Exact resolution of the sparse spectral unmixing problem

$$\min_{\boldsymbol{x}\in [0,1]^{Q}}\quad \frac{1}{2}\big|\big| \boldsymbol{y}-\mathbf{H}\boldsymbol{x}\big|\big|_{2}^{2}\quad \textrm{st. } \big|\big|\boldsymbol{x}\big|\big| _{0} \leq K, \quad\boldsymbol{1} _{Q} ^{\intercal} \boldsymbol{x} =1$$

Séminaire équipe SiMS - 23/09/2021

MimosaUnmix_1inst_meth $(pwd) 2 bb_homotopy_fcls eq
L2L0_ASC_ANC_BB_Rhom_fcls
Instance : SA_SNR40_K4_instance30
K = 2	 Q = 50	 N = 224	 ASC form : equality
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#(it) = 10	 #(node) = 19	 T = 0.083769	 card(L) = 2
xUB* = 1'	 34'	 
UB*  = 0.312598	sum(xUB*) = 1
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[...]
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#(it) = 100	 #(node) = 199	 T = 0.319659	 card(L) = 1
xUB* = 24	 39'	 
UB*  = 0.170461	sum(xUB*) = 1
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SA_SNR40_K4_instance30 - bb_homotopy_fcls
	T = 0.322625 (s)
	#(node) = 211	/ best(node) = 221
	UB*  = 0.170461
	xUB* :
		 x(24) = 	0.234965
		 x(39)' = 	0.765035
	sum(xUB*) = 1