this is for holding javascript data
Ardo Illaste edited res_fitting2.md
almost 10 years ago
Commit id: f9da871c2a8f4637bf24c903fe46d082ce98e47c
deletions | additions
diff --git a/res_fitting2.md b/res_fitting2.md
index cb56352..5e93d6f 100644
--- a/res_fitting2.md
+++ b/res_fitting2.md
...
In order to reconstruct the entire image with all the pixels it is also necessary to know the location of the pixels. The parameter vector \(\mathbf{p}_i\) is extended with the coordinates of the *i*-th pixel:
\[
\mathbf{r}_i \mathbf{p}_i =
\left[\mathbf{p}_i,x_i,y_i\right] \left[\mathbf{r}_i,x_i,y_i\right]
=\left[A_i, d_i ,\tau_{d,i},\tau_{r,i},\mu_i,x_i,y_i\right] =
\left[\mathbf{p}^s_{i}, \mathbf{p}^p_{i}\right],
\]
where \(\mathbf{p}^s_i=\left[A_i,d_i,\tau_{d,i},\tau_{r,i}\right]\) is the shape parameter vector, \(\mathbf{p}^p_i=\left[\mu_i,x_i,y_i\right]\) is the position parameter vector and the whole parameter vector
\(\mathbf{r}_i\) \(\mathbf{p}_i\) is obtained by combining the two.
The *k*-th event detected in pixel *i* is represented by vectors
\(\mathbf{p}^s_{i,k}\) and \(\mathbf{p}^p_{i,k}\). These vectors can be stacked to create an event matrix (E) for pixel *i*: