Spatially Adaptive Kernel Regression Using Risk Estimation
An important question in kernel regression is one of estimating the order and bandwidth parameters from available noisy data. We propose to solve the problem within a risk estimation framework. Considering an independent and identically distributed (i.i.d.) Gaussian observations model, we use Stein&...
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| Veröffentlicht in: | IEEE signal processing letters 2014-04, Vol.21 (4), p.445-448 |
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| container_title | IEEE signal processing letters |
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| creator | Krishnan, Sunder Ram Seelamantula, Chandra Sekhar Chakravarti, Purvasha |
| description | An important question in kernel regression is one of estimating the order and bandwidth parameters from available noisy data. We propose to solve the problem within a risk estimation framework. Considering an independent and identically distributed (i.i.d.) Gaussian observations model, we use Stein's unbiased risk estimator (SURE) to estimate a weighted mean-square error (MSE) risk, and optimize it with respect to the order and bandwidth parameters. The two parameters are thus spatially adapted in such a manner that noise smoothing and fine structure preservation are simultaneously achieved. On the application side, we consider the problem of image restoration from uniform/non-uniform data, and show that the SURE approach to spatially adaptive kernel regression results in better quality estimation compared with its spatially non-adaptive counterparts. The denoising results obtained are comparable to those obtained using other state-of-the-art techniques, and in some scenarios, superior. |
| doi_str_mv | 10.1109/LSP.2014.2305176 |
| format | Article |
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The denoising results obtained are comparable to those obtained using other state-of-the-art techniques, and in some scenarios, superior.</description><subject>Bandwidth</subject><subject>Cost function</subject><subject>Denoising</subject><subject>Estimating</subject><subject>Estimation</subject><subject>Fine structure</subject><subject>Kernel</subject><subject>Kernels</subject><subject>Mathematical models</subject><subject>Noise measurement</subject><subject>Noise reduction</subject><subject>nonparametric regression</subject><subject>Regression</subject><subject>Risk</subject><subject>Signal processing algorithms</subject><subject>Smoothing methods</subject><subject>spatially adaptive kernel regression</subject><subject>Stein's unbiased risk estimator (SURE)</subject><issn>1070-9908</issn><issn>1558-2361</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2014</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNpdkE1Lw0AQhhdRsFbvgpeAFy-ps1_ZXW9F6gcWlNaew6aZlK1pEndTof_eLS0ePM0cnvdl5iHkmsKIUjD30_nHiAEVI8ZBUpWdkAGVUqeMZ_Q07qAgNQb0ObkIYQ0Ammo5IA_zzvbO1vUuGZe2690PJm_oG6yTGa48huDaJlkE16ySmQtfyST0bhMjbXNJzipbB7w6ziFZPE0-H1_S6fvz6-N4mi45E31qFGesFAUqLBgFzq3QTIBBbYStikozxSpRFiVl1oLUCq01hamkQcoznfEhuTv0dr793mLo840LS6xr22C7DTmVDIwUSoqI3v5D1-3WN_G6SIEUkmZaRQoO1NK3IXis8s7Hn_wup5DvZeZRZr6XmR9lxsjNIeIQ8Q_PFBeZFvwXxuduYA</recordid><startdate>201404</startdate><enddate>201404</enddate><creator>Krishnan, Sunder Ram</creator><creator>Seelamantula, Chandra Sekhar</creator><creator>Chakravarti, Purvasha</creator><general>IEEE</general><general>The Institute of Electrical and Electronics Engineers, Inc. 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| subjects | Bandwidth Cost function Denoising Estimating Estimation Fine structure Kernel Kernels Mathematical models Noise measurement Noise reduction nonparametric regression Regression Risk Signal processing algorithms Smoothing methods spatially adaptive kernel regression Stein's unbiased risk estimator (SURE) |
| title | Spatially Adaptive Kernel Regression Using Risk Estimation |
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