Revert "Changed from T_j to indexing in comparison section"

This reverts commit c4a88363c5.

latex/thesis/chapters/analysis_of_results.tex

@@ -87,7 +87,7 @@ return $\boldsymbol{s}$
                 \underbrace{\boldsymbol{\gamma}^\text{T}\tilde{\boldsymbol{c}}}
                     _{\text{Likelihood}}
                 + \underbrace{\sum_{j\in\mathcal{J}} g_j\left(
-                    \tilde{\boldsymbol{c}}_{N_c\left( j \right) } \right) }
+                    \boldsymbol{T}_j\tilde{\boldsymbol{c}} \right) }
                     _{\text{Constraints}} \\
             \text{subject to}\hspace{5mm} &
                 \tilde{\boldsymbol{c}} \in \mathbb{R}^n
@@ -104,8 +104,8 @@ while stopping criterion not satisfied do
         \scaleto{\nu \cdot \boldsymbol{\gamma}^{\text{T}}\tilde{\boldsymbol{c}}}{8.5pt}}
         \left( \boldsymbol{z} - \boldsymbol{u} \right) $
     $\boldsymbol{z}_j \leftarrow \textbf{prox}_{\scaleto{g_j}{7pt}}
-        \left( \tilde{\boldsymbol{c}}_{N_c\left( j \right) }
-            + \boldsymbol{u}_{N_c\left( j \right) } \right) \hspace{1mm}\forall j\in\mathcal{J}$
+        \left( \boldsymbol{T}_j\tilde{\boldsymbol{c}}
+            + \boldsymbol{T}_j\boldsymbol{u} \right) \hspace{5mm}\forall j\in\mathcal{J}$
     $\boldsymbol{u} \leftarrow \boldsymbol{u}
         + \tilde{\boldsymbol{c}} - \boldsymbol{z}$
 end while
@@ -130,7 +130,6 @@ $\boldsymbol{\gamma}^\text{T}\tilde{\boldsymbol{c}}
     \left( \boldsymbol{T}_j\tilde{\boldsymbol{c}} - \boldsymbol{z}_j \right) 
     + \frac{\mu}{2}\sum_{j\in\mathcal{J}}
     \lVert \boldsymbol{T}_j\tilde{\boldsymbol{c}} - \boldsymbol{z}_j \rVert^2_2$}%
-\todo{Explain the notation $\tilde{\boldsymbol{c}}_{N_c\left( j \right) }$}%
 %
 \noindent The objective functions of both problems are similar in that they
 both comprise two parts: one associated to the likelihood that a given