Sparse multidimensional modal analysis using a multigrid dictionary refinement

EURASIP Journal on Advances in Signal Processing

Table 3 R-D sparse multigrid algorithm

- Input. A signal $y \in ℂ^{M_{1} M_{2} . . . M_{R}}$ R matrices $Φ_{0}^{(r)} \in ℂ^{M_{r} \times N_{r}}$ , a scaler λ and an integer L - Output. A sparse coefficient vector x_L-1∈ ℂ^N
For l = 0 up to l = L - 1 $\begin{gathered} Φ_{l} = Φ_{l}^{(1)} \otimes Φ_{l}^{(2)} \otimes \dots \otimes Φ_{l}^{(R)} \\ x_{l} = SAM(Φ_{l},y, λ) \end{gathered}$ For r = 1 up to r = R $Φ_{l + 1}^{(r)} = ADAPT(Φ_{l}^{(r)}, x_{l})$ End For End For.