ex-6: Finished writing RL deconvolution

notes/sections/6.md

@@ -92,7 +92,7 @@ of bins default set $n = 150$. In @fig:original an example is shown.
   $I(\theta)$.](images/6_original.pdf){#fig:original}
 
 
-## Gaussian noise convolution 
+## Gaussian noise convolution {#sec:convolution}
 
 The sample must then be smeared with a Gaussian noise with the aim to recover
 the original sample afterwards, implementing a deconvolution routine.  
@@ -316,7 +316,8 @@ the leght of the vector the same as it was produced by a DFT. This makes it
 necessary to rearrange the two halfs of the final result.
 
 At the end, the external bins which exceed with respect to the original signal
-are cut away in order to restore the original number of bins $n$.
+are cut away in order to restore the original number of bins $n$. Results are
+shown in @fig:convolved.
 
 
 ## Unfolding with Richardson-Lucy
@@ -367,6 +368,16 @@ $$
 where the division and multiplication are element wise, and
 $P^{\star}$ is the flipped point spread function.
 
+When implemented, this method results in an easy step-wise routine:
+
+  - create a flipped copy of the kernel;
+  - elect a zero-order estimate for {$c_i$};
+  - compute the convolutions with the method described in @sec:convolution, the
+    product and the division at each step;
+  - proceed until a given number of reiterations is achieved.
+
+In this case, the zero-order was set as $c_i = 0.5 \, \forall i$. Results are
+shown in @fig:convolved.
 
 ---