Computable performance guarantees for compressed sensing matrices

Cho, Myung; Vijay Mishra, Kumar; Xu, Weiyu

doi:10.1186/s13634-018-0535-y

EURASIP Journal on Advances in Signal Processing

Table 8 α_k comparison and execution time - Partial Fourier Matrix

From: Computable performance guarantees for compressed sensing matrices

\(\underset {(m \times n)}{A}\)	Algo.	α ₁	α ₂	α ₃	α ₄	α ₅	k _max ^d
(a) α_k comparison
20 × 40	Pick-1	0.19	0.39	0.59	0.78	0.98	2/2.0
	Pick-2	0.19	0.36	0.55	0.73	0.91	2/2.2
	Pick-3	0.19	0.36	0.47	0.64	0.80	3/2.7
	1-Step TSA	0.19	0.36	0.47	0.61	0.70	3/2.7
	2-Step TSA	0.19	0.36	0.47	0.61	0.70	3/2.7
	3-Step TSA	0.19	0.36	0.47	0.61	0.70	3/2.7
	LP^a	0.19	0.39	0.59	0.78	0.98	2/2.0
	SDP^b	0.19	0.39	0.59	0.78	0.98	2/2.0
	ESM^c	0.19	0.36	0.47	0.61	0.70	3/2.7
24 × 40	Pick-1	0.15	0.31	0.47	0.62	0.78	3/2.8
	Pick-2	0.15	0.27	0.42	0.55	0.69	3/3.0
	Pick-3	0.15	0.27	0.38	0.51	0.64	3/3.4
	1-Step TSA	0.15	0.27	0.38	0.49	0.59	4/3.5
	2-Step TSA	0.15	0.27	0.38	0.49	0.59	4/3.5
	3-Step TSA	0.15	0.27	0.38	0.49	0.59	4/3.5
	LP	0.15	0.31	0.47	0.62	0.78	3/2.8
	SDP	0.15	0.31	0.47	0.62	0.78	3/2.8
	ESM	0.15	0.27	0.38	0.49	0.59	4/3.5
28 × 40	Pick-1	0.12	0.25	0.37	0.50	0.62	4/3.6
	Pick-2	0.12	0.23	0.35	0.47	0.58	4/4.0
	Pick-3	0.12	0.23	0.32	0.44	0.54	4/4.0
	1-Step TSA	0.12	0.23	0.32	0.41	0.50	4/4.0
	2-Step TSA	0.12	0.23	0.32	0.41	0.50	4/4.1
	3-Step TSA	0.12	0.23	0.32	0.41	0.50	4/4.1
	LP	0.12	0.25	0.37	0.50	0.62	4/3.6
	SDP	0.12	0.25	0.37	0.50	0.62	4/3.6
	ESM	0.12	0.23	0.32	0.41	0.50	4/4.1
32 × 40	Pick-1	0.09	0.19	0.29	0.38	0.48	5/4.7
	Pick-2	0.09	0.17	0.27	0.36	0.44	5/4.7
	Pick-3	0.09	0.17	0.25	0.35	0.43	5/4.7
	1-Step TSA	0.09	0.17	0.25	0.33	0.39	5/4.7
	2-Step TSA	0.09	0.17	0.25	0.33	0.39	5/4.7
	3-Step TSA	0.09	0.17	0.25	0.33	0.39	5/4.7
	LP	0.09	0.19	0.29	0.38	0.48	5/4.7
	SDP	0.09	0.19	0.29	0.38	0.48	5/4.7
	ESM	0.09	0.17	0.25	0.37	0.39	5/4.7
(b) Execution time (Unit: second)
20 × 40	Pick-1	0.31	0.31	0.31	0.31	0.31
	Pick-2	0.31	10.85	10.85	10.85	10.85
	Pick-3	0.31	10.85	260.41	260.41	260.41
	1-Step TSA	0.47	9.72	70.57	329.28	3.60e3
	2-Step TSA	0.47	11.97	18.54	45.18	3.36e3
	3-Step TSA	0.47	11.97	291.29	297.45	633.12
	LP	0.49	0.77	0.53	0.59	0.51
	SDP	33.93	2.34e3	2.65e3	2.91e3	2.60e3
	ESM	0.31	10.85	260.41	4.1e3	6.0e4
24 × 40	Pick-1	0.39	0.39	0.39	0.39	0.39
	Pick-2	0.39	11.51	11.51	11.51	11.51
	Pick-3	0.39	11.51	302.86	302.86	302.86
	1-Step TSA	0.48	12.12	76.21	407.67	2.77e3
	2-Step TSA	0.48	12.52	21.46	107.00	1.83e3
	3-Step TSA	0.48	12.52	306.43	426.17	1.36e3
	LP	0.62	0.56	0.66	0.59	0.58
	SDP	41.13	2.39e3	2.66e3	2.63e3	2.56e3
	ESM	0.39	11.51	302.86	4.5e3	6.4e4
28 × 40	Pick-1	0.43	0.43	0.43	0.43	0.43
	Pick-2	0.43	13.29	13.29	13.29	13.29
	Pick-3	0.43	13.29	341.05	341.05	341.05
	1-Step TSA	0.50	8.70	31.53	272.68	731.90
	2-Step TSA	0.50	12.99	16.85	47.45	544.79
	3-Step TSA	0.50	12.99	317.40	410.47	553.67
	LP	0.65	0.67	0.71	0.67	0.75
	SDP	40.51	2.17e3	2.29e3	2.80e3	2.63e3
	ESM	0.43	13.29	341.05	4.7e3	6.5e4
32 × 40	Pick-1	0.57	0.57	0.57	0.57	0.57
	Pick-2	0.57	17.24	17.24	17.24	17.24
	Pick-3	0.57	17.24	385.26	385.26	385.26
	1-Step TSA	0.52	6.39	22.35	101.67	451.62
	2-Step TSA	0.52	13.38	18.65	49.46	372.35
	3-Step TSA	0.52	13.38	326.40	476.55	1.02e3
	LP	0.86	0.89	0.78	0.75	0.76
	SDP	46.51	2.41e3	2.62e3	2.53e3	2.75e3
	ESM	0.57	17.24	385.26	4.8e3	6.8e4

^aLinear programming [8]
^bSemidefinite programming [3]
^cExhaustive search method
^dMedian/arithmetic mean

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