In the last post, I was complaining about the necessity to perform continuous wavelet transform in one dimension.
The problem with that is nature of my own data. I have 3D data, two spatial and single time axis. But all I can do is pick the one axis and do the analysis.
Since I’m trying to detect the oscillations emitted in the solar atmosphere, I decided to go with the time dimension as a basis for my analysis. This means, I will take pixel by pixel of my spacial dimensions and for each pixel do the separate wavelet analysis.
But what happens if the source of the oscillations is bigger than one pixel, or moves through space? Well, in short, this means I will underestimate the amount of oscillations and power carried by the oscillations.
Surprisingly, that is actually not a problem in the science. If a scientist underestimates an event, that is an error, but it is considered less of the error than to overestimate an event. Because science is not static. It develops and progresses every day. Each and every scientist puts a little piece of the puzzle to the overall collection of the human knowledge, making it more detailed, and more accurate.
So, when a scientist underestimates an event, she/he can rest assured that in the future, some other scientist will use improved techniques to make an estimate closer to the real value.
But, when scientist overestimates an event, then when the other scientist in the future shows that real value is way smaller, the first scientist lose a bit in the reputation because he/she was too careless.
Another tit-bit about science and scientists. In principle, every scientific work should be done in such way that anyone could repeat it and get same results. This principle makes scientist painfully honest, and careful not to overestimate their results. Because if they are caught in a lie, or overstating results, their career is basically over. The only chance left for some job is if some special interests can benefit from a lie or overestimating results.
That’s why science has a bunch of checks and balances that control honesty.
But, sometimes those checks and balances fail, allowing the lie or faulty work to sneak by. And if there is a particular interest involved, then the situation becomes even murkier, because special interests tend to manipulate news and public, in the best Goering fashion.
I was aware of the controversy that exists in certain branches of science, and if you follow the news, you know about it too. So I went in the area that currently does not have too much controversy. There is a bit, trickling from a climate research, trying to find a cause of global warming in Sun’s behavior. But luckily, Sun does not collaborate. We are in the period of surprisingly low solar activity, and yet, temperatures on the Earth keep on rising.
I will not go further into this polemics because I consider it a waste of time. We should instead discuss what we can do about climate change. I will just emphasize, Sun has nothing to do with the current global warming on the Earth.
Back to my work. Yes, chopping the 3D data into 1D slices will underestimate detection of the oscillations, because I tend to ignore lower power oscillations. Meaning if the source is the bigger than 1D, then I will lose parts of the power emitted from the edge of the source because it contains the lower energy. If the source moves, I will lose part of its emissions while it is in transit from one pixel to another, or maybe even all of the emission, depending on the speed of the movement of the source.
This points out that it would be neat to use multidimensional wavelet transform, an event the one that is discreet. But, before I even try that, I have to see how reliable such method is and I have to have a reason why should I do so. A scientific reason. So I will tackle that idea later when I get some results with already proven and tested technique.