Characterizing Streaks in Printed Images: A Matching

Annual Conference of the Prognostics and Health ManagementSociety, 2010

Characterizing Streaks in Printed Images: A Matching PursuitMethod using Wavelet Decomposition

Juan Liu 1, Wencheng Wu 2, Bob Price 1, Eric Hamby 2, and Raj Minhas 2

1 Palo Alto Research Center, Palo Alto, CA

{jjliu, bprice}@parc.com

2 Xerox Research Center at Webster, Webster, NY

{wencheng.wu, eric.hamby, raj.minhas}@xerox.com

ABSTRACTPrinted pages from industrial printers can exhibit a num-ber of defects. One of the common defects and a keydriver of maintenance costs is the line streak. This pa-per describes an efficient streak characterization methodfor automatically interpreting scanned images using thematching pursuit algorithm. This method progressivelyfinds dominant streaks in signal profiles. It uses waveletdecomposition to speed up the element selection pro-cess and reduce computation complexity. Previous ap-proaches require the design engineer to pre-specify thecharacteristics for each possible streak that could be de-tected – an approach which is practically limited to de-tecting a few streak types in specific locations. TheMatching Pursuit algorithm, inc contrast, fully charac-terizes any and all streaks found on the scanned pagepermitting a generic analysis of a broad range of defectsfound in the field.

1. INTRODUCTIONPrinters are highly complex electro-mechanical systems.Hundreds of components are involved in the printingprocess, which in turn has multiple stages: charging,exposure, development, transfer, fusing, and cleaning(Duke, Noolandi, & Thieret, 2002). Printers are de-signed with remarkable reliability with failure rates mea-sured in incidents per millions of impressions; how-ever, modern printing applications print huge volumes ofsheets so diagnosis remains an important step in main-taining asset availability. Diagnosing a printer to iso-late a defective component is often a difficult task due tothe printer’s formidable complexity. Experienced tech-nicians learn to recognize signature defects in order toquickly narrow down the responsible components. In ourproject, we aim to automate defect diagnosis. Automa-tion would allow the printer to suggest required parts be-fore the technician departs for the site, speed up the diag-nostic process for less experienced technicians and allow

This is an open-access article distributed under the terms ofthe Creative Commons Attribution 3.0 United States License,which permits unrestricted use, distribution, and reproductionin any medium, provided the original author and source arecredited.

more sophisticated and demanding customers to take onmore of the maintenance tasks on site and without thedelays associated with service calls.

We propose the use of iterative diagnosis, in whichthree steps are interleaved and performed in each itera-tion:

1. printed pages are scanned and their image qualityfeatures are computed and characterized;

2. image quality features are used to update the healthstate of the machine and refine diagnostic hypothe-ses;

3. the set of hypotheses is used to recommend furthertests to rule out ambiguities or repair actions to cor-rect problems found so far

The process repeats until the problem with the machinehas been diagnosed.

There is a body of literature on fault diagnosis (thesecond step in iterative diagnosis). Various techniquesranging from qualitative to statistical inference havebeen proposed. The third step in iterative diagnosis is es-sentially evidence seeking. A few information-drivenap-proaches (e.g., (Liu et al., 2008), (de Kleer & Williams,1987)) have been suggested to find informative evidence.We will not address these two problems in this paper. In-stead, we focus on the first step of the iterative diagnosisprocess, namely characterization of image quality prob-lems. This can be considered as a pre-processing stage,or equivalently feature extraction. Printout data are dis-tilled into concise features, which are then fed to a diag-noser that classifies faults.

Banding and streaking are two typical image qualityproblems (Rasmussen, Dalal, & Hoffman, 2001). Band-ing is often caused by defects in rotational componentssuch as the rotating mirror used to raster-scan an image.It exhibits periodicity along the process direction of thepaper. This periodicity makes it easy to detect and char-acterize. Since the periodicity correlates with the cir-cumference of the part causing the banding, diagnosis isstraight forward. On the other hand, streaks appear asstripes whose major axis is along the process directionand are caused by defects or degradation in a variety ofcomponents related to the xerographic process. Streakstypically do not exhibit periodicity and vary considerably

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in appearance. In this paper, we focus on the complexi-ties of streak characterization.

Streak characterization has its own value even whendetached from fault diagnosis. Currently, experiencedtechnicians describe streaks using descriptions such as“light narrow streaks” or “dark medium streaks”. Thisis highly subjective, varying with individual perception,and hence inaccurate. The algorithm that we proposeeliminates the subjective nature of streak description andcan be used as an automated tool for assisting techni-cians in assessing image quality problems and providingobjective measures of whether or not a printer is meetingperformance standards.

The objective of this work is to develop an algorithmthat automatically characterizes streaks in printed pages.Such an algorithm needs to be:

• intuitive: the algorithm produces a representation ofstreaks consistent with artifacts identified by humanoperators;

• concise: streak characterization is clear and suc-cinct.

• flexible: the algorithm can successfully character-ize a wide variety of streaks.

Prior work in this area has focused on streak detection(Rasmussen et al., 2001). For instance, if the systems en-gineer anticipates that paper running through the systemcould create media edge wear on a roller at a particu-lar spot, the engineer could specify a specific filter thatwould fire when a streak appears in the expected loca-tion with the expected width and polarity. This approachis often implemented using matched filters, in which afilterbank is built based on the specified streak charac-teristics. The detection is straightforward and reliable.However, it is limited in flexibility because it requirespre-specification of streak patterns. Unfortunately, it isimpractical for engineers to prespecify specific filters forall streaks observed in the field. In this paper, we seek tobroaden the scope from streak detection to streak char-acterization, in the sense that we describe features ofany and all prominent streaks that can be observed ona printed sheet. Increased flexibility comes at the cost ofincreased computation complexity. However, we showthat discrete wavelet transform like techniques can makethese algorithms tractable for use in real systems.

2. EXAMPLE STREAKSFigure 1 shows a few representative streaks. As shown inthe figure, streaks vary in appearance. A streak could benarrow or wide, light or dark. It may occur at a fixed lo-cation over different pages, or occur at random locations.A streak defect could take the form of a single isolatedstreak (Figure 1 a, b, and d), or it could be a cluster ofstreaks (Figure 1 c).

Failure in various printer components can causestreaks. For instance, the streaks in Figure 1 a and dare caused by defects in the charging process (creating ahigh voltage field on a photoreceptor which is sculptedby the laser to make an electrostatic image). They tendto be fuzzy and occur in clusters. The streaks in Fig-ure 1c are due to defects in the cleaner blade (whichscrapes residual toner off the drum once the image hasbeen transferred). They tend to be sharper edged and ex-tend outside the printable area. Other defects such as the

failure to properly develop (distribute toner based on theelectrostatic image) or to transfer (move toner from themachine to paper) result in streaks with specific charac-teristics. Being able to precisely quantify such charac-teristics is crucial to diagnosis.

3. FORMULATION AS A SIGNALDECOMPOSITION PROBLEM

Ideally, a streak characterization algorithm would startwith a customer image. Due to the highly variable na-ture of these images, it is difficult to accurate identifyall streak types in such an image. We therefore assumethat the operator can print a preprogrammed test sheetwith homogeneous half-toned color test patches. Sincetest patches are homogeneous, and streaks generally runacross the entire patch in the process direction, we canproject the streak along the process direction via inte-gration or averaging, and reduce printed images to 1-Dsignal (see (Rosario, Saber, Wu, & Chandu, 2007)). Thecollapsed 1-D signal is known as the “density profile”1

and captures variation along the cross-process direction.In some cases, streaks can vary along their length. To ac-curately isolate features related to this variability wouldrequire analyzing the original unprojected 2-D intensityfield. We defer this to future work.

Key characteristics of streaks, include location, width,intensity, length, and edge sharpness. In this work, wecapture a subset of these properties in terms of a simplemathematical parameterization:(τ, α, h), whereτ de-notes location,α denotes scale (inversely proportional tostreak width), andh denotes intensity. The goal is to ex-tract a series of descriptor tuples{(τi, αi, hi)}i=1,2,···,N

from an 1-D profilef(t).We formulate the problem as the following: given the

1-D profilef(t), we would like to decompose it as a se-ries of superimposed streaks:

f(t) = c+∑

i

hix(αit− τi), (1)

wherec is a constant corresponding to the average inten-sity of the solid color test patch, andx(t) is streak tem-plate (e.g., raised cosine or block-wave function). Thestreak templatex(t) is stretched or squeezed to properwidth by the scale parameterαi, and shifted to locationτi. Its intensity is modified by the intensity or height pa-rameterhi. We would like to seek tuples(τi, αi, hi) suchthat the summation on the right-hand side of (1) matcheswith the observation profilef(t). Essentially, we have asignal decomposition problem, where{x(αit− τi)} is aset of basis functions, onto which the signalf(t) can beprojected. In practice, the profilef(t) is often contami-nated by noise and other printing and scanning artifacts.Hence, we would like to seek{(τi, αi, hi)}i=1,2,···,N tominimize the discrepancy

E =

∫t∈R

|f(t)− c−∑

i

hix(αit− τi)|2dt. (2)

The advantage of the signal decomposition approachis that it is capable of describing complicated streak ar-tifacts, for instance, two narrow streaks on top of a wide

1We use the convention that 1-D signal refers to a signal ofa single variable, e.g.,f(t), and 2-D signal/image/field to referto a signal of two variables, e.g.,f(x, y).

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(a) (b) (c) (d)

Figure 1: Example streaks. From left to right — (a) light and dark wide streaks; (b) dark streak with medium width;(c) clustered dark narrow streaks; (d) light wide streak.

streak. This can be easily expressed as the superimposi-tion of three streaks, two with largeαi values, and onewith smallαi. Another advantage is its remarkable flex-ibility. It only requires the engineer to specify a singlegeneric streak templatex(t). The algorithm looks for theoptimal set of instances{(τi, αi, hi)}i=1,2,···,N . There isno need for engineer to specify detailed streak informa-tion and pre-construction of any filterbanks.

This signal decomposition approach also has draw-backs. The foremost problem is the non-uniquenessin representation: the space of possible basis functions{x(αt − τ), τ ∈ R, α ∈ R

+} is clearly over-complete,(i.e., one member can be expressed as the linear combi-nation of other members). To make the difficulty clear,assume for a moment that we are using a block-wavestreak template. A block-wave function of width 1 can beexpressed as the sum of two adjacent block-wave func-tions each with width 1/2, and likewise four block-wavefunctions with width 1/4, and so on. This inherent over-completeness will result in non-uniqueness in the signaldecomposition{(τi, αi, hi)}i=1,2,···,N . In theory, thereexist an infinite number of signal decompositions withequal signal representation errorE . In our approach, weuse a matching pursuit method, described in Sec. 4., tolook for the most concise signal decomposition whichcircumvents the uniqueness problem.

Another difficulty with the signal representation ap-proach is the computation complexity. In principle,we compute the projection off(t) onto the basis set{x(αt − τ), τ ∈ R, α ∈ R

+}. This involves search-ing for the best decomposition overτ ∈ R, α ∈ R

+.In practice, our signal is sampled at finitely many pointson a finite extent so there will not be an infinite numberof decompositions, but there will still be an intractablylarge set. Our solution to this problem is to use the dis-crete wavelet transform (DWT) to speed up the search.The use of DWT in signal decomposition is similar toour signal decomposition problem in the sense that itprojects a signal onto a set of basis functions, but thebasis set in DWT is complete and structured (defined bythe wavelet function). Assuming that wavelet function

is similar to streak template, DWT could be used to ap-proximately match locations and scales. This truncatesthe search domain ofτ andα from the entire plane (orhalf plane) to much smaller neighborhood which can besearched directly. Furthermore, the DWT computationcan be implemented using efficient and readily availablealgorithms. The DWT acceleration of matching pursuitis described in more details in Sec. 5..

4. MATCHING PURSUIT

The previous section explains that signal decompositiononto the streak template basis is inherently non-unique.Given that multiple decompositions are equally goodin representing the original signalf(t), intuitively onewould like to favor the decomposition which is mostsparse, i.e., with the least number of basis functions.This is well-aligned with the principle of parsimony: thesimplest explanation should be favored.

Matching pursuit is an efficient and intuitive method,originally proposed by Mallat and Zhang (Mallat &Zhang, 1993) for basis selection. It has the notion ofa dictionary, which is a collection of waveforms thatcan be used to describe a signalf(t). For instance, theFourier basis is good at describing periodicity, and thewavelet basis is good for describing locality. The dic-tionary may contain one of the two, both, or even more.The task is to select members from the dictionary in or-der to best describef(t). This is very similar to ourstreak characterization problem, where the dictionary is{x(αt − τ), τ ∈ R, α ∈ R

+}. The dictionary is redun-dant, and hence the same non-uniqueness problem needsto be addressed. Matching pursuit proposes a greedystrategy: it progressively builds up a signal representa-tion by selecting an element that maximally improves therepresentation accuracy in each iteration.

Matching pursuit starts with the original signalf(t),and finds the elementg(t) in the dictionary which bestmatches withf(t). Given a templateg(t), the best ap-

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Figure 2: Progression of matching pursuit: top row —the 1st and 2nd iterations of matching pursuit; middlerow — the 3th and 7th iteration; bottom row — the 9thand 30th iteration. The black curves are the 1-D profilef(t). The green curves are the best template matchedsignal (fproj(t)) in iterations. The red curves are recon-structed signal by the end of each iteration.

proximation can be defined as

fproj(t) = 〈f(t),g(t)

||g(t)||〉 ·

g(t)

||g(t)||. (3)

Here the notation〈f, g〉 stands for inner product; and||g|| denotes Euclidean norm. The matching error isEg = ||f − fproj(t)||. We search over allg(t) to mini-mize the matching error. The signalf(t) is updated bythe approximation residual, i.e.,

f(t) ← f(t)− fproj(t)

= f(t)− 〈f(t),g(t)

||g(t)||〉 ·

g(t)

||g(t)||

Then the matching pursuit iterates and looks for the nextbest match. The iteration stops when a maximal num-ber of iterations is reached, or when the remainder sig-nalf(t) contains very little energy. The intuition behindmatching pursuit is that by progressively identifying themost dominant match, the signal representation will besparse. While there is no guarantee of sparsity, match-ing pursuit can successfully identify dominating basis,is easily implemented, converges quickly, and producesaccurate representation.

Figure 2 illustrates the progression of matching pur-suit, showing the optimal matched templates in iterations

Figure 3: Mexian hat (left) and Daubechies wavelet(right).

1, 2, 3, 7, 9, and 30. The original curve is shown in black.The green curve represents a greedy match of the bestsingle half-cosine basis function to the original curve.The red curve shows the signal reconstruction in termsof the basis curves identified so far. As we get to lateriterations, the red reconstruction curve comes to approx-imate the original black signal and the identified streaksare increasingly weak in terms of the energy the capture.This matching pursuit method is capable in characteriz-ing a variety of streak, wide (in the top row) or narrow (inthe bottom row). It allows us to describe artifacts suchas overlapping streaks.

While matching pursuit works efficiently, it does notguarantee sparsity. There is a body of literature on theoptimal tradeoff between sparsity and representation ac-curacy. Several heuristic methods have been developedto improve matching pursuit. Interested readers may re-fer to work on basis pursuit (Chen & Donoho, 1994;Huggins & Zucker, 2007) for more elaborate techniques.

5. USING WAVELET DECOMPOSITION TOSPEED UP

Matching pursuit is inherently computation-intense. Ineach iteration, matching pursuit finds the best basis func-tion in the dictionary. At each step it must scan the wholedictionary. In our case, the directory is parametrized bythe discretized locationτ and scaleα parameters. Foreach element(τ, α), computing the projection off(t)ontox(αt− τ) isO(N) whereN is the number of sam-ples inf(t). Therefore, the overall complexity for eachiteration isO(N · |τ | · |α|).

We can accelerate matching pursuit by using the dis-crete wavelet decomposition (DWT). Wavelet decompo-sition computes the projection off(t) onto a waveletfunctionψ(2k(t − τ)), wheret andτ are discrete, andk is the decomposition level. The decomposition levelkcorresponds to a scale or width of2k. Two facts justifythe choice of DWT as an approximation to half-cosinematching:

• The wavelet functionψ(t) is visually similar tostreak templatex(t). For instance, Figure 3 plotsthe Mexican hat and Daubechies wavelet. Mexicanhat is similar to a raised cosine streak template, andthe dominant peak in Daubechies wavelet is similarto a triangle template.

• DWT has fast algorithms. DWT is computed byconvolvingf(t) with filterbanks at dyadic scales.

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Listing 1: Matching pursuit iterations

xRec =0;ma tch In fo= [ ] ; %matchInfo contains tuple [loc,scale,intensity]f o r i t e r = 1 : maxIterNum

% compute the best match% returns the projection signal optimalTemp, best match location, and scale[ opt imalTemp , bestMatchLoc , o p t i m a l S c a l e ]= f i ndBes tTemp la teMatch ( XS igna l ) ;

% add the matched template to the reconstruction signalxRec= xRec+ opt imalTemp ;% record the descriptor (loc,scale,intensity)match In fo= [ ma tch In fo ; bes tMatchLoc o p t i m a l S c a l e opt imalTemp ( bes tMatchLoc ) ] ;

% subtract the matched template from the original signalXSigna l= XSignal− opt imalTemp ( : ) ;

i f ( norm ( XS igna l)> energyThresh ) % very little energy leftbreak ;

endendre tu rn ( ma tch In fo ) ;

Convolution can be efficiently implemented via fastFourier transform (FFT).

Peaks and valleys of DWT at decomposition levelkand locationτ indicates that there is a good match be-tweenf(t) and the wavelet basisψ(2k(t − τ)). Giventhe similarity between the wavelet functionψ(t) andstreak templatex(t), it is also reasonable to assume thatthe match is also good betweenf(t) andx(2k(t − τ)).Hence DWT is indicative of potential streak locationsand scales. Rather than searching through all the pos-sible elements in the(τ, α) domain, we can use DWT tospeed up for the optimal basis search: (1) first identifyingpotential match locations and scales, and (2) restrictingthe search to a much smaller neighborhood.

Furthermore, DWT also works well for pre-processing, including denoising and baseline removal.DWT is suitable for denoising due to its energy com-paction property — energy in smooth signal is com-pacted into only a few significant coefficients, whilenoise energy is widely scattered. Baseline removalcomes in for free because the coarsest subband natu-rally provides a low-pass approximation. We will discussthese in more details in the algorithm section.

Peak detection using continuous wavelet transformhas been proposed in bioinformatics application in (Du,Kibbe, & Lin, 2006). The basic idea is the same, but itdoes not enjoy the fast computation as DWT does.

6. ALGORITHM

6.1 From images to 1-D profilesAs we have discussed in Sec. 3., we first reduce 2-Dimages to 1-D profiles for streak characterization. Thisis a non-trivial preparation step. In practice, when theprinted page is scanned, it is often subject to mild dis-tortion such as translation, rotation, and skewing. Wehave developed an image registration algorithm to cor-rect such distortion. Each test page has fiducial marks(three on the top, two on the bottom in each page in

Figure 1). These fiducial marks are detected automati-cally. From the fiducial marks, the algorithm computesan affine transform, which transforms the scanned imageto a standard coordinate frame where process directionis perfectly aligned with the vertical axis of the imagecoordinate. Once the image has been correct for distor-tions, one can easily compute the 1-D profile, simply viaaveraging the transformed image across the vertical di-rection.

6.2 PreprocessingThe purpose of preprocessing is to prepare data formatching pursuit. For instance, profile signals obtainedfrom real-world images are often contaminated by non-streak noise in the printing/scanning process. Denois-ing is needed to reduce noise while preserving signif-icant streaks. This can be done effectively using theDWT. Like Karhunen-Loeve transform, DWT compactsenergy into just a few wavelet coefficients. In con-trast, white noise affects all coefficients. We uses ahard-thresholding scheme for denoising (Liu & Moulin,1997): if a wavelet coefficient’s amplitude is small withrespect to a threshold, it is considered to be due to noiseand is set to zero. Wavelet coefficients with large ampli-tude are considered signal and are preserved. In our im-plementation, the threshold is set to3σ, whereσ is thenominal standard deviation of noise, which is assumedknown a priori, or can be learned from a set of observa-tion samples. Figure 4a shows the raw 1-D profile (inblack) and its denoised version (in red). Visually the redsignal is much smoother but still preserves fine-level de-tails.

In addition to streaks which appear as stripes, there isoften slow variation from one margin to the other dueto, for example, the uneven nature of ROS power in thecross-processing direction. This is known as the inboard-outboard variation, also referred to as the “baseline”. Re-moval of the baseline is necessary because it has a sig-nificant magnitude but the variation has different char-acteristics than streaks. The baseline is slowly varying

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Figure 4: Removal of (a) non-streak scanning and print-ing noise and (b) inboard-outboard variation. Black isthe raw 1-D profile; red is the denoised profile; blue is theidentified baseline characterizing the inboard-outboardvariation, and green is the profile after noise/baseline re-moval.

and has wide support (often the whole page). It is some-what surprising that end users generally do not perceivethe baseline as problematic, but it is spread out over alarge enough area that it is not perceptually salient tohumans. In contrast, streaks are also smooth, but havemuch smaller support (in the millimeter range). On theother hand, the difference between baseline and streaksare purely qualitative. It is hard to precisely define whatpart of the profile is due to baseline and which part isdue to streaks. Perfect separation is impossible. This isan area that remains as our on-going research.

In our algorithm, with aN -level DWT, the signal isdecomposed intoN + 1 coarse-to-fine subbands. Thecoarsest subband is a low-pass version off(t), whilethe finer subbands are the projection off(t) onto thewavelet basisψ(2k(t − τ)) for k = 1, · · · , N . The pro-jections have a finite support proportional to2k. Thissubband structure provides a natural separation betweenbaseline and streaks. In our implementation, we chooseN so that2N is roughly the support of the widest streaks.For instance, the 1-D profile in Figure 4b is 4096 pixellong, we chooseN = 10 which corresponds to streaksof width 1024. Anything wider than that is consideredbaseline instead of streaks. The baseline is obtainedby reconstructing from the coarsest subband only. Fig-ure 4b shows the denoised 1-D profile in red and thebaseline in blue. The blue curve captures the generaltrend of inboard-outboard variation very well. The dif-ference between the two is shown in green. It removesthe low-frequency baseline fromf(t) but preserves thehigh-frequency variations. This is the input signal to thematching pursuit algorithm.

6.3 Combining DWT with matching pursuit

As we have discussed in Sec. 5., the purpose of DWTis to find potential streak candidates, in particular, theapproximate scale and location(α, τ), so that we cansearch over a small neighborhood instead of searchingover the whole domain(α, τ) ∈ R

2. This greatly savescomputation time. Figure 5 shows the 1-D streak pro-file, from which we identify 5 candidates for the mostdominant streaks. The candidate match locations aremarked with squares. The candidate identification pro-cess is straightforward — the location with a large am-plitude in the wavelet decomposition is identified as a po-

tential candidate. The figure shows that dominant streaksare located, but there are two problems: (1) the locationsmay not be accurate due to the fact that DWT uses dis-crete resolution (integer multiplier of2k, wherek is thewavelet decomposition level) hence is incapable of pre-cisely identifying location in between, and (2) the candi-dates could be repetitive, for instance, the top five candi-dates actually identifies three streaks in the profile. Bothproblems are not critical, since the matching pursuit al-gorithm will perform refined match to further improvelocation accuracy and remove redundancies.

The identified candidates{(αi, τi)} are then used todefine search neighborhood for the matching pursuit al-gorithm. The bottom panel of Figure 5 shows the streakcharacterization result. Each streak is marked with a hor-izontal bar. The center location of the horizontal bar in-dicates the streak locationτi; the vertical location indi-cates the intensity of the streakhi; the length of the barindicates the streak width1/αi. The top 5 streaks arelabeled with numbers. From the figure we see that thestreaks are identified correctly.

6.4 Finding correlated streaks across page oracross color separations

In some cases, a single component may generate a streakin multiple separations. For instance, the fuser fuses thetoner for all colors and therefore defects in the fuser rollcreate artifacts in all separations. To properly isolatedthe cause of these failures from image defects, it is nec-essary to compare streak characteristics between multi-ple pages.

The implication on streak characterization is thatwhen it comes to streak detection over multiple channels(page or color), we should not treat each channelfj(t)separately. Iffj=1(t) has a strong streak at(α, τ), weshould examinefj=2,···,J(t) in the(α, τ) neighborhoodfor potential streak presence. This has been implementedas the following in our algorithm:

• For each channel profilefj(t), use DWT to findstreak candidate setLj = {(α, τ)}j ;

• Generate an augmented signal as the Euclideannorm across all channels, i.e.,faug(t) = ||fj(t)||,and then compute the candidate listLaug ={(α, τ)}j=J+1 for faug(t);

• Augment each channel’s candidate list asLnewj ←

(Lj ∪ Laug);

• For each channel profilefj(t), perform matchingpursuit based on the augmented candidate listLnew

j .

The augmented channelfaug is a new 2-D profile, whichcaptures dominant streaks in any of the channels. Hencethe candidate listLaug identifies potential streaks acrosschannels.

Figure 6 shows the streak characterization result fora test page with four color separations. The correlatedstreaks are located roughly 2/3 of the paper width fromthe left margin. The algorithm correctly identifies streaksin the cyan, black, and magenta separations.

7. FUTURE WORKThe initial work here demonstrates the potential ofmatching pursuit and discrete wavelet transform in char-

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Figure 5: Top panel: red boxes show locations within1-D profile identified as match candidates using DWT;bottom panel: streak characterization result overlayed onoriginal scanned image

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Figure 6: Example of a printed image with streaks (toppatch, three strips due to scorotron fault). The 2-D pro-files are plotted in red for all test patches.

acterizing streaks. The present method only returns lo-cation, scale and intensity. Extensions of the algorithmto identify additional features of streaks highlighted bysubject matter experts as important for diagnosis repre-sent natural starting points for future work. A more am-bitious project would be the extension of the method tostreaks which vary across the page. Such streaks wouldrequire methods that operate efficiently on 2-D intensityfields which we expect will be a challenge for some timeto come.

8. CONCLUSIONSThe automated identification of streaks holds consider-able promise for improving diagnosis and health man-agement in printing systems but has proven difficult toformulate computationally. Prior methods have providedthe ability to identify specific types of streaks in pre-viously anticipated locations. In this paper we demon-strate a novel streak detector that dynamically identifiersa broad family of streaks anywhere on the page. A keycomponent to making this technology practical is to use

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the discrete wavelet transform as an approximate match-ing heuristic to focus search for analytically intractablebasis functions (half-cosines). The result is a robust andpractical mechanism that will enable new levels imagequality reliability throughout the printing industry.

REFERENCESChen, S., & Donoho, D. (1994). Basis Pursuit. InProc.

28th Asilomar Conf. Signals, System Computation(p. 41-44). Asilomar, CA.

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Characterizing Streaks in Printed Images: A Matching