Comments on ‘Area and power efficient DCT architecture for image compression’ by Dhandapani and Ramachandran
- Renato J. Cintra^{1}Email author and
- Fábio M. Bayer^{2}
DOI: 10.1186/s13634-017-0486-8
© The Author(s) 2017
Received: 24 November 2015
Accepted: 18 June 2017
Published: 10 July 2017
Abstract
In [Dhandapani and Ramachandran, “Area and power efficient DCT architecture for image compression”, EURASIP Journal on Advances in Signal Processing 2014, 2014:180] the authors claim to have introduced an approximation for the discrete cosine transform capable of outperforming several well-known approximations in literature in terms of additive complexity. We could not verify the above results and we offer corrections for their work.
Keywords
DCT approximations Low-complexity transforms1 Introduction
In a recent paper [1], a low-complexity transformation was introduced, which is claimed to be a good approximation to the discrete cosine transform (DCT). We wish to evaluate this claim.
We aim at analyzing the above matrix and showing that it does not consist of a meaningful approximation for the 8-point DCT. In the following, we adopted the same methodology described in [2–11] which the authors also claim to employ.
2 Criticisms
2.1 Inverse transformation
2.2 Lack of DC component
where \(\text {MSE} = \frac {1}{M\cdot N} {\sum \nolimits }_{i=1}^{M}{\sum \nolimits }_{j=1}^{N} (a_{i,j} - b_{i,j})^{2}\), a _{ i,j } and b _{ i,j } are the (i,j)-th element of the original and reconstructed images, respectively; and MAX is the maximum pixel valye. For 8-bit greyscale images, MAX = 255.
2.3 Fast algorithm
which is different from T. Therefore, the SFG is incorrect and does not correspond to the proposed matrix. We assume that the intended method is T _{SFG}, which is the matrix implied by the fast algorithm. Indeed, this transformation is shown again in the schematics of the hardware realization of their work. Nevertheless, hereafter, we analyze both matrices: T and T _{SFG}. Similar to T, the matrix T _{SFG} does not evaluate the DC value, being subject to the criticism detailed in the previous subsection.
2.4 Lack of energy concentration
Moreover, the lack of energy concentration in the first transform coefficients indicates that the standard zigzag pattern employed in the quantization step is not adequate for this transformation. Nevertheless, the authors claim to employ the zigzag pattern with success. We could not verify this claim.
Transform coding assessment
Method | Transform efficiency | Coding gain (dB) |
---|---|---|
DCT [12] | 93.99 | 8.83 |
SDCT [2] | 82.62 | 6.02 |
BAS-2008 [4] | 84.95 | 6.01 |
BAS-2009 [6] | 85.38 | 7.91 |
BAS-2010 [8] | 88.22 | 8.33 |
BAS-2011 [9] | 85.38 | 7.91 |
CB-2011 [13] | 87.43 | 8.18 |
CB-2012 [3] | 80.90 | 7.33 |
Transformation in [14] | 3 4 . 9 3 | − 1 . 6 5 |
Transformation in [15] | 3 3 . 6 7 | − 4 . 0 8 |
T [1] | 2 8 . 9 5 | − 1 . 8 6 |
T _{SFG} [1] | 2 8 . 9 5 | − 1 . 8 6 |
2.5 Irreproducibility of results
The results shown by Dhandapani and Ramachandran could not be repeated. The authors state that they employ simultaneously a quantization step, which corresponds to variable bitrate encoding, and a fixed number of retained transform-domain coefficients, which suggests constant bitrate. This seems contradictory. However, to examine the transformation suggested by the authors, we adopted a constant bitrate encoding based on the retention of r transform-domain coefficients, as suggested originally by Haweel and others [2–11].
PSNR of reconstructed images (r=6w0)
Transform | Lena | Boat | Goldhill | Barbara | Lighthouse | Mandrill | Grass |
---|---|---|---|---|---|---|---|
DCT [12] | 51.400 | 46.531 | 49.497 | 47.097 | 49.719 | 41.147 | 44.264 |
SDCT [2] | 45.708 | 41.593 | 44.308 | 40.532 | 43.044 | 35.956 | 36.517 |
BAS-2008 [4] | 43.996 | 39.498 | 42.449 | 38.304 | 41.139 | 33.886 | 34.364 |
BAS-2009 [6] | 48.096 | 44.828 | 46.470 | 40.143 | 44.035 | 37.982 | 36.869 |
BAS-2010 [8] | 50.976 | 46.483 | 48.912 | 46.657 | 48.193 | 40.617 | 42.486 |
BAS-2011 [9] | 48.010 | 44.874 | 46.328 | 40.073 | 44.690 | 38.085 | 37.191 |
CB-2011 [13] | 49.537 | 45.353 | 47.892 | 43.163 | 46.455 | 39.668 | 39.815 |
CB-2012 [3] | 46.621 | 44.217 | 45.027 | 39.763 | 41.939 | 36.486 | 35.223 |
Transformation in [14] | 30.193 | 29.635 | 32.107 | 29.411 | 29.777 | 26.575 | 20.612 |
Transformation in [15] | 27.895 | 27.463 | 29.797 | 27.260 | 27.547 | 24.530 | 18.445 |
T [1] | 30.560 | 30.034 | 32.565 | 29.851 | 30.090 | 26.862 | 20.982 |
T _{SFG} [1] | 30.889 | 29.867 | 32.920 | 29.117 | 30.189 | 26.779 | 20.900 |
PSNR of reconstructed images (r=10)
Transform | Lena | Boat | Goldhill | Barbara | Lighthouse | Mandrill | Grass |
---|---|---|---|---|---|---|---|
DCT [12] | 32.088 | 28.971 | 30.656 | 24.752 | 25.549 | 22.832 | 19.893 |
SDCT [2] | 27.443 | 25.570 | 27.543 | 23.488 | 23.348 | 21.095 | 17.019 |
BAS-2008 [4] | 29.509 | 27.150 | 28.994 | 24.285 | 24.444 | 22.279 | 18.849 |
BAS-2009 [6] | 29.916 | 27.354 | 29.288 | 24.520 | 24.381 | 22.223 | 18.661 |
BAS-2010 [8] | 31.143 | 28.292 | 30.072 | 24.666 | 25.063 | 22.581 | 19.376 |
BAS-2011 [9] | 29.916 | 27.354 | 29.288 | 24.520 | 24.381 | 22.223 | 18.661 |
CB-2011 [13] | 30.446 | 27.861 | 29.612 | 24.460 | 24.756 | 22.516 | 19.157 |
CB-2012 [3] | 27.015 | 25.190 | 27.141 | 23.595 | 23.087 | 21.596 | 17.170 |
Transformation in [14] | 2.159 | 1.856 | 2.877 | 2.936 | 2.582 | 1.992 | 1.981 |
Transformation in [15] | − 6 . 9 2 7 | − 7 . 2 1 3 | − 6 . 2 0 5 | − 6 . 1 2 0 | − 6 . 4 4 2 | − 7 . 0 5 3 | − 6 . 9 1 4 |
T [1] | 2.163 | 1.867 | 2.880 | 2.951 | 2.596 | 2.001 | 1.981 |
T _{SFG} [1] | 4.686 | 4.380 | 5.399 | 5.454 | 5.086 | 4.481 | 4.355 |
3 Conclusion
Declarations
Acknowledgements
This work was partially supported by CNPq, FACEPE, and FAPERGS.
Competing interests
The authors declare that they have no competing interests.
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Authors’ Affiliations
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