Under the DSP G framework, the gradient of a signal at a node is a scalar value. However, let us define a vector gradient ? i f at a node i such that the j th element of the gradient vector is ( ? i f)( j) = ? wij ( f ( i ) ? f ( j)). Therefore, the length of the gradient vector at node i is the number of incoming edges at the node.
(a) An image signal can also be considered as a graph signal lying on the graph shown in
Figure 10.11, where the edges are pointing rightward and downward. For an arbitrary
node, what is the vector gradient at the node?
(b) Describe under what conditions on a graph signal
f the relation ||?if||1= |(Linf)(i)| will
hold? Here Lin is the directed Laplacian (in-degree) of the graph.
(c) Do you think that defining a vector gradient might be a better choice for quantifying
the local variations in a graph signal and subsequently for quantifying global variation as
well? Why?
Consider the node labeling as shown in Figure 10.12. The gradient vector at an arbitary
node i will be zero except at four entries which are
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A(n) ____________________ field is added to the form but not displayed in the Web page.
Fill in the blank(s) with the appropriate word(s).
Consider the following relation:
This relation refers to business trips made by salesmen in a company. Suppose the trip has a single start_date but involves many cities and one may use multiple credit cards for that trip. Make up a mock-up population of the table. a. Discuss what FDs and / or MVDs exist in this relation. b. Show how you will go about normalizing it.
Using a single processor, finding the largest of N numbers takes ____ time.
A. ?(1) B. ?(NlogN) C. ?(N2) D. ?(N)
In a B-tree, we can delete only from a leaf node.
Answer the following statement true (T) or false (F)