Combined First- and Second-Order Variational Model for Image Compressive Sensing

Table 1

PSNRs of the reconstructed images.

Sampling ratio (%)	20		25		33		50
Noise level (dB)	30	40	30	40	30	40	30	40
Lena (256 × 256)
TVAL3	26.99	27.14	28.12	27.65	29.03	29.19	31.51	32.34
RecPF	29.93	30.92	30.76	32.06	32.01	34.06	34.03	37.94
Hybrid TVL1	30.12	31.13	30.97	32.26	32.24	34.43	34.26	38.41
Second-order TV	30.57	31.52	31.89	33.87	32.83	36.09	34.74	40.08
Our method	31.05	32.74	32.93	34.12	32.99	36.41	34.43	40.24
Pepper (256 × 256)
TVAL3	30.08	30.41	30.75	32.23	32.78	33.93	35.08	38.08
RecPF	30.92	31.95	31.72	33.79	33.01	35.68	34.91	39.25
Hybrid TVL1	31.10	32.29	31.93	34.10	33.24	36.05	35.06	39.65
Second-order TV	31.72	33.76	31.72	35.79	33.67	37.67	35.07	41.07
Our method	32.25	34.24	32.66	36.18	33.77	37.96	34.82	41.21
Barbara (256 × 256)
TVAL3	27.25	27.57	27.78	28.27	29.14	29.45	31.42	32.45
RecPF	28.70	29.29	29.45	30.28	30.67	31.80	33.07	35.62
Hybrid TVL1	28.86	29.50	29.63	30.55	30.93	32.20	33.36	36.20
Second-order TV	29.25	30.21	30.02	31.54	31.41	33.44	33.86	37.98
Our method	29.62	30.69	30.46	31.86	31.69	33.76	33.89	38.13
Brain (256 × 256)
TVAL3	32.63	33.22	33.76	34.49	35.23	36.32	37.52	40.18
RecPF	31.49	32.11	32.51	33.50	33.89	35.27	36.31	39.12
Hybrid TVL1	31.69	32.38	32.75	33.83	34.23	35.75	36.63	39.71
Second-order TV	32.65	33.64	33.66	35.13	35.20	37.29	37.52	41.11
Our method	33.19	34.72	34.02	35.63	35.46	37.70	37.35	41.55