使用 MATLAB 进行稀疏矩阵插值
如果我有一个像这样的矩阵，
A = [1 2; 3 4];
我可以使用 interp2 像这样对其进行插值
newA = interp2(A,2);
，然后得到一个 5x5 插值矩阵。
但是，如果我有一个像这样的矩阵怎么办：
B = zeros(20);
B(3,2) = 5;
B(17,4) = 3;
B(16, 19) = 2.3;
B(5, 18) = 4.5;
我将如何插入（或填充空白）这个矩阵。我研究过 interp2 和 TriScatteredInterp 但这些似乎都不完全符合我的需求。
If I have a matrix like this
A = [1 2; 3 4];
I can use interp2 to interpolate it like this
newA = interp2(A,2);
and I get a 5x5 interpolated matrix.
But what if I have a matrix like this:
B = zeros(20);
B(3,2) = 5;
B(17,4) = 3;
B(16, 19) = 2.3;
B(5, 18) = 4.5;
How would I interpolate (or fill-in the blanks) this matrix. I've looked into interp2 as well as TriScatteredInterp but neither of these seem to fit my needs exactly.
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一个好的解决方案是使用我的 inpaint_nans。只需提供不存在信息的 NaN 元素，然后使用 inpaint_nans。它将对 NaN 元素进行插值，填充它们以与数据点平滑一致。
编辑：
对于那些对inpaint_nans是否可以处理更复杂的表面感兴趣的人，我曾经拍过一张数字化的莫奈绘画（见左侧，然后通过删除随机 50% 的像素来破坏它。最后，我应用 inpaint_nans 来查看是否可以很好地恢复图像。右侧图像是修复后的图像。虽然分辨率较低，恢复的图像是一个不错的恢复
作为另一个示例，请尝试以下操作：
现在，删除该数组中大约 7/8 的元素，并
使用 z- 进行恢复。轴具有不同的缩放比例，因为边缘周围存在 +/-1 上方和下方的微小变化，但除此之外，后一个表面是一个很好的近似值
。 " alt="在此输入图像描述">
A good solution is to use my inpaint_nans. Simply supply NaN elements where no information exists, then use inpaint_nans. It will interpolate for the NaN elements, filling them in to be smoothly consistent with the data points.
Edit:
For those interested in whether inpaint_nans can handle more complex surfaces, I once took a digitized Monet painting (seen on the left hand side, then corrupted it by deleting a random 50% of the pixels. Finally, I applied inpaint_nans to see if I could recover the image reasonably well. The right hand image is the inpainted one. While the resolution is low, the recovered image is a decent recovery.
As another example, try this:
Now, delete about 7/8 of the elements of this array, replacing them with NaNs.
Recover using inpainting. The z-axis has a different scaling because there are minor variations above and below +/-1 around the edges, but otherwise, the latter surface is a good approximation.