Image Reconstruction

Fig. 6.33: Illustration of 3-pixel 1-measurement solutions with the minimum l2 norm, l1 norm, and l0 quasi-norm.

Example 10: When the system of imaging equations is under-determined, use 2-pixel (x1, x2) or 3-pixel (x1, x2, x3) examples to illustrate solutions with the minimum l2 norm, l1 norm, and l0 quasi-norm, respectively.

Solution

Let us consider a 2-pixel (x1, x2) case, and there is one measurement. This measurement can be represented as a straight line in the (x1, x2) coordinate system. Any point on the line is a valid solution. The solutions with the minimum l2 norm, l1 norm, and l0 quasi-norm are shown in Figure 6.32, respectively.