Comparison of decomposition algorithms for identification of single motor units in ultrafast ultrasound image sequences of low force voluntary skeletal muscle contractions

Table 1 A summary of the selected decomposition algorithms and their parameters

Algorithm	Parameter (λ or α)	Domain	Description
sPCA	λ = 150	Spatial	Extension of principal component analysis (PCA) by sparse constraint, i.e., uses L₁ penalty on the spatial loadings in the optimization procedure. λ denotes the number of non-zero pixels, a parameter equal to 150 and 250 corresponds to territories with 4.3 and 5.6 mm in diameter
sPCA	λ = 250	Spatial
stICA	α = 0.0	Temporal	Separation by optimizing a joint entropy energy function based on mutual entropy and infomax with a kurtosis-based cost function. α = 0.8 has been used previously [11, 12], i.e., weighs 0.8 in spatial and 0.2 in temporal separation
	α = 0.8	Spatiotemporal
	α = 1.0	Spatial
stJADE	α = 0.0	Temporal	Joint diagonalization of fourth-order cumulant tensor in separation procedure. A low α weighs more on temporal separation
	α = 0.5	Spatiotemporal
	α = 1.0	Spatial
stSOBI	α = 0.0	Temporal	Autocovariance matrices (fixed number, 12) for joint diagonalization of a set of symmetrized multidimensional autocovariances [28, 29]. Similar to stJADE, a low α weighs more on temporal separation
	α = 0.5	Spatiotemporal
	α = 1.0	Spatial

α-parameter weighs spatial- and temporal separation, a λ-parameter relates to the number of non-zero pixels
sPCA sparse principal components, stICA spatiotemporal independent component analysis, stJADE spatiotemporal joint approximation diagonalization of eigenmatrices, and stSOBI spatiotemporal second-order blind identification

ISSN: 1756-0500