python中缺少数据的二维卷积

我知道有scipy.signal.convolve2d函数来处理2d numpy数组的二维卷积，还有numpy.ma模块来处理丢失的数据，但这两种方法似乎互不兼容（这意味着即使在numpy中屏蔽2d数组，也不会影响convolve2d中的处理）。有没有办法只使用numpy和scipy包来处理卷积中缺少的值

例如：

            1 - 3 4 5
            1 2 - 4 5
   Array =  1 2 3 - 5
            - 2 3 4 5
            1 2 3 4 -

  Kernel =  1  0
            0 -1

卷积的期望结果（数组、内核、边界='wrap'）：

---

感谢Aguy的建议，这是帮助计算卷积后结果的一个非常好的方法。现在让我们假设我们可以从Array.mask获得数组的掩码，这将给我们一个

                   False True  False False False                       
                   False False True  False False
    Array.mask ==  False False False True  False
                   True  False False False False
                   False False False False True

---

如何使用此掩码将卷积后的结果转换为掩码数组？

我不认为用0s替换是正确的方法，而是将共变值推向0。这些遗漏应按字面上的“遗漏”处理。因为它们代表丢失的信息片段，没有理由仅仅假设它们可能是0，而且它们根本不应该参与任何计算

我尝试将缺失值设置为

numpy.nan

，然后进行卷积，结果表明，内核和任何缺失之间的任何重叠都会在结果中产生

nan

，即使重叠与内核中的0重叠，结果中的缺失孔也会增大。根据您的应用程序，这可能是期望的结果

---

但在某些情况下，你不想仅仅因为一个单一的缺失就放弃这么多信息（可能我发现了一个漏洞。使用虚数代替nan（如果是nan，则将其更改为1i）运行卷积运算，设置虚值高于阈值的地方为nan。无论何时低于阈值，只需取实值。下面是一段代码片段：

frames_complex = np.zeros_like(frames_, dtype=np.complex64)
frames_complex[np.isnan(frames_)] = np.array((1j))
frames_complex[np.bitwise_not(np.isnan(frames_))] =                         
frames_[np.bitwise_not(np.isnan(frames_))]
convolution = signal.convolve(frames_complex, gaussian_window, 'valid')
convolution[np.imag(convolution)>0.2] = np.nan
convolution = convolution.astype(np.float32)

---

卷积应该如何处理丢失的值？我觉得

结果[0,1]

应该是

0

，而不是

-

…您想用0替换屏蔽值，然后卷积，然后对结果重新应用屏蔽。请查看此repo（）在那里，我创建了一个用Fortran编译的python模块，这将大大加快速度。我更新了自己的解决方案，在这里，我有两个问题要问@Jason的解决方案：你能发布你是如何创建/使用fxn的代码吗？你为什么不使用convolve2d，我如何使用它的属性，比如不同的模式，例如“有效”，即不使用ep相同形状的图像？制作滚动窗口功能的高超技巧。

from astropy.convolution import convolve
inarray=numpy.where(inarray.mask,numpy.nan,inarray) # masking still doesn't work, has to set to numpy.nan
result=convolve(inarray,kernel)

def convolve2d(slab,kernel,max_missing=0.5,verbose=True):
    '''2D convolution with missings ignored

    <slab>: 2d array. Input array to convolve. Can have numpy.nan or masked values.
    <kernel>: 2d array, convolution kernel, must have sizes as odd numbers.
    <max_missing>: float in (0,1), max percentage of missing in each convolution
                   window is tolerated before a missing is placed in the result.

    Return <result>: 2d array, convolution result. Missings are represented as
                     numpy.nans if they are in <slab>, or masked if they are masked
                     in <slab>.

    '''

    from scipy.ndimage import convolve as sciconvolve

    assert numpy.ndim(slab)==2, "<slab> needs to be 2D."
    assert numpy.ndim(kernel)==2, "<kernel> needs to be 2D."
    assert kernel.shape[0]%2==1 and kernel.shape[1]%2==1, "<kernel> shape needs to be an odd number."
    assert max_missing > 0 and max_missing < 1, "<max_missing> needs to be a float in (0,1)."

    #--------------Get mask for missings--------------
    if not hasattr(slab,'mask') and numpy.any(numpy.isnan(slab))==False:
        has_missing=False
        slab2=slab.copy()

    elif not hasattr(slab,'mask') and numpy.any(numpy.isnan(slab)):
        has_missing=True
        slabmask=numpy.where(numpy.isnan(slab),1,0)
        slab2=slab.copy()
        missing_as='nan'

    elif (slab.mask.size==1 and slab.mask==False) or numpy.any(slab.mask)==False:
        has_missing=False
        slab2=slab.copy()

    elif not (slab.mask.size==1 and slab.mask==False) and numpy.any(slab.mask):
        has_missing=True
        slabmask=numpy.where(slab.mask,1,0)
        slab2=numpy.where(slabmask==1,numpy.nan,slab)
        missing_as='mask'

    else:
        has_missing=False
        slab2=slab.copy()

    #--------------------No missing--------------------
    if not has_missing:
        result=sciconvolve(slab2,kernel,mode='constant',cval=0.)
    else:
        H,W=slab.shape
        hh=int((kernel.shape[0]-1)/2)  # half height
        hw=int((kernel.shape[1]-1)/2)  # half width
        min_valid=(1-max_missing)*kernel.shape[0]*kernel.shape[1]

        # dont forget to flip the kernel
        kernel_flip=kernel[::-1,::-1]

        result=sciconvolve(slab2,kernel,mode='constant',cval=0.)
        slab2=numpy.where(slabmask==1,0,slab2)

        #------------------Get nan holes------------------
        miss_idx=zip(*numpy.where(slabmask==1))

        if missing_as=='mask':
            mask=numpy.zeros([H,W])

        for yii,xii in miss_idx:

            #-------Recompute at each new nan in result-------
            hole_ys=range(max(0,yii-hh),min(H,yii+hh+1))
            hole_xs=range(max(0,xii-hw),min(W,xii+hw+1))

            for hi in hole_ys:
                for hj in hole_xs:
                    hi1=max(0,hi-hh)
                    hi2=min(H,hi+hh+1)
                    hj1=max(0,hj-hw)
                    hj2=min(W,hj+hw+1)

                    slab_window=slab2[hi1:hi2,hj1:hj2]
                    mask_window=slabmask[hi1:hi2,hj1:hj2]
                    kernel_ij=kernel_flip[max(0,hh-hi):min(hh*2+1,hh+H-hi), 
                                     max(0,hw-hj):min(hw*2+1,hw+W-hj)]
                    kernel_ij=numpy.where(mask_window==1,0,kernel_ij)

                    #----Fill with missing if not enough valid data----
                    ksum=numpy.sum(kernel_ij)
                    if ksum<min_valid:
                        if missing_as=='nan':
                            result[hi,hj]=numpy.nan
                        elif missing_as=='mask':
                            result[hi,hj]=0.
                            mask[hi,hj]=True
                    else:
                        result[hi,hj]=numpy.sum(slab_window*kernel_ij)

        if missing_as=='mask':
            result=numpy.ma.array(result)
            result.mask=mask

    return result

frames_complex = np.zeros_like(frames_, dtype=np.complex64)
frames_complex[np.isnan(frames_)] = np.array((1j))
frames_complex[np.bitwise_not(np.isnan(frames_))] =                         
frames_[np.bitwise_not(np.isnan(frames_))]
convolution = signal.convolve(frames_complex, gaussian_window, 'valid')
convolution[np.imag(convolution)>0.2] = np.nan
convolution = convolution.astype(np.float32)