Most of the modeling we do requires linear operations that predict data from models. However, in Imaging, the usual task is to find inverse of these operators to find the models from the data. This is where the Adjoint operator comes to rescue as a part of the inversion process. Adjoint of a matrix is … Continue reading Enjoy(nt) the Adjoints

Angular wavenumber

A very interesting thing I re-discovered today is the angular wavenumber. Although it seems like I had understood that pretty well long back, I had forgotten quite some things about it. The rumination came from my continuous learning process of Fourier Transform. While I seem to have gotten a hang of temporal Fourier transform, spacial … Continue reading Angular wavenumber

Born Approximation

http://sepwww.stanford.edu/data/media/public/docs/sep123/huazhong1/paper_html/node3.html

My notes on Laplace transform

The Laplace transform of a function f(t), defined for all real numbers t ≥ 0, is the function F(s), which is a unilateral transform defined by: $latex F(s)=\int_{0}^{\infty} f(t)e^{-st} dt$ where s is a complex number frequency parameter $latex s=\sigma +i\omega$, with real numbers $latex \sigma$ and $latex \omega$. In the case of the Laplace transform, … Continue reading My notes on Laplace transform