Wednesday, June 6, 2012

I'm stuck, so going to try to redefine (simplify) the problem itself

Hmm my problem is motion compensation, in Computed Tomography (CT) (as in 'CT or CAT scans').

The usual tomographic reconstruction technique assumes that the body, or object, is stationary.

Now _my_ object is dynamic (think lung motion for example):
$f (x, t)$

So to scan and reconstruct a dynamic object like a breathing lung is the problem I chose to work on.

And after several attempts at it, I think I am going to simplify the problem itself, because currently I assume total generality of both original object and the motion, making no assumptions about either of them.
Several solutions exist because the problem is not invertible uniquely, because of the nature of the whole thing.
So I try to obtain one solution (among several solutions that exist) by minimizing some objective.

And i'm stuck. At least, the whole thing I have right now, looks inelegant and clumsy that I don't find any thrill of  continuing it this way. (In other words i ended up with some nasty nonlinear PDEs.)

And since I've been stuck for a while I am now going to simplify the problem itself, and then solve the simpler problem.

Monday, February 27, 2012

A book

Found this in the library.
Nice one.

"Linear operators and ill-posed problems" by M. M. Lavrentev and L. Ya. Savelev.

Sunday, January 1, 2012

Choosing multiple problems helps when you're stuck

From this page On choosing problems to work on: advice from John H. Conway

I quote:
"1. Work at several problems at a time. If you only work on one problem and get stuck, you might get depressed."

Hmmm I __had__ read about this earlier while doing my literature survey phase. Now that i'm working on a problem, and really getting stuck, I realize I am working on __only one__ problem! No wonder it feels depressing and highly stresful when I can't get things moving, also causing burn out due to mental hard work and extreme persistent focus on just one thing for too long.

It's the same long term stress that a deer in a cage would feel when the next cage has a hungry tiger in it. Long term persistent focused stress. Not good for my mental / physical health. Hmm... I'm waiting for the high that comes when I really solve the problem.

I continue the quoting:
"It is nice to have an easier back-up problem. The back-up problem will work as an anti-depressant and will allow you to go back to your difficult problem in a better mood. John told me that for him the best approach is to juggle six problems at a time."

Ah ... it's the right time to find a bunch of some easier problems. As a new beginner novice researcher I've just familiarized myself with the field and literature and have got deeply stuck on one single problem and is the right spot for me to find a bunch of smaller ones for dithering my emotions :)
The very thought of playing with smaller problems for a while now is relaxing....

(PS: I usually do have other 'problems' to chew on like the tiny ones coming out of my DIYing. But it's nice to have side-problems that directly aid the research-part of my life.)

Tuesday, October 4, 2011

Monday, August 1, 2011

Copied from the page:
"Asymptote is a powerful descriptive vector graphics language for technical drawing, inspired by MetaPost but with an improved C++-like syntax. Asymptote provides for figures the same high-quality typesetting that LaTeX does for scientific text."