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I am a graduate student in applied math, specializing mostly in harmonic analysis. My undergraduate studies were mostly in pure math but I realized I prefer the applied/computational side. I was hoping to undertake a reasonable project which will lead to a short, but publishable paper in the area of signal processing. I have toyed around with a few ideas but I just cannot come up with something concrete as of yet.

Topics of interest:

  1. Data compression
  2. Distortion/noise
  3. Optimization problems
  4. Image processing
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closed as primarily opinion-based by lennon310, Marcus Müller, MBaz, Peter K. Apr 27 '17 at 16:48

Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise. If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ I think this might be a bit too open-ended. I mean, each of the four topics is huge, and has thousands of published papers and books on them. So, toy around a little more to narrow things down! $\endgroup$ – Marcus Müller Apr 27 '17 at 8:32
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    $\begingroup$ But:I'd use your unique academic background: You come from pure math and now could take your knowledge and apply the methods to a more applied problem.That's how progress is often made in anything mathematical,so maybe actually pick your favourite topic(thesis topic, even?)from your undergrad and find an application of it in one of the four topics your mention.(e.g.you loved algebraic number theory, and now you apply that knowledge to transporting data over distorting/noisy channels)(or:you loved stochastic geometry,now you'd apply that to networks of nodes needing to exchange compressed data) $\endgroup$ – Marcus Müller Apr 27 '17 at 8:36
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    $\begingroup$ Notice, also, that you're setting yourself up for a task that typically is done by professors of significant experience:Deciding totally freely in which research direction to go to get publishable*(and, thus, *fundable)research(rather than just interesting)is,as far as I can tell from the professor hiring processes that I've observed,one of the main qualities that an experienced person that you'd hire to lead a team of researchers needs to bring,when he's not going to a lot of the research himself, but more coordinate and support his PhD candidates and postdocs.You're at the other end,yet! $\endgroup$ – Marcus Müller Apr 27 '17 at 8:42
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    $\begingroup$ So, I'd really take advantage of that: Find some PhD candidate, or some postdoc, or some professor that you feel you can relate to, research-wise. That's usually just based on a hunch, unless you've seen a scientific talk of them (which, by the way, is a great idea: if you can, find out when a local research group has their "we present each other with what we've figured out" meetings (often monthly, or so), and ask politely if you can be guest in one of these seminars.You'll typically understand nothing,but you'll see what topics are out there.Take a few notes,mail the cool folks,ask them! $\endgroup$ – Marcus Müller Apr 27 '17 at 8:51
  • $\begingroup$ Thanks for the detailed and helpful advice! If you put these comments as an answer, I'll upvote and accept it! $\endgroup$ – Kernel_Dirichlet Apr 27 '17 at 13:35
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This is very simple. You need an inter-disciplinary domain where all (and more) of your interests are satisfied, while being very publishable, employable and fun. Easy!! Jump into the bleeding edge of Speech Recognition.

There is TONS of current research is Automatic Speech Recognition (ASR). The domain is very multi-disciplinary (applied math, linguistics, computer science, optimization, electrical engineering) with applications to just about every part of life where a speech interface can work (healthcare, mobile assistants, in-car, entertainment/gaming, education, etc)

For example, state of the art systems like Baidu's Deep Speech 2 use convolutional neural networks (CNNs) to process speech spectrograms (DSP!). CNNs have revolutionized image processing since 2012. The CTC objective that is optimized during training is a very interesting loss function for supervised training of sequences. enter image description here

Finally, have a look at these 2016 Stanford University student projects, notably those on speech recognition. This should give you some ideas of what scope or size of project makes sense.

Good luck!!

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