3 questions

[Pavan Kumar B]

sir ,

1. Why irregularities and irregular structures often carry information?

2.any well behaved signal is represented as a linear combination of exponentials (by fourier series) but how can we represent an image .is there any basis function ?

3.How do the contours of  l1  and l2   norm look like in 3 dimensions?

[NOC16 March - May]

Hi Pavan,

Let me answer your questions one by one:

1) Irregularities/ singularities often carries information. You can take an example of a seismic activity. We don't always have seismic activities at all times, therefore we would have a seismic plot of smooth variations. Now whenever there is a seismic activity, we would get spikes in our plot. So if we want to analyze when in the past all the seismic events have occurred or is there any seismic event occurring anywhere at present then what we need to study is the spikes. So it carries information of what we want to analyze. Similarly you can think of other examples such as edge detection in image processing etc.    

2) Similar to exponential (Fourier) basis, you can take wavelet basis. It would be then considered as wavelet representation of the image. What ever decomposition you can think in continuous domain there is an equivalent decomposition scheme for discrete domain also(which can be applied to images). e.g Cosine basis (as in DCT), exponentials (as in DFT), Wavelet bais (as in wavelet transformation) etc.

3) In 3D l1 norm would look like a octahedron (3 dimensional diamond structure) and l2 norm would look  like a 3 dimensional circle i.e. Sphere

Thanks

TA