We introduced an efficient technique to suppress speckle noise in medical ultrasound images while maintaining low computational complexity. The medical ultrasound image is divided into overlapping subimages, and Lanczos decomposition is then applied to the average Hermitian covariance matrix of all subimages. The resultant orthonormal vectors are used for filtering speckle noise through orthogonal and oblique projections, i.e., by projecting noisy signal onto the signal subspace. After sorting the orthonormal vectors, an orthogonal projection matrix is formed by selecting the first K vectors contributing to the signal, whereas an oblique projection matrix is formed by selecting the first K vectors contributing to the signal and the last K vectors contributing to the noise. The procedure of Lanczos is also followed with singular value decomposition (SVD). Schemes are applied to real ultrasound images and two types of speckle noise simulations: fine and rough speckle noise. Numerical and visual results depict that proposed technique has outperformed various popular benchmark schemes, i.e., Frost, Lee, probabilistic nonlocal means, geometric nonlinear diffusion filter, guided speckle reducing bilateral filter, and SVD, while maintaining a competitive computational complexity. Lanczos-based scheme showed a relatively lagging performance in terms of resolution, which was always outshone by a leading performance in terms of key measures such as signal-to-noise ratio (SNR), peak signal-to-noise ratio (PSNR), feature similarity, and mean structural similarity. Orthogonal and oblique projections were found to perform the same except when speckle noise is fine, where insignificant differences were found in terms of SNR, PSNR, and resolution. Lanczos-based scheme tends to offer a better estimation of orthonormal vectors than SVD, consequently a better speckle noise suppression. Furthermore, it offers an efficient tuning parameter per block/subimage size to treat various speckle noise patterns.

中文翻译：

---

基于Lanczos分解的正交和斜子空间投影进行超声图像恢复

我们引入了一种有效的技术来抑制医学超声图像中的斑点噪声，同时保持较低的计算复杂度。医学超声图像被分成重叠的子图像，然后将Lanczos分解应用于所有子图像的平均Hermitian协方差矩阵。所得的正交向量用于通过正交和倾斜投影（即通过将有噪信号投影到信号子空间上）来过滤斑点噪声。在对正交向量进行排序之后，通过选择对信号有贡献的前K个向量来形成正交投影矩阵，而通过选择对信号有贡献的前K个向量和对噪声有贡献的最后K个向量来形成倾斜投影矩阵。Lanczos的过程也遵循奇异值分解（SVD）。该方案适用于实际超声图像和两种类型的斑点噪声模拟：精细和粗糙斑点噪声。数值和视觉结果表明，所提出的技术优于各种流行的基准方案，即Frost，Lee，概率非局部均值，几何非线性扩散滤波器，引导斑点减少双边滤波和SVD，同时保持了竞争性的计算复杂性。基于Lanczos的方案在分辨率方面显示出相对滞后的性能，在诸如信噪比（SNR），峰值信噪比（PSNR），特征相似性和平均结构相似性。正交投影和斜投影的表现相同，只是散斑噪声很好时，在SNR，PSNR和分辨率方面没有明显差异。基于Lanczos的方案倾向于提供比SVD更好的正交向量估计，因此，可以更好地抑制斑点噪声。此外，它为每个块/子图像的大小提供了有效的调整参数，以处理各种散斑噪声模式。