Two of the most popular denoising algorithms are ℓ ₂ and ℓ ₁ trend filtering, which are used in science, engineering, and statistical signal and image processing. They are typically treated as separate entities, with the former as a linear time-invariant (LTI) filter, which is commonly used for smoothing the noisy data and detrending the time-series signals, while the latter is a nonlinear filtering method suited for the estimation of piecewise-polynomial signals (e.g., piecewise constant, piecewise linear, piecewise quadratic, and so on) observed in additive white Gaussian noise.

中文翻译：

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ℓ2 和 ℓ1 趋势过滤：卡尔曼滤波器方法 [讲义]

两种最流行的去噪算法是ℓ ₂和ℓ ₁趋势过滤，它们用于科学、工程以及统计信号和图像处理。它们通常被视为单独的实体，前者作为线性时不变 (LTI) 滤波器，通常用于平滑噪声数据和去除时间序列信号的趋势，而后者是一种非线性滤波方法，适用于在加性高斯白噪声中观察到的分段多项式信号（例如分段常数、分段线性、分段二次等）的估计。