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 7 α_k comparison and execution time - Gaussian 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	0.28	0.55	0.81	1	1	1/1.1
	Pick-2	0.28	0.45	0.66	0.85	1	2/1.9
	Pick-3	0.28	0.45	0.57	0.76	0.92	2/1.9
	1-Step TSA	0.28	0.45	0.57	0.67	0.75	2/1.9
	2-Step TSA	0.28	0.45	0.57	0.67	0.75	2/1.9
	3-Step TSA	0.28	0.45	0.57	0.67	0.75	2/1.9
	LP^a	0.28	0.50	0.67	0.84	0.98	2/1.6
	SDP^b	0.28	0.49	0.66	0.81	0.95	2/1.8
	ESM^c	0.28	0.45	0.57	0.67	0.75	2/1.9
24 × 40	Pick-1	0.23	0.46	0.67	0.87	1	2/2.0
	Pick-2	0.23	0.37	0.53	0.69	0.85	2/2.1
	Pick-3	0.23	0.37	0.46	0.61	0.75	3/2.8
	1-Step TSA	0.23	0.37	0.46	0.57	0.65	3/2.8
	2-Step TSA	0.23	0.37	0.46	0.57	0.65	3/2.8
	3-Step TSA	0.23	0.37	0.46	0.57	0.65	3/2.8
	LP	0.23	0.41	0.56	0.71	0.84	2/2.0
	SDP	0.23	0.41	0.55	0.70	0.82	2/2.0
	ESM	0.23	0.37	0.46	0.57	0.65	3/2.8
28 × 40	Pick-1	0.18	0.36	0.53	0.70	0.86	2/2.0
	Pick-2	0.18	0.31	0.46	0.59	0.72	3/3.0
	Pick-3	0.18	0.31	0.41	0.54	0.66	3/3.0
	1-Step TSA	0.18	0.31	0.41	0.49	0.57	4/3.5
	2-Step TSA	0.18	0.31	0.41	0.49	0.57	4/3.5
	3-Step TSA	0.18	0.31	0.41	0.49	0.57	4/3.5
	LP	0.18	0.34	0.49	0.61	0.72	3/3.0
	SDP	0.18	0.34	0.48	0.60	0.71	3/3.0
	ESM	0.18	0.31	0.41	0.49	0.57	4/3.5
32 × 40	Pick-1	0.14	0.29	0.42	0.55	0.67	3/3.0
	Pick-2	0.14	0.24	0.37	0.47	0.58	4/3.8
	Pick-3	0.14	0.24	0.33	0.44	0.53	4/4.2
	1-Step TSA	0.14	0.24	0.33	0.40	0.47	5/4.9
	2-Step TSA	0.14	0.24	0.33	0.40	0.47	5/4.9
	3-Step TSA	0.14	0.24	0.33	0.40	0.47	5/4.9
	LP	0.14	0.27	0.38	0.49	0.58	4/3.9
	SDP	0.14	0.27	0.38	0.48	0.57	4/4.0
	ESM	0.14	0.24	0.33	0.40	0.47	5/4.9
(b) Execution time (Unit: second)
20 × 40	Pick-1	0.35	0.35	0.35	0.35	0.35
	Pick-2	0.35	10.96	10.96	10.96	10.95
	Pick-3	0.35	10.96	313.65	313.65	313.65
	1-Step TSA	0.50	2.14	11.78	128.98	1.62e3
	2-Step TSA	0.50	13.20	14.11	58.93	3.77e3
	3-Step TSA	0.50	13.20	320.20	346.43	695.53
	LP	0.55	0.55	0.58	0.55	0.56
	SDP	56.92	6.02e3	5.14e3	5.12e3	5.61e3
	ESM	0.35	10.96	313.65	4.5e3	6.0e4
24 × 40	Pick-1	0.44	0.44	0.44	0.44	0.44
	Pick-2	0.44	13.00	13.00	13.00	13.00
	Pick-3	0.44	13.00	311.27	311.27	311.27
	1-Step TSA	0.50	2.05	9.63	77.45	429.48
	2-Step TSA	0.50	12.92	13.60	35.08	634.62
	3-Step TSA	0.50	12.92	319.27	378.10	481.29
	LP	0.84	0.94	0.88	0.83	0.82
	SDP	62.18	5.59e3	4.89e3	4.75e3	5.37e3
	ESM	0.44	13.00	311.27	4.6e3	6.4e4
28 × 40	Pick-1	0.58	0.58	0.58	0.58	0.58
	Pick-2	0.58	14.67	14.67	14.67	14.67
	Pick-3	0.58	14.67	326.80	326.80	326.80
	1-Stpe TSA	0.52	1.41	4.39	32.43	119.86
	2-Stpe TSA	0.52	13.54	13.82	29.35	126.62
	3-Stpe TSA	0.52	13.54	327.79	404.23	383.61
	LP	1.12	1.20	1.12	1.09	0.68
	SDP	71.27	5.55e3	4.90e3	4.98e3	4.72e3
	ESM	0.58	14.67	326.80	4.7e3	6.9e4
32 × 40	Pick-1	0.42	0.42	0.42	0.42	0.42
	Pick-2	0.42	13.29	13.29	13.29	13.29
	Pick-3	0.42	13.29	331.80	331.80	331.80
	1-Step TSA	0.55	1.14	2.89	13.50	40.67
	2-Step TSA	0.55	14.22	14.32	18.13	40.35
	3-Step TSA	0.55	14.22	340.87	336.29	355.06
	LP	0.70	0.71	0.72	0.70	0.70
	SDP	56.12	7.17e3	5.43e3	5.07e3	4.79e3
	ESM	0.42	13.29	331.80	4.9e3	7.1e4

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

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