Optimum piecewise-constant Wiener filters

Leonard J. Cimini; Saleem A. Kassam

doi:10.1364/JOSA.71.001162

Journal of the Optical Society of America
Vol. 71,
Issue 10,
pp. 1162-1171
(1981)
•https://doi.org/10.1364/JOSA.71.001162

Optimum piecewise-constant Wiener filters

Leonard J. Cimini and Saleem A. Kassam

Not Accessible

Your library or personal account may give you access

Get PDF
Email
Share
Get Citation
Copy Citation Text
Leonard J. Cimini and Saleem A. Kassam, "Optimum piecewise-constant Wiener filters," J. Opt. Soc. Am. 71, 1162-1171 (1981)

Export Citation
- BibTex
- Endnote (RIS)
- HTML
- Plain Text
Citation alert
Save article

Abstract

Wiener filters are often used for the restoration of images embedded in additive noise. However, it is often desirable to have a simpler filter structure that is easily implemented and performs well. In this paper we present the necessary conditions for a filter with an optimum piecewise-constant frequency-response function. Such a filter has a simpler implementation than the Wiener filter, and, in general, it suffers only a small loss in mean-square-error performance, as is illustrated in numerical examples.

Full Article | PDF Article

More Like This

Class of optimum spatial filters

N. C. Gallagher and B. Liu
J. Opt. Soc. Am. 65(2) 182-187 (1975)

Fractional Wiener filter

Zeev Zalevsky and David Mendlovic
Appl. Opt. 35(20) 3930-3936 (1996)

Optimum Fourier-transform division filters with magnitude constraint

B. Liu and N. C. Gallagher
J. Opt. Soc. Am. 64(9) 1227-1236 (1974)

Previous Article Next Article

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Figures (2)

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Tables (8)

You do not have subscription access to this journal. Article tables are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Equations (74)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

SNR (σs²/N_o)	S (dB)	e_o/σ_s²	e_o/σ_s² (dB)	e_opc/σ_s²	e_opc/σ_s² (dB)	dB Loss with Respect to (e_o/σ_s²)
1	0	0.316	−5.0	0.452	−3.5	1.5
5	7.0	0.111	−9.5	0.142	−8.5	1.0
10	10.0	0.066	−11.8	0.082	−10.9	0.9
20	13.0	0.039	−14.1	0.046	−13.3	0.8
30	14.8	0.028	−15.6	0.033	−14.8	0.8
40	16.0	0.022	−16.6	0.026	−15.9	0.7
50	17.0	0.018	−17.4	0.021	−16.7	0.7

SNR (σ_s²/N_o)	SNR (dB)	r₁	r₂	C_{2_opc}	e_opc/σ_s²	e_opc/σ_s² (dB)	e_o/σ_s²	e_o/σ_s² (dB)	dB Loss with Respect to (e_o/σ_s²)
1	0	0.128	3.059	0.511	0.602	−2.2	0.543	−2.7	0.5
2	3.0	0.087	3.439	0.639	0.467	−3.3	0.407	−3.9	0.6
5	7.0	0.047	4.060	0.774	0.305	−5.2	0.257	−5.9	0.7
7	8.5	0.036	4.316	0.812	0.255	−5.9	0.213	−6.7	0.8
10	10.0	0.027	4.601	0.847	0.208	−6.8	0.172	−7.6	0.8
15	11.8	0.019	4.940	0.880	0.163	−7.9	0.134	−8.7	0.8
20	13.0	0.015	5.188	0.900	0.137	−8.6	0.112	−9.5	0.9
30	14.8	0.011	5.547	0.922	0.105	−9.8	0.086	−10.7	0.9
40	16.0	0.008	5.808	0.936	0.087	−10.6	0.071	−11.5	0.9
50	17.0	0.007	6.014	0.945	0.074	−11.3	0.061	−12.2	0.9

SNR (σ_s²/N_o)	SNR (dB)	r_o	C_{2_copc}	e_copc/σ_s²	e_copc/σ_s² (dB)	dB Loss with Respect to (e_o/σ_s²)
1	0	3.062	0.511	0.602	−2.2	0.5
2	3.0	3.440	0.639	0.467	−3.3	0.6
5	7.0	4.062	0.774	0.305	−5.2	0.7
7	8.5	4.314	0.813	0.255	−5.9	0.8
10	10.0	4.601	0.847	0.208	−6.8	0.8
15	11.8	4.940	0.880	0.163	−7.9	0.8
20	13.0	5.189	0.900	0.137	−8.6	0.9
30	14.8	5.548	0.922	0.105	−9.8	0.9
40	16.0	5.808	0.936	0.087	−10.6	0.9
50	17.0	6.013	0.945	0.074	−11.3	0.9

γ	SNR (σ_s²/N_o)	r₀	C₂	e_copc/σ_s²	e_copc/σ_s² (dB)	e_o/σ_s²	e_o/σ_s² (dB)	dB Loss with Respect to (e_o/σ_s²)
0.5	1	1.295	0.927	0.716	−1.5	0.665	−1.8	0.3
	5	1.587	1.359	0.557	−2.5	0.491	−3.0	0.6
	10	1.713	1.475	0.514	−2.9	0.425	−3.7	0.8
	20	1.837	1.552	0.486	−3.1	0.367	−4.4	1.3
	30	1.906	1.583	0.474	−2.2	0.336	−4.7	1.5
	40	1.955	1.601	0.468	−3.3	0.315	−5.0	1.7
	50	1.991	1.612	0.464	−3.3	0.300	−5.2	1.9
2.0	1	1.841	0.816	0.499	−3.0	0.475	−3.2	0.2
	5	2.266	1.127	0.264	−5.8	0.249	−6.0	0.2
	10	2.450	1.206	0.205	−6.9	0.182	−7.4	0.5
	20	2.628	1.258	0.166	−7.8	0.132	−8.8	1.0
	30	2.728	1.279	0.151	−8.2	0.109	−9.6	1.4
	40	2.798	1.290	0.142	−8.5	0.095	−10.2	1.7
	50	2.850	1.297	0.137	−8.6	0.085	−10.7	2.1
4.0	1	2.011	0.770	0.433	−3.6	0.404	−3.9	0.3
	5	2.476	1.033	0.191	−7.2	0.180	−7.5	0.3
	10	2.680	1.098	0.132	−8.8	0.121	−9.2	0.4
	20	2.876	1.139	0.094	−10.3	0.081	−10.9	0.6
	30	2.987	1.156	0.079	−11.0	0.063	−12.0	1.0
	40	3.064	1.165	0.071	−11.5	0.053	−12.8	1.3
	50	3.123	1.171	0.065	−11.8	0.046	−13.4	1.6

γ	SNR (σ_s²/N_o)	r₁	r₂	C₃	C₂	e_copc/σ_s²	e_copc/σ_s² (dB)	dB Loss with Respect to (e_o/σ_s²)
0.5	1	0.294	1.293	0.866	0.935	0.716	−1.5	0.3
	5	0.661	1.536	1.146	1.683	0.542	−2.7	0.4
	10	0.759	1.636	1.227	2.106	0.480	−3.2	0.5
	20	0.842	1.734	1.293	2.591	0.429	−3.7	0.7
	30	0.887	1.790	1.326	2.903	0.404	−3.9	0.8
	40	0.916	1.829	1.347	3.136	0.388	−4.1	0.9
	50	0.938	1.860	1.363	3.324	0.377	−4.2	1.0
2.0	1	1.584	2.115	0.858	0.409	0.483	−3.2	0.0
	5	0.848	2.239	1.038	1.209	0.260	−5.9	0.1
	10	1.023	2.400	1.090	1.396	0.193	−7.2	0.2
	20	1.158	2.556	1.129	1.585	0.144	−8.4	0.4
	30	1.224	2.645	1.147	1.693	0.122	−9.1	0.5
	40	1.265	2.707	1.158	1.768	0.110	−9.6	0.6
	50	1.295	2.756	1.166	1.825	0.102	−9.9	0.8
4.0	1	1.683	2.306	0.817	0.5	0.414	−3.8	0.1
	5	0.750	2.468	0.995	1.052	0.191	−7.2	0.3
	10	1.017	2.655	1.035	1.165	0.129	−8.9	0.3
	20	1.199	2.834	1.064	1.275	0.087	−10.6	0.3
	30	1.282	2.935	1.078	1.335	0.069	−11.6	0.4
	40	1.334	3 007	1.085	1.376	0.059	−12.3	0.5
	50	1.370	3.061	1.109	1.406	0.053	−12.8	0.6

γ_real	γ_assumed	SNR	Normalized MSE^a	Normalized MSE^b	Normalized MSE^c
2.0	0.5	5	−4.2	−3.5	−4.0
2.0	0.5	20	−5.4	−2.2	−1.6
1.0	0.5	10	−4.3	−4.0	−4.5
1.0	0.5	40	−5.0	−4.2	−4.2
2.0	1.0	20	−7.3	−6.7	−6.5
1.0	2.0	10	−3.9	−4.0	−4.1
1.0	2.0	30	−5.2	−5.6	−5.9
4.0	2.0	10	−8.4	−8.2	−8.4
4.0	2.0	30	−10.4	−9.7	−9.5
1.0	4.0	10	−4.3	−4.3	−4.4

SNR (σ_s²/N_o)	SNR (dB)	r_opc	C_{2_opc}	e_opc/σ_s²	e_opc/σ_s² (dB)	dB Loss with Respect to (e_o/σ_s²)
1	0	2.216	0.701	0.359	−4.4	0.6
5	7.0	2.715	0.893	0.130	−8.9	0.6
10	10.0	2.937	0.935	0.078	−11.1	0.7
20	13.0	3.146	0.962	0.045	−13.5	0.6
30	14.8	3.273	0.972	0.032	−14.9	0.7
40	16.0	3.399	0.978	0.026	−15.9	0.7
50	17.0	3.482	0.981	0.021	−16.7	0.7

SNR (σ_s²/N_o	SNR (dB)	r_oq	C_{2_oq}	e_oq/σ_s²	e_oq/σ_s² (dB)	(e_oq−e_opc)/σ_s² (dB)
1	0	2.308	0.609	0.369	−4.3	0.1
5	7.0	2.804	0.763	0.148	−8.3	0.6
10	10.0	3.014	0.802	0.096	−10.2	0.9
20	13.0	3.216	0.832	0.062	−12.1	1.4
30	14.8	3.332	0.846	0.049	−13.1	1.8
40	16.0	3.412	0.855	0.041	−13.9	2.0
50	17.0	3.473	0.861	0.036	−14.4	2.3

Abstract

Cited By

Figures (2)

Tables (8)

Equations (74)

Journal of the Optical Society of America