Global Vision Media Focus
The company was featured on CCTV a total of 15 times, and its reach through Party media, central media, and local official media reached a total of 50 million people.
"Hidden Contamination" in Interference Signals: The Impact and Removal Methods of Baseline Drift
Background Introduction
In practical interferometric imaging systems, we often focus on the Fourier transform and spectral reconstruction algorithms themselves, easily overlooking a more fundamental issue—whether the original interference signal itself is "clean." Ideally, the interference signal corresponding to each pixel should oscillate symmetrically around zero, with its energy mainly concentrated in the effective interference fringes. However, in real systems, this ideal state almost never occurs. The original signal often contains a slowly changing trend term, causing the entire interference curve to show an overall rise or sloping drop, as shown in Figure 1. This slowly changing but not negligible trend term is what we call the baseline.
Figure 1. Original interferometric signal (with baseline)
While the baseline may appear to be a "slight offset," its impact is amplified during subsequent processing. Especially during Fourier transforms, this low-frequency tendency translates into strong low-frequency components, contaminating the entire spectral structure and potentially affecting the entire spectral range through spectral leakage. This not only raises the spectral floor but can also introduce spurious peaks, ultimately leading to distorted spectral energy distribution. In other words, what we often perceive as a "poor reconstruction algorithm" is actually a problem that arises before the signal even undergoes the Fourier transform. Therefore, before performing any spectral analysis, the primary issue should not be "how to reconstruct," but rather how to remove this type of low-frequency contamination hidden within the signal.
Common baseline correction methods currently include differential filtering, adaptive differential filtering (ADF), empirical mode decomposition (EMD), and polynomial fitting, with the following characteristics:
In practical applications, it can be observed that while these methods each have their advantages, it is difficult to simultaneously achieve both computational efficiency and processing stability. Differential filtering, although fast, tends to amplify noise. While ADF and EMD improve accuracy to some extent, their computational complexity and time consumption make them unsuitable for large-scale data processing. In contrast, polynomial fitting, while maintaining a certain level of accuracy, can achieve rapid processing through matrix pre-computation, significantly reducing computational overhead. In engineering practice, it achieves a better balance between processing speed, computational efficiency, and relative accuracy, thus becoming a more suitable choice.
Technical Principles
To remove the baseline, we first need to model the interference signal in a simple and intuitive way. For each pixel, the signal can be understood as consisting of two parts: a slowly changing background trend and a rapidly oscillating interference fringe.
Y = L + S
In most engineering scenarios, the baseline can be approximated as an additive low-frequency trend. Here, Y represents the original signal, L represents the baseline, and S represents the actual interference information. Our goal is to extract L from Y and then remove it to obtain the clean signal S. The key question is: how to describe this baseline L? In practical systems, baseline changes are usually smooth and slow, so they can be approximated using a low-order polynomial, for example:
L(x) ≈ a0 + a1*x + a2*x^2 + ... + an*x^n
The essence of this step is to use a "simple function" to describe low-frequency trends in a complex system.
Next, we need to make this polynomial fit the original signal as closely as possible. The most common method is least-squares fitting, the goal of which can be simply understood as (making L as close to Y as possible). In traditional approaches, this step requires individual fitting calculations for each pixel, which becomes very slow when the data volume is large. However, in engineering implementations, this process can be optimized all at once. For cases where the number of sampling points in the interferogram is the same for all pixels, a fixed matrix P can be pre-calculated, turning the "fitting" into a simple matrix operation:
L = P * Y
In this way, regardless of the number of pixels, the same P can be used directly to extract the baseline, greatly improving processing speed. The baseline removal process then becomes very straightforward:
S = Y – L
Compared to direct filtering, this method doesn't simply "cut off certain frequencies." Instead, it models and isolates the baseline, thus better preserving the detailed structure of the interference fringes while removing trends. Furthermore, since matrix P only needs to be calculated once, this method is both stable and efficient when processing large-scale data, making it ideal for engineering applications. In practical processing, attention should be paid to errors at the fitting boundaries; typically, a weighted strategy or retaining only the effective interference region can be employed.
Results Analysis
In practical data processing, the changes before and after baseline removal can be observed intuitively. The original interference signal usually exhibits a clear overall trend; whether it's a linear rise or a slow bend, it disrupts the original symmetry of the signal. After polynomial fitting and projection processing, this low-frequency trend is effectively stripped away, and the signal returns to oscillating around zero, resulting in a clearer interference fringe structure. To illustrate this process more clearly, the following comparison results of the single-pixel signal before and after processing are given:
Figure 2. Comparison of original single-pixel baseline removal before and after.