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Archive for November, 2008

Career Advices to MS Students

When global economy is gloomy, it becomes even more important to understand the job market, the profession you plan to engage and the psycology behind all career development processes.
1. Preparation in the school. There is no doubt that your training in the graduate school will play an important role in your career. However, what is [...]

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I am writing this essay for first-year or second-year PhD students who are still early in their research training. Since students taking my wavelet course have diverse background, I try to provide general advices regardless of the technical field (of course your PhD advisor should be a better resource on research methodology in your own [...]

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I hope my effort on connecting two-channel filter banks in the discrete space to scaling/wavelet functions in the continuous space at least makes some sense to you. This part is not the meat of this course (you certainly don’t need to worry about it for exams :->). But the underlying relationship between two seemingly different [...]

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Scientific discovery, as of today, still largely remains a mystery. How do we think? This question has puzzled philosophers and scientists for centuries. Many important scientific discoveries are the consequence of prepared mind (those who intentionally pursue the truth in a logical path and manage to be the first to touch the finish line); but [...]

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The idea of multiresolution

It is not easy to find out when and where exactly this idea of multiresolution came about. Apparently wikipedia attributes multiresolution analysis (MRA) to S. Mallat and Y. Meyer for their pioneering work on wavelet-based MRA. However, the idea of MRA appeared much earlier than the born of wavelets. The pyramid-based image representation was suggested [...]

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If you are curious about how I graded the midterm project, here is what I did: for each of the five problems, I grouped your submissions and picked the best submission to each problem (these sample submissions have been posted to the course website). Among these five best submissions, I think Othman’s work clearly stands [...]

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Restoration of a signal contaminated by additive white Gaussian noise is a classical problem in signal processing which dated back as early as Wiener’s filter solution. Despite the optimality of Wiener filtering for stationary Gaussian processes, most signals in real worlds are characterized by nonstationarity and non-Gaussianity. That is why signal modeling plays an essential [...]

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