I'm learning about the Polar Sine Transform equation, which is denoted by:
Sorry i had to attach an image, as I do not know how to write the integral part in Mathjax
I'm implementing this in Matlab for an image processing task, $r$ and $\theta$ are polar coordinates of an image block, hence matrices of equal dimension. $n$ and $l$ are integers denoting order and repetition.
Now, I need some help on the $[sin(\pi n r^2) e^{il\theta}]*$ part of the equation. You see I mentioned before that $r$ and $\theta$ are polar coordinates and are represented as a matrix in Matlab for an image block, but I'm not entirely sure if $r^2$ is a power of the matrix $r$ or the element wise power of $r$.
Could anyone explain if it should be interpreted as ordinary matrix power or element wise? Also, for the exponential part of the equation, $i$ is an imaginary unit, hence i wonder if the "*" complex conjugate symbol is used just for that purpose?
EDIT I forgot to add that for digital images, the PST can be approximately calculated where integral is basically replaced as a sum instead, hence programming wise, we would use the sum.
$H_{nl}(x,y)$ is the same for $sin(\pi n r^2)$ above.
You're mixing up programming and math. In the math, $r$ is a number, which is being integrated over. This is easily seen in this formula because you can see where $r$ is being integrated over. In your implementation, you might define $r$ to be a matrix, so that you can then define a matrix of values of the integrand at each pair $(r,\theta)$ in some grid, and then apply some quadrature rule to this matrix (for fixed $n,l$) to compute each entry of $M$. If you do that, then definitely the $r^2$ in this formula will appear as r.^2 in your program.