Well-posed problem & Ill-posed problem.

适定问题(Well-posed problem)是指满足下列三个要求的问题:

a solution exists:解必须存在;
the solution is unique:解必须唯一;
the solution’s behavior changes continuously with the initial conditions:解能根据初始条件连续变化,不会发生跳变,即解必须稳定。
上述三个要求中,只要有一个不满足,则称之为不适定问题(ill-posed problems)。

图像处理中不适定问题(ill posed problem)或称为反问题(inverse Problem)的研究从20世纪末成为国际上的热点问题,成为现代数学家、计算机视觉和图像处理学者广为关注的研究领域。典型的图像处理不适定问题包括:

  • 图像去噪(Image De-nosing)
  • 图像恢复(Image Restorsion)
  • 图像放大(Image Zooming)
  • 图像修补(Image Inpainting)
  • 图像去马赛克(image Demosaicing)
  • 图像超分辨(Image super-resolution)


In most cases, there are several possible output images corresponding to a given input image and the problem can be seen as a task of selecting the most proper one from all the possible outputs.