## 3 Proposed Joint Decoding (JD) Framework for Video  
In this section, the proposed joint decoding (JD) framework for single view video is discussed. The archetype of the complete system is shown in Figure 1. At the encoder side, we consider a visual node S, capturing a scene (video), and block-based compressive sensing (BCS) is applied on each frame in the video sequence for encoding. The encoded frames are then independently transmitted to the host workstation. \begin{table}
\begin{tabular}{p{56.9 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Work** & **Scheme** & **Description** & **Issues** \\ \hline \multirow{11}{*}{[12]} & \multirow{6}{*}{[13]} & \multirow{6}{*}{[14]} & \multirow{6}{*}{[15, 16]} & It is usually viable for video applications, as it assumes that the sparsity pattern develops progressively from frame to frame. Besides, Prediction make use of state dynamics and measurement models. The prediction might fail due to incorrect initialization of the model and filter. \\  & & & \\ \cline{3-4}  & & & \\ \cline{3-4}  & & & \\ \cline{3-4}  & & & \\ \cline{3-4}  & & & \\ \hline \multirow{11}{*}{[15, 16]} & \multirow{6}{*}{[17]} & \multirow{6}{*}{[18]} & Incorporates disparity estimation and compensation prediction methods into the reconstruction process of BCS-SPL that generate side information aiding final reconstruction. \\ \cline{3-4}  & & & \\ \cline{3-4}  & & & \\ \cline{3-4}  & & & \\ \cline{3-4}  & & & \\ \cline{3-4}  & & & \\ \cline{3-4}  & & & \\ \hline \multirow{11}{*}{[17]} & \multirow{6}{*}{[18]} & \multirow{6}{*}{[19]} & Uses motion-based prediction and residual encoding to optimize the sample allocation among the estimated and residual encoding steps. \\ \cline{3-4}  & & & \\ \cline{3-4}  & & & \\ \cline{3-4}  & & & \\ \cline{3-4}  & & & \\ \cline{3-4}  & & & \\ \cline{3-4}  & & & \\ \cline{3-4}  & & & \\ \hline \multirow{11}{*}{[19]} & \multirow{6}{*}{[19]} & \multirow{6}{*}{[18]} & The scheme uses low sample rate, ME/MC and fusion method to produce a view prediction, which helps in the generation of an ultimate view for the multi-view video. \\ \cline{3-4}  & & & \\ \cline{3-4}  & & & \\ \cline{3-4}  & & & \\ \cline{3-4}  & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary of various CS-based residual coding schemes for visual reconstruction. At the host workstation (decoder), a sequence of J recurrent frames is received from the visual node S, referred to as a group of pictures (GoP). As the video is uninterrupted, it is established that the current GoP is tailed by another GoP. The GoP comprises a keyframe and J-1 non-key frames, represented as \(\mathrm{F_{K}}\) (the primary) and \(\mathrm{F_{NK}}\). The encoding of \(\mathrm{F_{K}}\) and \(\mathrm{F_{NK}}\) is performed at the subrate of \(\mathrm{M_{K}}\) and \(\mathrm{M_{NK}}\), respectively, with \(\mathrm{M_{K}}>\mathrm{M_{NK}}\). At the visual node (encoder), each frame \(\mathrm{F_{x}}\) (where x is the frame number) in the video sequence is initially portioned into a small block of \(16\times 16\). Then, the sensing matrix \(\Phi_{\mathrm{x}}\) as in Equation (1) is used to sample each block within a frame producing a set of measurements (\(\mathrm{Y_{x}}\)) as in Equation (2) [20; 21; 22]:  
\[\Phi_{\mathrm{x}}=\left[ \begin{array}{ccc}\Phi_{\mathrm{x}}&\cdots&0\\ \vdots&\ddots&\vdots\\ 0&\cdots&\Phi_{\mathrm{x}}\end{array} \right] \tag{1}\]  
Figure 1: Archetype of the complete system for single-view video coding using the proposed JD (joint decoding). \[\mathrm{Y_{x}}=\Phi_{x}\mathrm{F_{x}} \tag{2}\]  
The set of measurements (\(\mathrm{Y_{x}}\)) produced at the encoder is sent to the host workstation (server) independently. At the server side (decoder), firstly, the received encoded frames (\(\mathrm{Y_{x}}\)) are decoded independently (frame by frame) using the total variation (TV) minimization [23; 24] problem till a complete GoP is obtained.