Sparse Representation of Transients Based on Wavelet Basis and Majorization-Minimization Algorithm for Machinery Fault Diagnosis

Table 1

Procedures of these two methods: the proposed algorithm and wavelet-assisted SALSA algorithm.

The proposed algorithm	Wavelet-assisted SALSA Algorithm
(1) Set k, 𝑐0, 𝜆	(1) Set 𝑘=0, 𝑣0, 𝑑0, 𝑐0, 𝜆, 𝜇
(2) Repeat	(2) Repeat
Λ𝑘=diag𝑐𝑘	𝑐𝑘+1=argmin𝑐Mor⋅𝑐𝑘−𝑦^22+𝜇𝑐𝑘−𝑣𝑘−𝑑𝑘^22
𝑐𝑘+1=argmin𝑐12𝑦−Mor⋅𝑐𝑘^22+𝜆2𝑐𝑘^∗Λ𝑘^−1𝑐𝑘	𝑣𝑘+1=argmin𝑣𝜆𝑣𝑘1+𝜇2𝑐𝑘+1−𝑣𝑘−𝑑𝑘^22
𝑘⟵𝑘+1	𝑑𝑘+1=𝑑𝑘−𝑐𝑘+1−𝑣𝑘+1
until stopping criterion is satisfied.	𝑘⟵𝑘+1
	until stopping criterion is satisfied.