K-SVD: ALGORITHM FOR FINGERPRINT COMPRESSION BASED ON SPARSE REPRESENTATION

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INTERNATIONAL JOURNAL OF INNOVATIONS IN ENGINEERING RESEARCH AND TECHNOLOGY [IJIERT]
ISSN: 2394-3696
VOLUME 2, ISSUE 9, SEP.-2015
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K-SVD: ALGORITHM FOR FINGERPRINT COMPRESSION
BASED ON SPARSE REPRESENTATION
Trishala K. Balsaraf
PG Student,
Department of Electronics and Telecommunication Engineering,
Shree Tulja Bhavani College of Engineering,
Tuljapur, Maharashtra, India
Mahesh N. Karanjkar
Assistant Prof.
Department of Electronics and Telecommunication Engineering,
Shree Tulja Bhavani College of Engineering,
Tuljapur, Maharashtra, India
ABSTRACT
In current years there has been an increasing interest in the study of sparse representation of
signals. Using an overcomplete glossary that contains prototype signal-atoms, signals are
described by sparse linear combinations of these atoms. Recognition of persons by means of
biometric description is an important technology in the society, because biometric identifiers
cannot be shared and they intrinsically characterize the individual’s bodily distinctiveness.
Among several biometric recognition technologies, fingerprint compression is very popular
for personal identification. One more fingerprint compression algorithm based on sparse
representation using K-SVD algorithm is introduced. In the algorithm, First we construct a
dictionary for predefined fingerprint photocopy patches. For a new given fingerprint images,
suggest its patches according to the dictionary by computing ݈଴
-minimization by MP method
and then quantize and encode the representation.This paper comparesdissimilarcompression
standards like JPEG,JPEG-2000,WSQ,K-SVDetc. The paper show that this is effective
compared with several competing compression techniques particularly at high compression
ratios.
INDEX TERMS - Compression, sparse representation, JPEG, JPEG 2000, WSQ, K-SVD.
INTRODUCTION
In the world today we are identified by the various biometric characteristics such as
fingerprint recognition and in this paper we explain the fingerprint recognition based on
sparse representation. Because in recent years there will be growing interest in the field of
sparse representations of signals. Applications that use sparse representation are many that
include compression, regularization in converse problems, feature extraction, and more.
Among many biometric recognition technologies, fingerprint compression is very popular for
personal identification due to the uniqueness, universality, collectability and invariance [1].
Large volumes of fingerprints are collected together and stored daily in a wide range of
applications, includingforensics, access controland fingerprint square measure evident from

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the information of Federal Bureau of Investigation (FBI). Large volume of data requires the
large amount of memory. Fingerprint compression is a key technique to solve the
problem.Compared with general normal images the fingerprint images contain simpler
configuration. They are only composed of ridges and valleys. In the local regions, they seem
to be the same. Therefore, to solve these two problemsthe pre-processing,pre-aligned the
whole image is sliced into square and non-overlapping small patches.
Generally, compression technologies can be classed into lossless and lossy. The 8 × 8 small
block of images. This transform has been used in JPEG [4]. The JPEG compression theme
has several benefits likesimplicity, catholicity and accessibility. However, it has abad
performance at low bit-rates mainly due to theunderlying block-based DCT format. For this
motive, asearly as 1995, the JPEG-committee begins to develop anew wavelet-based
compression for still images, especially JPEG 2000[5].
Targeted at fingerprint images, there are specialcompression algorithms. The most common
is WaveletScalar Quantization (WSQ)[7]. It became the FBI standardfor the compression of
500 dpi fingerprint images. Motivatedby the WSQ algorithm, a few wavelet packet
basedfingerprint compression schemes such as Contour let Transform (CT) have been
developed. But,these algorithms have a common shortcoming namely, without the ability of
knowledge. The fingerprint images can’t be compacted well now. They will not be
compressed well later. In this paper, ainnovative approach based on sparse representation is
given [8]. The proposed method has the ability by updating the dictionary. The effects on
actual fingerprint matching or recognition are not examined. In this paper, we will take it into
contemplation. In most Automatic Fingerprint identification System (AFIS), the main feature
used to match two fingerprint images are minutiae (ridges endings and bifurcations).
Therefore, the difference of the minutiae among pre- and post-compression is considered in
the paper.
RELATED WORKS
In this section, we describe the various image compression techniques and also we compare
the proposed method withexisting fingerprint compression algorithms likeJPEG,JPEG-
2000,WSQ,K-SVD etc.Generally, compression technologies can be classed into lossless and
lossy.
Lossless compression is a type of image compression algorithms that allows the original data
to be perfectly reconstructed from the compressed data. Typical image file formats of lossless
compression are like PNG or GIF;It is also often used as a component within lossy data
compression technologies. Lossless compression is used where it is essential that the original
and the decompressed data be identical, or where deviations from the original data could be
deleterious. Lossless compression methods may be classified according to the type of data
they are designed to compress.
Lossy compression technologies usually transform an image into another domain, quantize
and encode its coefficients. lossy compression is the type of image encoding methods that
uses inexact approximations to represent the content. These methods are used to reduce data
size for storage, handling, and transmit content. The amount of data reduction achievable
using lossy compression is often much higher than through lossless techniques. In lossy

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transform codes, samples of image are taken, chopped into small segments, transformed into
a new basis space, and quantized. The resulting quantized values are then encoded using
entropy coding.There are transform-based image compression methods have been implicitly
researched and some principles have appeared. Two most common options of transformation
are the Discrete Cosine Transform (DCT) [2] and the Discrete Wavelet Transform (DWT)[3].
JPEG
JPEG is a commonly used technique of lossy compression for digital images, particularly for
those images which are produced by digital photography. Image files that use JPEG
compression are generally called "JPEG files", and are stored in variants of the JIF image
format. The term "JPEG" is an acronym for the Joint Photographic Experts Group.The DCT-
based encoder is use for compression of a stream of 8 × 8 small block of images. This
alterationhas been used in JPEG [4]. The JPEG compression technique has some benefits
such as simplicity, universality and availability. However, it has a bad performance at low
bit-rates because of the essential block-based DCT scheme. For this reason, as early as 1995,
the JPEG-committee start to develop a new wavelet-based compression model for still
images, namely JPEG 2000[5][6].
JPEG 2000
JPEG 2000 (JP2) is a type of image compression and coding system. It was created by
the Joint Photographic Experts Groupin 2000 with the purpose ofsuppressing their
original discrete cosine transform-based JPEG standard (created in 1992) with a newly
designed, wavelet-based method.Thereis a modest increase in compression performance of
JPEG 2000 compared to JPEG; the main advantage of JPEG 2000 is the significant elasticity
of the codestream. The DWT-based algorithms consist of three steps: a DWT computation of
the normalized image, quantization of the DWT coefficients and lossless coding of the
quantized coefficients. The detail can be found in [7] [12]and. Compared with JPEG, JPEG
2000 provides many qualities that maintain scalable and interactive access to large-sized
image. In additionit allows extraction of different resolutions, pixel fidelities, regions of
interest, components etc. There are some other DWT-based algorithms, such as Set
Partitioning in Hierarchical Trees (SPIHT) Algorithm. The aim of JPEG 2000 is not only
improve compression performance over JPEG but also adding features such as scalability and
editability. The improvement of JPEG 2000's in compression performance relative to the
original JPEG standard is actually rather modest and should not ordinarily be the primary
suggestion for evaluating the design. Very low and very high compression rates are supported
in JPEG 2000. The capability of the design to handle a very large range of effective bit rates
is one of the strengths of JPEG 2000. For example, to decrease the number of bits for aimage
below a certain amount, the advisable thing to do with the image before encoding it. That is
unnecessary when using JPEG 2000, because JPEG 2000 automatically does this through its
multiresolution decomposition structure.
WSQ
The Wavelet Scalar Quantization algorithm (WSQ) is a compression algorithm used for gray-
scale fingerprint images. It is based on wavelet theory and has become a standard for the
replace and storage of fingerprint images. WSQ was developed by the Federal Bureau of

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Investigation(FBI)[7] for the compression of 500 dpi fingerprint images.The WSQ
compression technique developed by the FBI and alternative entities was designed to
compress fingerprint pictures between ratios of 10:1 and 20:1. At these compression ratios,
sufficient friction ridge and pore detail is maintained for the needs of identification, by
fingerprint matching hardware and by human latentfingerprint examiners.This compression
method is chosen over standard compression method like JPEG because at the same
compression ratios WSQ doesn't present the "blocking artifacts" and failure of fine-scale
features that are not suitable for identification in financial environments and criminal justice.
K-SVD
K-means clustering process.K-SVD is an iterative method that alternates between sparse
coding of the examples based on the existing dictionary and a process of updating the
dictionary atoms to better fit the data [9]. The update of the dictionarycolumns is grouped
with an update of the sparse representations, thereby accelerating convergence. The K-SVD
algorithm is expandable and can work with any pursuit method (e.g., basis pursuit, FOCUSS,
or matching pursuit). We evaluate this algorithm and express its results both on synthetic
tests and in applications on real image data.
PROPOSED SYSTEM IMPLEMENTATION
In this section, we give the details about how to use K-SVD algorithm for fingerprint
compression based onspares representation. The part includes construction of the dictionary,
compression of a given fingerprint, quantization and coding and analysis of the algorithm
complexityas shown in figure (1).
Input image
Compressed data
Fig.1. Proposed System Block Diagram.
Obtaining an overcomplete dictionary from a set of fingerprint patches allows us to represent
them as a sparse linear combination of dictionary atoms.
Divide the
fingerprint in
small patches
Calculate the
mean of each
patch
Encode the
coefficients
Find݈଴
-
minimization
by MP
Use sparse
method for
compression
Quantize the
coefficients

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Construction of the Dictionary
In this paper, the dictionary will be assembled in three ways. First, we construct a training set.
Then, the dictionary is obtained from the set.Cut the whole fingerprint image in fixed size
square patches as in figure (2).
Fig.2.A fingerprint image with its fixed square patches
The specific process is as follows: create a base matrix whose columns characterize features
of the fingerprint images, referring the matrix dictionary whose columns are called atoms; for
a whole fingerprint, divide it into small blocks called patches whose number of pixels are
identical to the dimension of the atoms use the method of sparse representation to obtain the
coefficients then quantize the coefficients; last encode the coefficients and other related
information using lossless coding methods. Greedy algorithm is used to construct training
sample. Then the dictionary is obtained by the following steps.
• The first patch is added to the dictionary, which is initially empty.
• Then we check whether the next patch is adequately similar to all patches in the
dictionary. If yes, then next patch is tested; otherwise, the patch is added into the
dictionary. Here, the similarity measure between two patches is calculated by solving
the optimization problem (1).
Where
2
F
• is the Frobeniusnorm. 21 PandP are the corresponding matrices of two patches. t, a
parameter ofthe optimization problem (1), is a scaling factor.
• Repeat the second step until all patches have been tested.
( ) 1 2
2 2 21
2
, min * (1)
1 2
t
F F
P P
S P P t
P P
F
= −

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In the preceding paragraphs, it is mentioned that the dictionary will be constructed in three
ways the first is select the patches at random and arrange them as columns of the dictionary
(Random-SR).The second is to select patches according to orientations called Orientation-SR.
See Figure (3), there are 100 patches with orientation 45 and size 20×20.
Fig.3.100 Patches with Size 20*20
The third is to prepare the dictionary by K-SVD method (K-SVD-SR in short)[9]. The
dictionary is obtained by solving an optimization problem (4).Y is the training patches, A is
the dictionary, X are the coefficients and iX is the i th column of X. The dictionary for the K-
SVD algorithm is constructed as follows.
Given A = [aଵ,aଶ,… … … … … , a୒] ∈ Rሺ୑∗୒ሻ
, any new sample y ∈ Rሺ୑∗ଵሻ
canbe represented as
a sparse linear combination of few columns from the dictionary A, as shown in formula
(2).This is the only prior knowledge about the dictionary in ouralgorithm. Later, we will see
the property can be ensured byconstructing the dictionary properly.
1 1
1 2
( 2 )
, , [ , , ...... ] .M M N T N
N
Y A X
W h e re y R A R a n d x x x x R× × ×
=
∈ ∈ = ∈
If M < N. and A is a full-rank matrix, an infinite number of solutions are available for the
illustrationof problem, hence constraints on the solution must be set. The solution with the
fewest number of nonzero coefficients is definitely an appealing representation.A proper
solution canbe obtained by solving the following sparsest optimization problem:
0
0
( ) : min . . (3)x s t Ax y=l
Where 0
• is thel଴
- norm, counting the nonzero entries of a vector.Solution of the
optimization problem is very sparse if Nx <<0
. The notation 0
x counts the nonzero entries
in x actually it is not a norm. However, withoutuncertainty, we still call it 0
l -norm. In fact,

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the compression of y can be achieved by compressing X. To solve the optimization problem
0
l we should compute the coefficients matrix Xusing MP method, which guarantees that the
coefficient Vector iX has no more than T non-zero elements. Then, update each dictionary
element based on the singular value decomposition (SVD) method.
( )
2
0
,
. . 4m i n i
FA X
s t i X TY A X ∀ <−
In the following paper, the three kinds of dictionaries will be compared.
Compression of a Given Fingerprint
For the fingerprint compression based on sparse representation, thesize of patches and thesize
of the dictionary arethe most important parameters. The size of patches has a direct impact
oncompression efficiency. The larger the size is, the higher theefficiency is. However, to
represent an arbitrary patch well, thesize of the dictionary needs to be sufficiently large. This
causes more computational complexity.
There for the proper size of patch should be chosen. So far, there is no good way to estimate
the parameter. For our proposed system implementation we can chose the 12×12, 16×16 and
20×20 sizes of patches. There are two reasons that the size 8 × 8 is not tested. The patches of
this size are too small to contain the structure of fingerprints and it’s difficult to compress
such small patches at high compression ratios. From Figure(4), it is seen that the size 12×12
has better performance when the number of atoms in the dictionary is 4096.
In addition, to make the patches fit the dictionary superior, the mean of each patch is to be
calculated and subtracted from the patch. After that, calculate the sparse representation for
each patch by solving the 0
l minimisation problem. Those coefficients whose absolute values
are less than a specified threshold are treated as zero.
Fig.4. Average Performance ofthe Proposed Algorithms with
Different Sizes of Patches.

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For every patch, four kinds of information require to be recorded. They are the mean value,
the number regarding how many atoms to use, the coefficients and their locations.
Quantization and Coding
Entropy coding of the atom number of each patch, the mean value of each patch, the
coefficients and the indexes is calculated by static arithmetic coders [10]. The atom number
of each patch is individually coded. The mean value of each patch is also individually coded.
The quantization of coefficients is achieve using the Lloyd algorithm [11], The first
coefficient of each block is quantized by means of a larger number of bits than other
coefficients i.e. in proposed system the first coefficient is quantized with 6 bits and all other
coefficients are quantized with 4 bits and entropy-codedwith a separate arithmetic coder. The
model for the indexes is estimated by using the source statistics achieved off-line from the
training set. The first index as well as other indexes is coded by the same arithmetic encoder.
Testing of the Algorithm Complexity
The algorithm includes two parts that is the training process and the compression process.
Because the training process is off-line, simply the complexity of compression process is
analyzed.
Algorithm 1 K-SVD algorithm for fingerprint compression based on sparse representation
1. For a given fingerprint cut it into small patches.
2. For each patch its mean is calculated and subtracted from the patch.
3. For each patch, solve the l଴
-minimization problem by MP method.
4. Those coefficients whose absolute values are less than a given threshold are treated as
zero. Record the remaining coefficients as well as there locations.
5. Encode the atom number of each patch, the mean value of each patch, and indexes;
quantize and encode the coefficients.
6. Output the compressed stream.
Algorithm 1 summaries the entire compression process. The compressed stream doesn’t
include the dictionary and the information about the models. It consistsexclusively of the
encoding of the atom number of each patch, the mean value of each patch, the coefficients
and also the indexes. In practice, only the compressed stream needs to be transmitted to
restore the fingerprint. In both encoder as well as the decoder, the dictionary, the quantization
tables of the coefficients and the statistic tables for arithmetic coding need to be stored.
CONCLUSION
The different compression techniques are adapted to compress the fingerprint images are
studied and compared their Performance especially at high compression ratios.New
compression algorithm based on sparse representation in introduced.Due to the block-by-
block processing mechanism, however, the algorithm has higher complexities. The paper
shows that the K-SVD algorithm for fingerprint compression based on sparse representation

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is more efficient than other compression technique such as JPEG, JPEG2000,WSQ. One of
the main problems in developing compression algorithms for fingerprints resides in the
needfor protection of the minutiae which are used in the identification. Our algorithmcan be
able to hold most of the minutiae forcefully during the compression and reconstruction.
Further, we think the technique based on sparse representation do not work very well in the
general image compression field. The reason are as follows: the content of the general images
are so rich thereforethere is no proper dictionary under which the given image can be
characterize sparsely; stillthere is one, the size of the dictionary may be too large to be
computeefficiently. For example deformation, rotation, translation and the noise all can make
the dictionary become very large. Therefore sparse representation should be employed in
special image compression field in which there are no above shortcomings. The field of
fingerprint image compression is one of them.
REFERENCES
[1] D. Maltoni, D. Miao, A. K. Jain, and S. Prabhakar, Handbook of Fingerprint Recognition,
2nd ed. London, U.K.: Springer-Verlag, 2009.
[2] N. Ahmed, T. Natarajan, and K. R. Rao, “Discrete cosine transform,”IEEE Trans.
Compute., vol. C- 23, no. 1, pp. 90–93, Jan. 1974.
[3] C. S. Burrus, R. A. Gopinath, and H. Guo, Introduction to Wavelets andWavelet
Transforms: A Primer. Upper Saddle River, NJ, USA: Prentice-Hall, 1998.
[4] W. Pennebaker and J. Mitchell, JPEG—Still Image Compression Standard. New York,
NY, USA: Van Nostrand Reinhold, 1993.
[5] M. W. Marcellin, M. J. Gormish, A. Bilgin, and M. P. Boliek, “An overview of JPEG-
2000,” in Proc. IEEE Data Compress. Conf., Mar. 2000, pp. 523–541.
[6] A. Skodras, C. Christopoulos, and T. Ebrahimi, “The JPEG 2000 still image compression
standard,” IEEE Signal Process. Mag., vol. 11, no. 5,pp. 36–58, Sep. 2001.
[7] T. Hopper, C. Brislawn, and J. Bradley, “WSQ gray-scale fingerprint image compression
specification, Federal Bureau of Investigation Criminal Justice Information Services,
Washington, DC, USA,Tech.Rep. IAFIS-IC-0110-V2, Feb. 1993.
[8] Guangqi Shao, Yanping Wu, Yong A, Xiao Liu, and Tiande Guo Fingerprint
Compression Based on Sparse Representation, IEEE Trans. on Image Processing, vol. 23,
no. 2, february 2014

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[9]M. Aharon, M. Elad, and A. M. Bruckstein, “The K-SVD: An algorithm for designing of
overcomplete dictionaries for sparse representation,”IEEE Trans. Signal Process., vol. 54,
pp. 4311–4322, 2006.
[10] K. Sayood, Introduction to Data Compression, 3rd ed. San Mateo, CA, USA: Morgan
Kaufman, 2005, pp. 81–115.
[11] S. Lloyd, “Least squares quantization in PCM,” IEEE Trans. Inf. Theory,vol. 28, no. 2,
pp. 129–137, Mar. 1982.
[12] C. M. Brislawn, J. N. Bradley, R. J. Onyshczak, and T. Hopper, “FBIcompression
standard for digitized fingerprint images,” Proc. SPIE,vol. 2847, pp. 344–355, Aug. 1996.

K-SVD: ALGORITHM FOR FINGERPRINT COMPRESSION BASED ON SPARSE REPRESENTATION

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