This paper proposes a Kalman filter framework for signal denoising that simultaneously utilizes conventional linear time-invariant (LTI) filtering and total variation (TV) denoising. In this approach, the desired signal is considered to be a mixture of two distinct components: a band-limited (e.g., low-frequency component, high-frequency component) signal and a sparse-derivative signal. An iterative Kalman filter/smoother approach is formulated where zero-phase LTI filtering is used to estimate the band-limited signal and TV denoising is used to estimate the sparse-derivative signal.

中文翻译：

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用于同时 LTI 滤波和总变化去噪的卡尔曼滤波器框架


本文提出了一种用于信号去噪的卡尔曼滤波器框架，该框架同时利用传统的线性时不变（LTI）滤波和全变分（TV）去噪。在该方法中，期望信号被认为是两个不同分量的混合：带限（例如，低频分量、高频分量）信号和稀疏导数信号。制定了迭代卡尔曼滤波器/平滑器方法，其中使用零相位 LTI 滤波来估计带限信号，并使用 TV 去噪来估计稀疏导数信号。