Math 2270-1 Project 1, Fall 2002

It's all getting blurry now...

Warm-ups (don't turn in)

  • Spend a few minutes running the "demo" command in Matlab. Be sure to look at the "Matrices" section.
  • Use the "help" command to find out about the rref and rank commands.
  • Use matlab to find the rref and rank of the matrix A = [1 2 3 4; 5 6 7 8; 9 10 11 12; 13 14 15 16].
  • Use the "imagesc" command to look at the pictures contained in imdemos/saturn2, imdemos/eight, and imdemos/vertigo2. For example, to view the first picture, execute the commands "load imdemos saturn2", then "imagesc(saturn2)", then "axis('image')", then "colormap(gray)".

    • The project:

  • Select one of the following images from imdemos: saturn, tire, pout, trees, quarter, circuit, alumgrns, flower, rice, bonemarr.
  • Reshape your image (matrix) into a vector x, and convert the entries to double precision.
  • Construct a sparse matrix A which will blur your image over 5x5 neighboring pixels. You will need to use the "spdiags" command. Don't worry about what A does to the edges of your image.
  • Produce a plot of the blurred image y = A*x.
  • Turn in:
    (1) A plot of your original image.
    (2) The commands you used to produce the matrix A.
    (3) A plot of the blurred image y = A*x.
    (4) Suppose that you were given the blurred image y and the matrix A, you knew that y = A*x for some x, but you had no knowledge of the "true" image x. Could you recover x? Why or why not?