with reference to fig1 , an imaging apparatus is illustrated which compensates for artifacts or errors introduced during the acquisition of a physical document 12 into electronic format . an exemplary method to acquire or convert a physical image or hard copy 12 to a digital image representation is to employ a scanner 14 or the like . typically , scanner 14 includes an array lens , conventional optics , or other light focusing devices . because the optics employed in scanners are typically imperfect , errors or artifacts are induced during conversion or acquisition of the physical image 12 as a digital image representation 16 . an exemplary array lens 20 is illustrated in fig2 . the array lens includes a plurality of small rods 22 disposed adjacent to one another in a line . typically , the rods 22 are formed from glass or fiber optic cable and the like . during use , the lens is used to focus or direct light 24 from one side of the lens 26 to the other 28 . particular attention to individual rods 22 f and 22 k illustrate an imperfection in the array 20 . that is , at times the individual rods are not disposed in a perpendicular arrangement within the lens and can cause light 24 to appear transposed on the output side 28 of the array lens . this artifact or error is best illustrated by dashed line 30 indicating the path a particular light beam travels through the array . while the array lens 20 illustrated includes a single row of rods those skilled in the art will recognize that typical “ one - dimensional ” arrays often employ several rows of closely spaced rods . the “ one - dimensional ” name refers here to the object plane or target area intended to be observed or imaged with the lens . similarly , but not illustrated , a “ two - dimensional ” array employs multiple rows of rods , with the “ two - dimensional ” name referring to the two - dimensional object plane or target area to be observed or imaged . referring back to fig1 , the image representation containing artifacts 16 is forwarded from the scanner 14 to an image processor 36 . as will be more thoroughly discussed below , image processor 36 generally proceeds to a specified image location , for example a target pixel within the image representation , and then performs a restoration operation . the restoration operation for any particular pixel is retrieved from memory 38 and , when applied to the image representation 16 yields an estimate of the image as if it were scanned with idealized optics producing a nominal uniform error such as a preferred point spread function . the restoration operation employs neighboring pixels about the target pixel in determining the restored value . following the compensation by the processor 36 , a post - compensated digital image representation 40 is output for further manipulation , storage , or distribution or the like as exemplified by the illustrated devices 42 . memory 38 is loaded with compensation parameters determined , for example , by performing a lens characterization or performance measurement 44 on the array lens 20 . an exemplary lens characterization employs classical modulation transfer function ( mtf ) measurement and / or estimation techniques sampled across the field of the array lens . for example , image scans may be obtained of an edge , line , point , and / or a periodic pattern . alternately , whole field characterizations may be accomplished using speckle techniques , and / or periodic objects such as “ on and off ” lines at different spatial frequencies . moreover , those skilled in the art will appreciate that the lens characterization 44 can be accomplished in a variety of locations , such as in an assembly plant prior to delivery to a customer , in a refurbishing shop , or in the field , i . e . at a user &# 39 ; s location . from the characterization 44 , parameters are determined 46 according to the specific compensation method in use by the image processor 36 . for example , point spread function ( psf ) parameters at various locations along the array lens are extracted for the maximum likelihood - expectation maximization ( ml - em ) method , modulation transfer function ( mtf ) parameters are extracted for the windowed wiener spectrum method , and a wide variety of sharpening filter coefficients are extractable such as linear , non - linear and the like . once these parameters are determined , they are forwarded to the memory 38 for access by the image processor as discussed above . specifically , a digital image f ″ digitized by an input scanner can be represented as an ideal digital image f that has been imaged by a “ convolution ” process psf ( i , j ; i , j ), where psf denotes the point spread function of an imaging system that can vary with location ( i , j ): f ″ ⁡ ( i , j ) = ∑ i ′ , j ′ ⁢ f ⁡ ( i ′ - i , j ′ - j ) ⁢ psf ⁡ ( i ′ , j ′ ; i , j ) ( 1 ) for an ideal scanner , psf is constant across the imaging field , i . e . psf ( i , j ; i , j )= psf ideal ( i , j ) for all i and j . in this case , conventional image restoration techniques , such as wiener filtering technique , can be suitably applied to estimate the original documents from the scanned images . however , if there are defects in the system , such as a tilted rod in a selfoc ® lens array , psf ( i , j ; i , j ) may vary with i and j . in general , psf ( i , j ; i , j ) can be represented by two components within another nonlocal “ convolution ” process as shown by eq . ( 2 ): psf ⁡ ( i , j ; i , j ) = ∑ i ′ , j ′ ⁢ psf ideal ⁡ ( i ′ - i , j ′ - j ) ⁢ psf sv ⁡ ( i ′ , j ′ ; i , j ) ( 2 ) where psf ideal is the uniform component and psf sv denotes a spatially varying component . those skilled in the at will appreciate that the techniques more fully explained below is capable of correcting for both of the effects simultaneously . note that the variation in psf sv due to defects in a selfoc ® lens array typically appears only in the fast scan direction ( i ). hence , in the typical scenario of interest psf can be rewritten as to better understand the spatially varying nature of this nonlogical “ convolution ” process , consider an example where psf sv can be characterized by a gaussian distribution . for this example , according to eq . ( 3 ), the standard deviation of the gaussian varies with the fast scan location of the distribution ( location i ). the equations below show the relationship between the actual scanned image f ″ ideal scanned image f ′, , and component point spread functions . equation ( 4 ) shows the nonlocal “ convolution ” process relating f ″ with f ′. f ″ ⁡ ( i , j ) = ∑ i ′ , j ′ ⁢ f ′ ⁡ ( i ′ - i , j ′ - j ) ⁢ psf sv ⁡ ( i ′ , j ′ ; i ) ( 4 ) f ′ ( i , j )= f ( i , j ){ circle around ( x )} psf ideal ( i , j ) ( 5 ) artisans will recognize that other defects might also yield spatially varying psf . for example , when the scanning bars are not parallel to the platen surface or when an object is not placed in close contact with the scanning surface ( e . g . bound book , wrinkled sheets , and 3d objects ), psf also varies with spatial location . when a spatially varying psf is present , a correction method based on a uniform psf might produce images with artifacts due to over - or under - corrections . as an example of a specific lens characterization and compensation parameter determination , a spatially varying psf is obtained as follows . we assume the spatially varying psf of a system is generally constant over time or varying at such a rate that a sensing or re - calibration can be suitably performed . there are two general approaches to obtain the spatially varying psf : the use of an imaging model of the system to predict the psf at a point ; or a calibration procedure . alternately , a combination of a calibration procedure and an imaging model can be employed . the following image measurement - based method is exemplary : position a fine line in the object plane of an array lens ( such as those manufactured under the trademark ‘ selfoc ’) scanner perpendicular to the array length ; scan the image plane with a slit detector to obtain the local line spread function ; repeat the above process for all positions of interest in the imaging field ; rotate the line and slit in the opposite direction , and repeat the above process . if an effect is periodic , such as the nominal variation along the array lens when it is defocused , one can acquire data for one period of the effect and use it when operating on all periods . the general methodology at this step is that an algorithm would first proceed to an image location ( target pixel ). then a restoration operation suitable for that location is performed . the restoration yields an estimate of the image as if it was scanned with idealized optics producing a nominal uniform preferred psf . the restoration operation employs neighboring pixels about that target pixel in determining the restored value of the pixel . for example , the operation could be like a “ local convolution ,” or other local restoration method . equation ( 6 ) shows this operation abstractly . { tilde over ( f )}′ ( i , j )= f ( i , j ){ circle around ( x )}, res ( i , j ; i ) ( 6 ) where { tilde over ( f )}′( i , j ) is the estimate of the image at point ( i , j ) as if it were scanned with idealized optics producing nominal uniform preferred psf ; { circle around (×)} i is a local neighborhood operation about pixel i ( similar to a local convolution ); and res ( i , j ; i ) is a restoration kernel that contains processing coefficients or information for restoration about pixel i . below , we show a specific local restoration process which effectively corrects image doubling artifacts like those encountered with selfoc ® tilted rods . to compensate for the spatially varying psf , it is desirable to develop an image restoration technique that can directly incorporate this psf into its operation . also , the method should work well in an image doubling setting , such as one might encounter with array lens tilted rods . one such method is the maximum likelihood - expectation maximization method ( ml - em ) as shown by f ~ ′ ( k + l ) ⁡ ( i , j ) = f ~ ′ ⁡ ( k ) ⁡ ( i , j ) ⁢ ∑ t , s ⁢ f ~ ″ ⁡ ( t - i , s - j ) ⁢ psf sv ⁡ ( t , s ; i ) ∑ m , n ⁢ f ~ ′ ⁡ ( k ) ⁡ ( m - t , n - s ) ⁢ psf sv ⁡ ( m , n ; i ) ( 7 ) where { tilde over ( f )}′ ( k + 1 ) is the estimate at the ( k + 1 ) iteration , and the operation is being performed about pixel i as seen in the psf sv distribution . with reference now to fig3 , an imaging apparatus is shown to pre - compensate a digital image representation prior to outputting where the output engine employs non - ideal optics . a digital image representation 50 is created or retrieved from a digital image source 52 . at this point the image representation is error free , that is , it does not include artifacts . image processor 54 applies pre - compensation parameters to the desired digital image representation 50 to produce a pre - compensated image representation 56 . in other words , the image processor 54 applies an inverse of the errors or artifacts expected to be induced later during image output . the pre - compensated image representation 56 is then forwarded to an output engine 58 which includes non - ideal optics such as a lens array 20 ( fig2 ). the physical output 60 thus appears to have been printed on an ideal or error free output terminal . those skilled in the art will appreciate that in some instances pre - compensation processing occurring in processor 54 will require producing or applying negative values to the pre - compensated image representation 50 . these negative values can be implemented in an offset gain system , or alternately they may be truncated with the errors diffused locally via an error diffusion method . the invention has been described with reference to the preferred embodiments . modifications and alterations will naturally occur to others upon reading and understanding the preceding detailed description . it is intended that the invention be construed to include all such modifications and alterations insofar as they come within the scope of the appended claims or the equivalents thereof .