there are three images named terrain, trees, and noise, respectively, and you are given the corresponding three matrices for the three images as an excel file. Consider each image as a data collection where each column vector is a data item.
1. Write a function DCT_item that takes a data item (a vector) and returns the DCT of this data item.
2. Write a function DCT_collection that takes a data collection of vectors or data items (e.g., an image) and then call the DCT_item function to all the data items of this collection.
3. Given a collection of data items with all of the items transformed under DCT, propose a method to uniformly and consistently cut off the dimensionality of all the data items in the collection, and implement the method as another function. Call this function CUTOFF.
4. Apply CUTOFF to all the three image files respectively to generate three collections in a reduced dimensionality.