fix important bug: use unfolding operator instead of Smooth Projection Operator

Author: haotian127

src/LP-HGLET.jl

@@ -69,8 +69,8 @@ function LPHGLET_Synthesis(dvec::Matrix{Float64}, GP::GraphPart, BS::BasisSpec,
                 # standardize the eigenvector signs
                 standardize_eigenvector_signs!(vec)
 
-                # construct smooth orthognal projector custom to current region
-                P = Uf[indrs, :]' * Uf[indrs, indrs]
+                # construct unfolder operator custom to current region
+                P = Uf[indrs, :]'
 
                 # reconstruct the signal
                 f += (P * vec) * dmatrix[indr, j, :]
@@ -150,8 +150,8 @@ function LPHGLET_Analysis_All(G::GraphSig, GP::GraphPart; ϵ::Float64 = 0.3)
             vec_sym = vec_sym[:, end:-1:1]
             standardize_eigenvector_signs!(vec_sym)
 
-            # construct smooth orthognal projector custom to current region
-            P = Uf[indrs, :]' * Uf[indrs, indrs]
+            # construct unfolding operator custom to current region
+            P = Uf[indrs, :]'
             # obtain the expansion coefficients
             dmatrixlH[indr, j, :] = (P * vec)' * G.f
             dmatrixlHsym[indr, j, :] = (P * vec_sym)' * G.f

src/LP-NGWP.jl

@@ -230,8 +230,8 @@ end
 
 function const_meyer_wavelets(𝚽, Uf; idx = 1:size(Uf, 1))
     N = size(𝚽, 1)
-    # assemble smooth orthogonal projector custom to nodes `idx`
-    P = Uf[idx, :]' * Uf[idx, idx]
+    # assemble unfolding operator custom to nodes `idx`
+    P = Uf[idx, :]'
     if diag(P) == χ(idx, N)
         B = 𝚽[:, idx]
     else