A FAST AND ROBUST FRAMEWORK FOR IMAGE FUSION AND ...

Chapter 2
Robust Multi-Frame Super-resolution
of Grayscale Images
2.1 Introduction
As we discussed in the introduction section, theoretical and practical limitations usu-
ally constrain the achievable resolution of any imaging device. In this chapter, we focus on the
incoherent grayscale imaging systems and propose an effective multi-frame super-resolution
method that helps improve the quality of the captured images.
A block-diagram representation of such an imaging system is illustrated in Figure 2.1,
where a dynamic scene with continuous intensity distribution X(x, y) is seen to be warped at
the camera lens because of the relative motion between the scene and camera. The images are
blurred both by atmospheric turbulence and camera lens (and CCD) by continuous point spread
functions Hatm(x, y) and Hcam(x, y). Then they will be discretized at the CCD resulting in a
digitized noisy frame Y . We represent this forward model by the following equation:
Y =[Hcam(x, y) ∗∗F (Hatm(x, y) ∗∗X(x, y))] ↓ +V, (2.1)
in which ∗∗ is the two dimensional convolution operator, F is the warping operator (projecting
the scene into the camera’s coordinate system), ↓ is the discretizing operator, V is the system
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