The anisotropic total variation (TV) denoising model suppresses noise for two-dimensional signals that are vertically and horizontally piecewise constant. However, two-dimensional signals may have sparse derivatives in other directions. We propose a modification of the classical anisotropic two-dimensional TV regularizer from a spectral point of view. In the frequency domain, the TV regularizer can be considered as penalizing the high-frequency component of original signals and promoting only low-frequency components. The classical anisotropic TV, which applies $l_1$-norm on vertical and horizontal differences, suppresses high-frequency components of the signals. The proposed operator, named Haar total variation (Haar-TV), penalizes two-dimensional signals that have more varied high-frequency regions. Furthermore, we propose non-convex penalties based on the Haar-TV operator since non-convex penalties can preserve edges and thus enhance the quality of the estimation. We derive a condition that preserves the strong convexity of the total cost function so the global minimizer can be reached.

各向异性总变化（TV）去噪模型可抑制垂直和水平分段恒定的二维信号的噪声。但是，二维信号可能在其他方向上具有稀疏导数。从光谱的观点出发，我们提出了对经典各向异性二维电视调节器的改进。在频域中，TV正则器可被视为对原始信号的高频分量进行了惩罚，而仅提升了低频分量。适用于古典各向异性电视${升}_{\mathrm{1个}}$-垂直和水平差异的范数，抑制信号的高频分量。提议的运营商名为Haar总变化（Haar-TV），对具有更多变化的高频区域的二维信号进行了惩罚。此外，我们建议基于Haar-TV算子的非凸罚分，因为非凸罚分可以保留边缘，从而提高估计的质量。我们得出一个条件，该条件保留了总成本函数的强凸性，因此可以实现全局最小化。