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Pattern recalling analysis of an auto-associative memory network using FFT and DWT

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Abstract

This study focused on recalling efficiency analysis of three different learning rules in Hopfield content addressable recurrent network for fingerprint image patterns. DWT and FFT feature extraction methods have been applied individually and combining one after another to gather the final feature vectors which are then normalized to trained into Hopfiled network by dividing the pattern into four non-overlapping equal sub-regions. To get the relevant features from each sub-region and to reduce the dimensionality of the pattern, DWT is applied first and then followed by FFT feature extraction methods. These feature vectors are normalized to pass into Hopfield network for training with three rules such as Hebbian, Pseudo-inverse and Storkey learning rules. Hamming distance method is used for recalling test pattern with the previously stored patterns. FVC2002 and FVC2004 fingerprint databases are used in simulation process. Performance of the network in terms of recalling efficiency is measured for originally stored patterns and several new patterns by introducing different noise percentages. Results achieved from various observations of this study demonstrated that recalling efficiency in case of DWT plus FFT is outperformed as compared to individual feature extraction techniques as well as work done in the literature. It has been observed that Storkey rule with combined features surpasses other two rules in terms of recalling efficiency. Recalling accuracy is almost 100% for 80, 160 and 240 patterns packing density network for both fingerprint databases used in this study with up to 30% of noise.

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Data availability

The datasets generated during and/or analysed during the current study are available in the [FVC (Fingerprint Verification Competition)] repository, [http://bias.csr.unibo.it/fvc2004/databases.asp; http://bias.csr.unibo.it/fvc2002/databases.asp].

Abbreviations

CLBP:

Compound local binary pattern

CHNN:

Complex-valued Hopfield neural network

CORDIC:

Coordinate Rotation digital Computer

DCT:

Discrete cosine transform

DTCWT:

Dual tree complex wavelet transform

DWT:

Discrete wavelet transform

FFT:

Fast fourier transform

FVC:

Fingerprint verification competition

HH:

High-high

HL:

High-low

HHNN:

Hyperbolic hopfield neural network

LH:

Low-high

LL:

Low-low

NMCA:

Modified multi connect architecture

ROI:

Region of Interest

SMSCED:

Smallest minimum sum of closest Euclidean distance

SOM:

Self-organizing map

E:

Energy function

\( {\mathrm{e}}^{-\mathrm{j}\frac{2\uppi \mathrm{nk}}{\mathrm{N}}} \) :

DFT coefficient

I+ :

Moore Penrose pseudoinverse

Ip, k :

External input to kth neuron for pthinput

N:

Number of Neurons

w k, j :

Synaptic weight between connection jth to kth neuron

X(k) :

k th harmonic in FFT

x(n) :

N th input to FFT

x p, j(t) :

Generated value by jth neuron of pth input pattern at time t

ϕ i, j[n]:

Sampling function

ψ i, j[n]:

Wavelet function

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Authors and Affiliations

  1. Department of Computer Science & Engineering, FET, MRIIRS, Faridabad, India

    Ramesh Chandra Sahoo

  2. Deaprtment of Computer Science, Utkal University, Bhubaneswar, India

    Sateesh Kumar Pradhan

  3. School of Computing & IT, Manipal University Jaipur, Jaipur, India

    Biswa Mohan Sahoo

  4. Department of CSE, National Institute of Technology, Shillong, Meghalaya, India

    Bunil Kumar Balabantaray

Authors
  1. Ramesh Chandra Sahoo
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  2. Sateesh Kumar Pradhan
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  3. Biswa Mohan Sahoo
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  4. Bunil Kumar Balabantaray
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Correspondence to Biswa Mohan Sahoo.

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Sahoo, R.C., Pradhan, S.K., Sahoo, B.M. et al. Pattern recalling analysis of an auto-associative memory network using FFT and DWT. Multimed Tools Appl 82, 9113–9135 (2023). https://doi.org/10.1007/s11042-022-13778-z

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