis part. Section 4 is a discussion of phase unwrapping methods. Section 5 is the conclusion of this paper.