While studying image denoising, students often ask the following question: for a given noisy image (assume we know the noise power level \sigma_w), what is the lowest MSE that can be achieve by the best algorithm? Answering this question is not easy; in fact this question is pathological – a better-defined problem is to ask [...]
Archive for August, 2008
What is the lowest MSE we can achieve?
Posted in ee565 on August 28, 2008 | Leave a Comment »
What is aliasing?
Posted in wavelets on August 27, 2008 | Leave a Comment »
If you have never touched this topic, it is always good to start from wiki it:
http://en.wikipedia.org/wiki/Aliasing
Please keep in mind the definition given in wiki is not necessarily error-free, but since it can be modified by anyone and it is likely the collective wisdom brings it closer to the truth.
It is also important to note that [...]
The role of experiments in image processing
Posted in ee565 on August 25, 2008 | Leave a Comment »
Experimental chemists such as Belousov and Zhabotinskyuse chemicals, cups and heat source to show how a chemical reaction could show periodic patterns (if you have not seen it before, here is a Youtube link: http://www.youtube.com/watch?v=g3JbDybzYqk); and come up with theories to explain this fascinating phenomenon. Theoretical chemists then strive hard to explain why [...]
The classical image denoising problem
Posted in ee565 on August 25, 2008 | Leave a Comment »
There are several reasons why we start from the denoising problem. First, purely academically speaking, this is one of the mostly studied problems in image processing – you can easily find tons of papers in the literature and people’s interest has renewed in recent years. Secondly, it is the stepping stone to study other related [...]
Deterministic vs. Stochastic
Posted in wavelets on August 25, 2008 | Leave a Comment »
I would like to add another note before moving on to the main story of this course. The perspective we take on understanding wavelets is deterministic – just like Fourier transform, we always assume a deterministic input. However, it does not necessarily mean that transforms (Fourier or wavelet) only work for deterministic signals. In fact, [...]
A side track of Spectral Analysis: Fractals
Posted in wavelets on August 24, 2008 | 1 Comment »
Usually when you read stories about wavelets, it goes from FT to short-time FT (that is what Morlet and Grossmann have pursued). Another more interesting (in my own opinion) track is the one taken by B. Mandelbrot (the father of fractals). Even though the relationship between wavelet theory and fractal theory is not that tight [...]
Interest is the best teacher
Posted in ee565 on August 22, 2008 | Leave a Comment »
The first message I pass on to you is: if you have to learn something right, you had better learn to love it first.
To learn image processing right, you got to have an interest in this subject. How to have a passion for image processing? Here are some tips:
1. If you love sports (say WVU [...]
Spectral analysis and digital filters
Posted in wavelets on August 21, 2008 | 2 Comments »
Spectral (frequency-domain) analysis has a long history since the invention by J. Fourier in the early 19-th century. Although now Fourier transform appears such a versatile tool, it is interesting to note the initial setback met by Fourier to get his work published. You can simply go to http://en.wikipedia.org/wiki/Joseph_Fourier and learn more about the [...]
Where do wavelets come from?
Posted in wavelets on August 18, 2008 | 3 Comments »
In 1996, Ingrid Daubechies – one of the pioneers in wavelet theory – wrote an article titled “Where do wavelets come from? A personal point of view” (it can be found in the course website). This article contains lots of useful non-technical background information about the historical development of wavelet theory in 1980s. Although the [...]
Welcome to the wavelet course
Posted in wavelets on August 17, 2008 | 1 Comment »
This is a new course I design for graduate students with diverse background. I expect that students taking this course come from a wide range of fields: math, statistics, engineering and health science. The theory of wavelets and filter banks (the engineering jargon) also roots from several technical fields that appear irrelevant at first: Harmonic [...]
