*2.2. BPL Reconstructions*

The Q.Clear algorithm introduces a noise control termβR(x) to the objective function used in OSEM reconstructions, where β is the parameter controlling the strength and R(x) is defined as (1):

$$\mathbf{R(x)} = \sum\_{\mathbf{j}=1}^{\text{B}\_{\text{V}}} \sum\_{\mathbf{k} \in \text{N}\_{\text{j}}} \mathbf{w}\_{\mathbf{j}} \mathbf{w}\_{\mathbf{k}} \frac{\left(\mathbf{x}\_{\text{j}} - \mathbf{x}\_{\text{k}}\right)^{2}}{\left(\mathbf{x}\_{\text{j}} + \mathbf{x}\_{\text{k}}\right) + \gamma \left|\mathbf{x}\_{\text{j}} - \mathbf{x}\_{\text{k}}\right|} \tag{1}$$

where nv refers to the number of voxels, Nj is the set of neighboring voxels of voxel j, wjwk is the weight of the local smoothing value which depends on the distance between voxels j and k, x is the activity in a voxel and γ is the parameter controlling edge preservation [36].
