When there are several close objects or a smaller object is overlaid on a bigger one, the objects can become entangled in one connectivity tree and should be deblended. A structure $Sj,k$ will be detached from the tree as a new root node if there exists at least one other structure at the same level belonging to the same tree and the following condition is fulfilled: $wj\u22121m<wjm>wj+1m$. Here, $wjm$ is the maximum wavelet coefficient of $Sj,k$; $wj\u22121m=max{Sj\u22121,l}$, where $Sj\u22121,l$ is the structure connected to $Sj,k$, such that the position of its maximum wavelet coefficient is closest to the position of the maximum of $Sj,k$, if $Sj,k$ is not connected to any structure at scale $j\u22121$ then $wj\u22121m=0$; and $wj+1m=max\u2009wj+1(x,y)|wj(x,y)\u2208Sj,k$, i.e., the maximum wavelet coefficient at scale $j+1$, such that its location belongs to $Sj,k$. Recursive application of this deblending procedure to the connectivity tree yields objects as independent structures of significant wavelet coefficients. Partial reconstruction of these objects as images is a nontrivial task. The simplest solution is to perform inverse wavelet transforms for each object, setting all wavelet coefficients not belonging to the object to zero.