Linear Algebra for Digital Image Processing

[SpaceDomain]

Hello all,

I am taking a course on Digital Image Processing that starts in a week.

I do not know linear algebra very well and am concerned this will be a problem.

I understand the stuff that is taught at the beginning of a linear algebra course, which I guess is better called Matrix Algebra.

I understand most of the non-abstract things such as:
-Systems of linear equations (with and without matrices)
-Vectors
-Matrix Operations
-Gaussian Elimination
-Inverse Matrices
-Determinants
-Solving the Ax = b equation
-Spanning a Set

And here are the more abstract things that I understand at a CONCEPTUAL level:
-Linear Transformations
-The basics of Eigenvalues
-Subspaces
-Linear Independence
-Standard Basis
-Eigenvalues and Eigenvectors

But here are the things that I never learned to fully understand:
-General Bases (and change of basis)
-Dimension
-Rank
-Kernel and Range of Subspaces
-Orthogonality
-WHAT THE PURPOSE OF SUBSPACES ARE!


For anyone that has taken an Image Processing Course, what portions of linear algebra should I brush up on?

I am of course using the book "Digital Image Processing" by Gonzales and Woods.

 

[AlephZero]

You may find that the "abstract" linear algebra topics make more sense when you get some concrete examples of what they useful for in image processing.

Rather than more linear algebra, you might also want to revise Fourier transforms and any other digital signal processing you have done. One way to think about image processing is that it is "2-dimensional DSP", or even 3-dimensional DSP in the case of movies as compared with single images.

 

[SpaceDomain]

What parts of Fourier Transform should I brush up on?

I of course have studied the CTFT, DTFT, DFT, and Z-transform.

Is it safe to say I won't see much of the CTFT in an intro digital image processing course?

I didn't really understand the FFT, but I do understand the DFT (sampling the DTFT at equally spaced intervals, etc.).

What about up/down sampling?