Where has been Tampered? From a Sparse Manipulation Perspective Yi-Lei Chen 1 and Chiou-Ting Hsu *2 Department of Computer Science, National Tsing Hua University, Taiwan 1 2

[email protected] [email protected]

Abstract—Existing forensic fingerprints mostly rely on robust statistical estimates, which usually hinder accurate image tampering detection at fine-grained level. To date, people still put a big question mark behind “where has been tampered?” In this paper, we try to answer this question from a counterfeiter’s perspective, devil in the details, that image tampering is usually sparsely and delicately manipulated. Thanks to recently wellestablished rank-sparsity incoherence, we formulate the finegrained tampering detection as a constrained minimization problem in order to discriminate the authentic areas (sharing similar feature behaviours) from the tampered areas (inconsistently and sparsely distributed) in a forensic feature space. Our formulation could incorporate with any applicable forensic features and, unlike existing methods, needs neither statistical analysis nor model factor estimation. Our experimental results show that the proposed method successfully locates various kinds of image tampering, including copy-move forgery, resampling and recompression, at fine-grained level.

(a)

I. INTRODUCTION The devil is in the details. Proverb

Nowadays every one could be an excellent image-creator! Using well-developed image editing softwares (e.g., Photoshop), we all could easily manipulate a given image and create a realistic “digital fake” in need of no expertise. For example, in Fig. 1 (a), the image popularly used in image inpainting [1] could be easily manipulated to convert the bungee-jumper into a superman! To date, as much research keep devoting to development of powerful editing tools, these easy-to-use techniques also open the door to realistic image tampering. Since visually-pleasant contents could easily convince people regardless of their authenticity, tampering detection as well as localization is becoming indispensible in digital image forensics. Through this decade, instead of using digital watermark, many passive/non-intrusive methods have been proposed for image tampering detection. Existing methods mainly rely on detecting the traces left by image acquisition or tampering operations; e.g., color filter array (CFA) interpolation [2-3], sensor noise pattern [4-5], resampling [6-7], and other image post-processing [8]. Although these forensic fingerprints could verify the presence/absence of image tampering, their performance mostly depends on reliable estimates from a whole image or sub-image (e.g., a given suspected window) rather than from a small image unit at fine-grained level (e.g.,

(b) Fig. 1. (a) An example of image tampering [1]. The three images from left to right are original image, tampered image, and the binary mask for tampered area. Notice that, the tampered area is relatively sparse in comparison with the authentic area. (b) An illustration of forensic feature space, where the tampered areas should be well discriminated from the authentic areas.

pixel, block). The reason is that a reliable statistical analysis, which usually involves the hypothesis of correct tampering location, is required to expose these tampering traces. In contrast, JPEG recompression artifacts [9-11] effectively reveal blocking inconsistency at every 8x8 block if the parameters used in the primary quantization could be correctly estimated. However, a robust estimate of those parameters again relies on a sufficient number of recompressed blocks to gather statistical support. To date, even though various forensic fingerprints have been proposed, there still lacks a general and effective solution to locate tampered area at finegrained level. Two recent work [12-13] have pointed out this limitation and proposed a Bayesian approach for tampering localization with either CFA or JPEG recompression traces. Nevertheless, the two methods are based on different probability models, which both need an accurate estimate of model factors and also the task-dependent information (e.g., CFA pattern, interpolation kernel, 1st and 2nd quantization tables, etc).

To break this bottleneck, we propose a unified solution to locate various kinds of image tampering from a counterfeiter’s perspective toward image tampering: as shown in Fig. 1(a), one tends to manipulate only a small amount of pixels without destroying the image credibility or leaving noticeable artifacts. Our goal is to expose such sparse manipulation, which we call devil in the details, in an optimized scheme. Suppose there exists a reliable forensic feature space (see Fig. 1(b)). We assume that authentic areas share similar feature behaviours while tampered areas are sparsely and inconsistently distributed. These two observations could be characterized by rank-sparsity incoherence [14], which has been recently wellstudied in computer vision field. Considering the tampering detection scenario, we propose a novel probabilistic ranksparisy decomposition to explicitly estimate the tampering score at fine-grained level and also incorporate human priors to ensure spatially-contiguous detection results. To sum up, the superiority of our method over existing work is twofold: 1) our method correctly locates various kinds of image tampering in a unified model by adopting different yet very simple forensic features; and 2) unlike existing methods, our method needs neither statistical analysis nor model factor estimation. In addition, we only need to determine two parameters in our method. Since we employ “devil in the details” (i.e., sparse user manipulation) as our problem priors, our method shows impressive results and also outperforms existing approaches in experiments. A. Notations We first summarize the notations used in this paper. Lower case letters ( , , …) denote scalar, bold lower case letters ( , , …) denote vector, and bold upper case letters ( , , …) denote matrix. is the element of , and , and are the , element and the column of , respectively. Diag denotes a diagonal matrix whose , element denotes the sum of all diagonal equals to , and trace elements in . In addition, the singular value decomposition T . (SVD) of is written by is defined by ∑ , where The nuclear norm is the largest singular value of . The -norm of , indicates the number of nonzero , , and F are defined by ∑ , , and ∑ , , respectively. , II. RELATED WORK AND MOTIVATION Modern techniques of rank-sparsity decomposition could be traced back to Robust Principal Component Analysis (RPCA) [15], where a corrupted matrix is decomposed into a clean matrix and a matrix containing gross errors. When assuming exhibits a low-rank structure and most elements of are zero, RPCA aims to solve s. t. . (1) , argmin rank Equation (1) is non-convex and also NP-hard because of the complex behaviors in rank function and -norm. Hence the by their tightest convex authors replaced rank and and , respectively, and recast RPCA into surrogates a convex problem:

, argmin s. t. . (2) In [16], the authors proved that, under rather weak assumptions, one could exactly solve equation (2) and also recover the low-rank component and sparse component . Although RPCA gives a theoretical guarantee, the -norm relaxation tends to bias the estimates of when the corrupted entries are not sparse and random enough [17]. In addition, in many applications, we may only concern about the sparseness of instead of their exact values; also, we usually only know the sparseness of a priori rather than itself. For example, in the application of image tampering detection and localization, our goal is to detect the location of tampered pixels but not to estimate the tampered content. If we use the RPCA solver, then a post-processing on is needed to determine the tampered area. This post-processing only implicitly relates to the tampering score and may also lose the problem precision. To overcome this drawback, we propose a novel probabilistic rank-sparsity decomposition method in section 3. Different from RPCA, our method explicitly determines the tampering score and also captures spatiallycontiguous tampered areas by including the spatial coherency priors. We will show that both modifications improve RPCA formulation in image tampering detection. III. LOCATING TAMPERED AREA A. Scenario Given an observed image , where Ω denotes the set of tampered pixels and Ω is its complement with respect to . Note that, the tampering operation applied on Ω is not restricted to any specific operation. We could include any existing forensic features applicable to different tampering operations to create a forensic feature space from the observed image. In order to discriminate Ω from Ω in this feature space (as shown in Fig. 1(b)), we make the following two assumptions: z The pixels in Ω should share similar feature behaviors while the other set Ω does not. z The cardinality of the set Ω is relatively smaller than Ω . that of Ω ; i.e., |Ω | The 1st assumption relies on the discriminative power of the so-called forensic feature space. The 2nd assumption did come from a common scenario: when tampering an image, general users usually manipulate only a small portion of the image to make the tampered result appear realistic and unnoticeable. Under the two assumptions, Ω should reveal strong dependency in a low-rank subspace where Ω are sparsely and inconsistently distributed. Therefore, we recast the problem of locating tampered area into a generalized problem: finding the sparse inconsistency in a low-rank subspace. This novel perspective enables us to derive a unified formulation for locating tampered area in fine-grained detail. B. Problem Formulation We first divide an image into units (e.g., pixels, patches, regions or super-pixels, etc) and then represent the image by a ,…, , where denotes the feature matrix

–dimensional forensic feature vector of the unit. Assuming there exists an underlying low-rank matrix spanned by the authentic forensic features, our goal is to estimate and explicitly determine the tampering score of : each unit. We thus introduce a probabilistic support P tampered| and P authentic| . (3) 1 In addition, we further consider a Gaussian noise model between our observation , and the estimation , : . (4) , , , and , ~N 0, σ Finally, we propose to formulate our fine-grained tampering detection as a constrained minimization problem: ∑ , argmin ∑ ∑, 1 , s. t. 0 1 . (5) In equation (5), the 1st term measures the feature dependency between authentic units, and the 4th term measures their observation noise under P authentic| . On the other hand, the 2nd term penalizes the sparseness of tampered units under , and the 3rd term encodes the relation P tampered| between image units with the prior knowledge defined by , . Observing that most of the tampered units are spatiallycontiguous, we consider the spatial coherency to define , : ,

exp 0

, if the

and

units are spatially‐adjacent ,

otherwise

(6) where denotes the center coordinate of the unit. In other words, equation (5) would encourage two image units to have similar tampering scores if they are spatially-adjacent. C. Optimization Methodology In practice, equation (5) is non-convex and difficult to solve. However, if we solve either or with the other one fixed, the two corresponding sub-problems are both convex and could be solved exactly. By ignoring those terms independent of , we have: T trace , (7) argmin T where Diag 1 , … ,1 . To make equation (7) tractable, we adopt the linearization technique and obtain

elements; i.e., max / ,0 . On the other hand, to estimate the probabilistic support , we ignore those terms independent of in equation (5) and have a constrained minimization problem: T s. t. 0 1, (11) argmin T T where ,…, , and is the graph Laplacian matrix defined by ( denotes a ∑ , ). Equation (11) is a typical diagonal matrix with , quadratic programming. In our experiments, we solve it using the Matlab toolbox quadprog(). To sum up, we solve equations (9) and (11) iteratively until the changes of and between consecutive iterations are smaller than a predefined threshold. Because we reduce the objective cost at each iteration, the proposed algorithm guarantees to obtain a local optimum. Nevertheless, since equation (5) is a non-convex formulation, our method could be quite sensitive to parameters. To address this issue, we use an image-dependent approach to determine , , . We set for different images, and adaptively adjust , / at each iteration, where is set as times of variance of T ,…, and . After obtaining the probabilistic support , we assign into those pixels belonging to the unit and then generate a probability map, where higher responses (usually close to 1 in our experiments) indicate the tampered areas. This probability map is finally used as our tampering detection result. D. Forensic Features It is worthy noting that our method is insensitive to the discriminative power of each individual forensic feature, because equation (5) inherently explores both the feature dependency (i.e., low-rank) and feature inconsistency (i.e., sparsity). Therefore, neither feature selection nor complex feature extraction (e.g., statistical model-based [12-13]) is required. Our method works very well even using pixel-level features, which could be easily measured but are usually very sensitive to image content, to locate various image tampering. In this paper, we investigate three types of forensic features to validate our rank-sparsity model.

1) Demosaicing evidences Most digital cameras embed a color filter array (CFA) to argmin , (8) F gather one particular color for each sensor. Since different where is the approximation from previous iteration, demosaicing algorithms are built in different cameras to T 2 , and . Because is denotes interpolate missing pixel values, the algorithm parameters diagonal, its singular values are equal to the diagonal elements. could be used for camera source identification. In [3], the ( is the minimum Therefore, is equal to 2 2 authors proposed to estimate 7x7 interpolation kernels under element of ). We thus rewrite equation (8) and have 36 CFA patterns and then used the one with minimal argmin F , where reconstruction error to identify the demosaicing algorithm. , and Here, we adopt a subset of the forensic features proposed in [3] / 1 , is identity matrix. (9) and utilize the reconstruction errors under 12 CFA patterns (from (with the same color filter at diagonal) as our pixel-level In equation (9), exhibits a convex combination of previous iteration) and (from observation). The optimum of features. Although these features seem quite simple, we will show that the 12 local features, followed by our proposed equation (9) is derived by SVD shrinkage technique [18]: T , (10) model, could correctly locate copy-move tampering on images where denotes the shrunk with all shrunk diagonal coming from different camera sources.

(a)

(b)

(c)

Fig. 2. (a) An example of copy-move tampering from different camera sources; (b) the reconstruction error maps under 12 CFA patterns [3]; and (c) our detection result.

(a)

(b)

(d)

(c) Fig. 3. (a) The dog image “AnAn” ;(b) an example of copy-move tampering with resampling; (c) the 8 high frequency features [7] measured in spatial domain (the first 4 images) and in frequency domain (the last 4 images); and (d) our detection result.

2) Resampling traces Resampling process (e.g., scaling and rotation) is one of the commonest operations when manipulating tampered images. In [7], the authors measured the second-order difference and its zeros crossing to detect interpolated samples in pixel domain, and also conducted high-pass filtering in frequency domain (either DCT or DWT) to detect the loss of highfrequency details. Both the two types of feature are measured at pixel level. We therefore adopt these features (8 features in total) to characterize the traces of resampling in our method. 3) JPEG recompression artifacts Existing research have shown that JPEG recompression would leave inconsistent artifacts in both pixel and frequency domains [9]. Here, we consider a simple yet practical method, JPEG ghosts [10], to measure the recompression artifacts at pixel level. JPEG ghosts calculate the difference between a given image and its recompressed counterpart and would reveal ghost-like artifacts when the recompression quality factor is close to the primary one. This feature is usually very sensitive to image content; in addition, determining the best

recompression factor itself is also a critical problem. In our method, there is no such concern because the proposed model automatically explores the feature dependency. We simply try 17 recompression factors {51, 54,…, 99} and utilize all of the 17 JPEG ghosts as our forensic features without further feature selection. Recall that denotes the feature representation of the image unit. After we obtain forensic features at pixel level, we determine by averaging the features from those pixels in the image unit. IV. EXPERIMENTAL RESULTS In this section, we demonstrate that our method is able to locate various kinds of image tampering by adopting different forensic features . Note that, although the proposed ranksparsity model works well on pixel-level, solving equation (11) for all the image pixels would be very time-consuming. In order to balance such tradeoff, we divide our test image (see Fig. 4(a)), which is captured using Pentax K100D and is of size 1024x1024, into non-overlapping patches of size 16x16

(a)

(b)

(c)

(d)

(e)

Fig. 4 (a) Two examples of recompression tampering, where the red areas are composed of single compressed blocks (compression factor is 80) and the blue areas are composed of double compressed blocks (1st compression factor is 60 and 2nd compression factor is 80); and their detection results obtained by (b) RPCA [15]; (c) DCT coefficient analysis [11]; (d) our method; and (e) JPEG ghost with the best recompression factor 60 [10].

To overcome this challenging issue, we create two scenarios of JPEG recompression tampering in Fig. 4 (a), where one has 1/16 recompressed 8x8 blocks and the other one has 15/16. We compare our method with [11] and RPCA. A. Copy-Move Tampering from Different Camera Sources [11] used the histogram analysis of DCT coefficients to We create a copy-move tampering in Fig. 2(a), where the estimate the period left by primary quantization. Both RPCA tampered area is cropped from the other image captured using and our method utilize the same 17 JPEG ghosts as features. Nikon D80. Here we use the 12 reconstruction errors under We measure the tampering score of RPCA by because different CFA patterns as our features. As shown in Fig. 2(b), RPCA penalizes -norm in the objective function (see the pixel-wise error maps are noisy and unreliable to show the equation (2)). The three detection results are shown in Fig. 4 demosaicing inconsistency. However, using the same set of (b)-(d). One could observe that RPCA is sensitive to image features, our method accurately locates the tampered areas (as content and obtains noisy results. This is because RPCA shown in Fig. 2(c)). This encouraging result shows that our implicitly determines the tampering score and its convex method is able to detect fine-grained tampering without any relaxation would lose the problem precision on . On the additional feature selection [3] or statistical analysis. other hand, [11] accurately detects the tampered areas only in the case of 15/16 recompressed blocks; otherwise, their B. Image Tampering with Resampling performance is even inferior to RPCA. In contrast, our method To generate a tampered image (see Fig. 3(b)), we paste an achieves very accurate detection results in both scenarios. enlarged (with the scale factor of 3) and rotated (by 30 This success mainly lies in three aspects: 1) our method degrees) dog image “AnAn” (see Fig. 3(a)) into our test image. explicitly estimates the tampering score under an optimization Here we use the 8 high-frequency features [7] to detect the scheme; 2) we incorporate the spatial coherency as prior resampling traces left by scaling and rotation. As shown in Fig. knowledge of tampering areas to suppress misestimates; and 3) 3(c), some of these features only roughly capture the tampered our method characterizes the feature inconsistency without areas but are still very sensitive to image content. In contrast, any additional factor estimation (e.g., primary compression using the same set of features, our method accurately locates factor [10] and primary quantization trace [11]). In addition, the dog “AnAn” (see Fig. 3 (d)). our formulation could incorporate with any local forensic features even without knowing their physical meaning. For C. Image Tampering with Recompression example, as shown in Fig. 4(e), when the target recompression To date, the JPEG recompression artifacts are probably the factor is given, JPEG ghosts reveal either very large or very most effective forensic feature for locating image tampering. small responses (corresponding to different physical meanings) Once the primary compression factor (or the quantization in two different cases. In contrast, regardless of their different table) could be correctly estimated, the blocking inconsistency feature response, our method correctly detects the tampered would then reveal the recompression traces. However, areas. existing methods require a sufficient number of recompressed blocks for robust estimate. If the recompressed blocks are V. CONCLUSION relatively sparse in comparison with authentic blocks, then In this paper, we give a general answer for image tampering many methods may fail due to lack of recompression statistics. localization. We first introduce a counterfeiter’s perspective, and use the image patch as the unit in our formulation. The two parameters , are fixed as 0.75 and 1 in all experiments.

devil in the details, which indicates that users tend to manipulate only a small amount of pixels during tampering process. By assuming authentic areas share similar feature behaviours but tampered areas are sparsely and inconsistently distributed in a forensic feature space, we formulate tampering detection as a constrained minimization problem under the proposed probabilistic rank-sparsity model. Different from existing approaches, our method employs both feature dependency and feature inconsistency without knowing their physical meaning, and needs neither statistical analysis nor model factor estimation. In comparison with classical ranksparsity decomposition, our method explicitly estimates the tampering score and further incorporates spatial coherency to detect spatially-contiguous tampered areas. These two benefits enable accurate localization for various kinds of image tampering. The major advantage of our method is its flexibility to any forensic features for different tampering detection problems. Experimental results show that we could accurately locate tampered areas even using very simple features at pixel level. In the future, we plan to investigate 1) more robust forensic features and also 2) the feasibility of our method in combinational cases of image tampering (e.g., resampling + recompression). REFERENCES [1] [2] [3] [4] [5] [6] [7] [8] [9]

[10] [11] [12] [13]

M. Bertalmio, G. Sapiro, V. Caselles, and C. Ballester, “Image inpainting,” in Proc. SIGGRAPH, PP. 417-424, 2000. A.C. Popescu and H. Farid, “Exposing Digital Forgeries in Color Filter Array Interpolated Images,” IEEE Trans. on Signal Processing, vol. 53, no. 10, pp. 3948-3959, 2005. A. Swaminathan, M.Wu, and K.J.R. Liu, “Non-intrusive Component Forensics of Visual Sensors Using Output Images,” IEEE Trans. on Info. Forensics and Security, vol. 2, no. 1, pp. 91-106, 2007. J. Lukas and J. Fridrich, “Digital Camera Identification From Sensor Pattern Noise,” IEEE Trans. on Info. Forensics and Security, vol. 1, no. 2, pp. 205-214, 2006. H. Gou, A. Swaminathan and M. Wu, “Intrinsic Sensor Noise for Forensic Analysis on Scanners and Scanned Images,” IEEE Trans. on Info. Forensics and Security, vol. 4, no. 3, pp. 476-491, 2009. A.C. Popescu and H. Farid, “Exposing Digital Forgeries by Detecting Traces of Re-sampling,” IEEE Trans. on Signal Processing, vol. 53, no.2, pp 758-767, 2005. S. Prasad and K. R. Ramakrishnan, “On resampling detection and its application to detect image tampering,” in Proc. ICME, pp. 1325-1328, 2006. M. C. Stamm and K. J. R. Liu, “Forensic detection of image manipulation using statistical intrinsic fingerprints,” IEEE Trans. on Info. Forensics and Security, vol. 5, no. 3, pp. 492-506, 2010. Y. L. Chen and C. T. Hsu, “Detecting recompression of JPEG images via periodicity analysis of compression artifacts for tampering detection,” IEEE Trans. on Info. Forensics and Security, vol. 6, no. 2, pp. 396-406, 2011. H. Farid, “Exposing digital forgeries from JPEG ghosts,” IEEE Trans. on Info. Forensics and Security, vol. 4, no. 1, pp. 154-160, 2009. Z. Lin, J. He, X. Tang, and C. K. Tang, “Fast, automatic and finegrained tampered JPEG image detection via DCT coefficient analysis,” Pattern Recognition, vol. 42, no. 11, pp.2492-2501, 2009. P. Ferrara, T. Bianchi, A. D. Rosa, and A. Piva, “Image forgery localization via fine-grained analysis of CFA artifacts,” IEEE Trans. on Info. Forensics and Security, vol. 7, no. 5, pp. 1566-1577, 2012. T. Bianchi and A. Piva, “Image forgery localization via block-grained analysis of JPEG artifacts,” IEEE Trans. on Info. Forensics and Security, vol. 7, no. 3, pp. 1003-1017, 2012.

[14] V. Chandrasekaran, S. Sanghavi, P. A. Parrilo, and A. S. Willsky, “Rank-sparsity incoherence for matrix decomposition,” SIAM J. Optim., vol. 21, no. 2, pp. 572-596, 2011. [15] J. Wright, A. Ganesh, S. Rao, and Y. Ma, “Robust principal component analysis: exact recovery of corrupted low-rank matrices via convex optimization,” In Proc. NIPS, 2009. [16] E. Candes, X. Li, Y. Ma, and J. Wright, “Robust principal component analysis?” JACM, vol. 58, no. 3, 2011. [17] Y. She and A. B. Owen, “Outlier detection using nonconvex penalized regression,” Arxiv preprint arXiv:1006.2592, 2010. [18] J. Cai, E. Candes, and Z. Shen, “A singular value thresholding algorithm for matrix completion,” SIAM J. Optim., vol. 20, no. 4, pp. 1956-1982, 2010.

Where has been Tampered? From a Sparse ...

Department of Computer Science, National Tsing Hua University, Taiwan ..... degrees) dog image “AnAn” (see Fig. ... RPCA [15]; (c) DCT coefficient analysis [11]; (d) our method; and (e) JPEG ghost with the best recompression factor 60 [10].

2MB Sizes 2 Downloads 217 Views

Recommend Documents

Company has been removed from Dissemination Board of National ...
Dec 28, 2017 - 11 Aakar Leasing and Financial Services Limited. 12 Bharat Explosives Limited Ltd. 13 Peony Investments Limited Ltd. Amalgamated with another company. 14 Arihant Exports Limited. Continue to be on the Dissemination. Board of Designated

This email has been sent to you from Conard High School .pdf ...
Page 2 of 2. Page 2 of 2. This email has been sent to you from Conard High School .pdf. This email has been sent to you from Conard High School .pdf. Open. Extract. Open with. Sign In. Main menu. Displaying This email has been sent to you from Conard

Reaching your audience has never been easier Services
Google and the Google logo are trademarks of Google Inc. All other company and product names may be trademarks of the respective companies with which they are associated. GANL-CS-1401. About the Google Analytics 360 Suite. The Google Analytics 360 Su

my Garden. Everything here has been grown using ... - Urban Emissions
1) The decomposing waste releases water and so it needs less watering. 2) it is virtually maintenance free. Bio-culture waste/garden clippings. Bio-culture.

This email has been sent to you from Conard High School .pdf ...
This email has been sent to you from Conard High School .pdf. This email has been sent to you from Conard High School .pdf. Open. Extract. Open with. Sign In.

Page 1 www.ubs.com/economics This report has been prepared by ...
With lower savings, external income pressures, reduced credit expansion and .... Figure 5: Savings have fallen to their lowest level in 20 years ..... Authority (ISA).

Texture recognition has been widely implemented in ...
Dec 18, 2009 - components such as camera, LCD screen, power supply, light source ...... CC. 1. 2. 1. 2. 2. 1. , ln. , λ ρ. (3.33) where λi(C1,C2) represents the ...

Page 1 www.ubs.com/investmentresearch This report has been ...
information in this document is provided for the purpose of offering, marketing and sale by any means of any capital market instruments and services in the Republic of. Turkey. Therefore, this document may not be considered as an offer made or to be

Reaching your audience has never been easier Services
Finding the right people to take your survey can be a challenge, especially when trying to reach a niche or hard-to-find audience. Sure, you could ask screening questions, but these take up valuable space in your survey and can be inefficient for low

Much has been written, talked and discussed about ...
captive call centers and has now advanced to include risk analytics and other ..... increase seat utilization, call centers handle their voice-based services during ...

Page 1 www.ubs.com/investmentresearch This report has been ...
UBS does and seeks to do business with companies covered in its research reports. As a result, investors should be aware ..... REGENT GROVE. 2.37. 790. 3.6%. -7%. -4%. -12. NORTHVALE. 2.48. 827. 3.6%. -2%. 5%. -25. MI CASA. 2.84. 940. 3.6%. 1%. -3%.

Transparency has long been Auctionata's top priority - cloudfront.net
Mar 31, 2016 - KPMG Governance and Compliance report was commissioned by ... monitoring adherence to the legal and regulatory requirements and has ...

Much has been written, talked and discussed about ...
information security certification and quality certifications. ..... industry standard process methodologies focused on key/priority horizontal/vertical markets (e.g., ...

What Has–and Has Not-Been Learned about
1 also discuss the “great leveraging" that accompanied the much better ... funds rate before that rate hit the zero lower bound in December 2008. I address the critique that a Fed policy error in 2003–05 of keeping the federal funds rate .... the

Thirty-Salawat-for-Easing-That-Which-Has-Been-Decreed.pdf
O Allah send blessings upon our master Muhammad, a blessing by which our lifespan is increased. -- لل. ل. ص. ع. س. د. ي. ن. ا م. ح. مد. ل. لا. ص. ب. ق. ت. ن. ال. م. ا*ع ا.

5. The functions that LGA has been broken.pdf
Page 1 of 4. THE FUNCTIONS LGA HAS BEEN. BROKEN: LOTTERIES AND OTHER GAMES. [CAP. 438. 1. CHAPTER 438. LOTTERIES AND OTHER GAMES. ACT. To make provision for the regulation of lotteries and other games and gaming. operations in Malta, for the setting

Transparency has long been Auctionata's top priority - cloudfront.net
Mar 31, 2016 - KPMG Governance and Compliance report was commissioned by ... monitoring adherence to the legal and regulatory requirements and has ...

"rihanna where have you been".pdf
... apps below to open or edit this item. "rihanna where have you been".pdf. "rihanna where have you been".pdf. Open. Extract. Open with. Sign In. Main menu.