Non-stationary linear restoration of noisy images

Abstract

EE?s white noise is performed by non-stationary filtering T h e restoration of images degraded by an additive problem is modified to take into account the edge the noisy image. The standard Wiener aFproach to this information of the image. Various f i l t e r s of results are shown a d ccmpared to the standard Wiener increasirq caqlexity are derived. Experimental fiiter results and other earlier attempts involving no*stationary f i l t e r s . INTKWCFIoNImage restoration is often defined as the process of reawering an original image fran a distorted version.bhenever the exact restoration is not feasible (this happens for e x w l e when a ramjan noise is involved in the distorting process) , the restoration problem becaDes an awoximation problem. One has then to define a distance between tw images and try to minimize the distance between the original to the case where the distorted image is the sun of image and its restored version. our paper is related the original image and a stationary white noise K a l m a n filtering techniques to the case of 2-D process.By extending the wel1-m Wiener and signals, Helstran [l] , Pratt [2] , Nahi [3], Habibi [41 , A t t a s i 151 , Aboutalib et al. [61, woods and Radewan (71, Arvlrews and Hunt [dl have proposed various algorithns to perform the restoration. 'Ihese algorithrs have i n caamn two basic assunptions.F i r s t , the original image is considered to be the Second, the distance between two images is an L~ realization of a 2-D stationary randcla process distance, generally a mean-quare error between two randcm processes. AS a v n c e of those assurqtions, the restored image 1s obtained as the output of 2-D linear filter whs? irplt is the noisy image.The algorithus differ i n the type of f i l t e r s chosen (recursive or nowrecursive) tut all of them are essentially lowpss filters. This is due to the fact that the noise is supposed to be wider-band than the signal. They are also stationary f i l t e r s due to the stationarity assamption for the image m o d e l .Unforttnately, these a s a q t i o n s a d their consqmces produce unsatisfactory results &m dealirq with images. Edges which are often of great matter of fact, edges can be viewed as. highfrequency interest, are smeared by the l-pass f i l t e r s . AS a information of the original image that is not taken into account in the ucdel. Another way t o look a t it, is to interpret edges as locations i n the image where the model changes, contrary t o the staticnarity assumption. w a r d i n g these issues more recent work i n restoration of noisy images has tried to derive nmstationary and/or nonlinear algorithus. N a h i and Habibi [91 first dealt with the case Of tw models. Ingle et al. [lo] a l l o w e d the paraPeters describing the image m o d e l to change inside the image, deriving then an identification-estimation algorithn. Ingle He has been a v i s i t i n g research scientist at Usc fran en Informatique e t Automatique) Le (heslay, France. January to August 1979. ami woods 1111 considered the case of five...

Vector-valued image regularization with PDEs: a common framework for different applications

“…For these reasons, a lot of regularization frameworks have already been proposed in the literature. Pioneering works in this area have been initiated, for instance, in [1], [3], [18], [19], [21], [34].…”

A nonrecursive filter for edge preserving image restoration

“…The ML estimates of 8, , and y corresponding to a eight nearest neighbor GMRF model representing the original image were obtained from the noisy image as described above. The estimates are the restored image in bottom left hand image was computed using these estimates and (8). As may be seen, the edges in the restored image are somewhat blurred.…”

“…2.3 Cramer-Rao lower bound for ML estimates (8) Let the vector of parameter 0, v, and i be represented as 0 = col [ 1' 0, ', I I for rCN5…”

“…Since restoration of images is considered as a preprocessing technique, it is desirable to develop restoration filters that can preserve the sharp edges and features. Using the notion of masking function [8,9] derived from the fact that noise is perceived differently by a human eye depending (1) upon whether it occurs close to or far from an edge, we develop an EPF along the lines of [8] but without requiring that a prototype of the original image be available.…”

Vector-valued image regularization with PDE's: a common framework for different applications

“…For these reasons, a lot of regularization frameworks have already been proposed in the literature. Pioneering works in this area have been initiated, for instance, in [1], [3], [18], [19], [21], [34].…”