A Novel Image Compression Approach Inexact Computing

International Journal of Trend in Scientific Research and Development (IJTSRD)
Volume 6 Issue 6, September-October 2022 Available Online: www.ijtsrd.com e-ISSN: 2456 – 6470
@ IJTSRD | Unique Paper ID – IJTSRD52197 | Volume – 6 | Issue – 6 | September-October 2022 Page 1988
A Novel Image Compression Approach-Inexact Computing
Sonam Kumari1
, Manish Rai2
1
Student, 2
Assistant Professor,
1,2
Bhabha Engineering Research Institute, Bhopal, Madhya Pradesh, India
ABSTRACT
This work proposes a novel approach for digital image processing
that relies on faulty computation to address some of the issues with
discrete cosine transformation (DCT) compression. The proposed
system has three processing stages: the first employs approximated
DCT for picture compression to eliminate all compute demanding
floating-point multiplication and to execute DCT processing with
integer additions and, in certain cases, logical right / left
modifications. The second level reduces the amount of data that must
be processed (from the first level) by removing frequencies that
cannot be perceived by human senses. Finally, in order to reduce
power consumption and delay, the third stage employs erroneous
circuit level adders for DCT computation. A collection of structured
pictures is compressed for measurement using the suggested three-
level method. Various figures of merit (such as energy consumption,
delay, power-signal-to-noise-ratio, average-difference, and absolute-
maximum-difference) are compared to current compression
techniques; an error analysis is also carried out to substantiate the
simulation findings. The results indicate significant gains in energy
and time reduction while retaining acceptable accuracy levels for
image processing applications.
KEYWORDS: Approximate computing, DCT, inexact computing,
image compression
How to cite this paper: Sonam Kumari |
Manish Rai "A Novel Image
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1. INTRODUCTION:
TODAY’S amount of information that is
computational and power computing system usually
process a significant intensive. Digital Signal
Processing (DSP) systems are widely used to process
image and video information, often under
mobile/wireless environments. These DSP systems
use image/video compression methods and
algorithms. However, the demands of power and
performance remain very stringent. Compression
Methods are often used to ease such needs.
Image/video compression techniques are classified
into two types: lossless and lossy.
The latter type is more hardware efficient, but at the
sacrifice of ultimate decompressed image/video
quality. The Joint Photographic Experts Group
(JPEG) technique is the most extensively used lossy
approach for image processing, while the Moving
Picture Experts Group (MPEG) method is the most
widely used lossy method for video processing. As
the first processing stage, both standards use the
Discrete Cosine Transform (DCT) algorithm. Many
other rapid DCT [1], [2] computing techniques have
been developed for picture and video applications;
however, since all of these algorithms still use
floating point multiplications, they are
computationally demanding and require substantial
hardware resources. To solve these problems, many
algorithms, such as [3], may have their coefficients
scaled and approximated by integers, allowing
floating-point multiplications to be substituted by
integer multiplications [4], [5].
Because the resultant algorithms are substantially
quicker than the original ones, they are widely
employed in practical applications. As a result, the
design of excellent DCT approximations for
implementation by lower bus width and simpler
arithmetic operations (such as shift and addition) has
gained a lot of attention in recent years [6].
Image/video processing has the benefit of being
extremely error-tolerant; human senses cannot
typically detect decrease in performance, such as
visual and audio information quality. As a result,
IJTSRD52197

International Journal of Trend in Scientific Research and Development @ www.ijtsrd.com eISSN: 2456-6470
imprecise computing may be employed in many
applications that allow some loss of accuracy and
uncertainty, such as image/video processing [7, 8].
The introduction of inaccuracy at the circuit level in
the DCT calculation is difficult and targets certain
figures of merit (such as power dissipation, latency,
and circuit complexity [9], [10], [11], [12], [13],
[14]). This method is aimed towards low-power users.
A logic/gate/transistor level redesign of an exact
circuit is used to achieve process tolerance. A logic
synthesis technique [9] has been described for
designing circuits for implementing an inexact
version of a given function using error rate (ER) as a
parameter for error tolerance. Reducing the
complexity of an adder circuit at the transistor level
(for example, by truncating the circuits at the lowest
bit positions) reduces power dissipation more than
conventional low power design techniques [10]; in
addition to the ER, new figures of merit for
estimating the error in an inexact adder have been
presented in [11]. This study introduces a novel
framework for approximation DCT image
compression, which is based on inexact computation
and has three layers. Level 1 is a multiplier-less DCT
transformation that uses just adds; Level 2 is high
frequency component (coefficient) filtering; and
Level 3 is computation utilizing inexact adders. Level
1 has received much attention in the technical
literature [16], [17], and [18]; Level 2 is an obvious
strategy for reducing computing complexity while
achieving just a minimal loss in picture compression.
Level 3 employs a circuit level method to pursue
inexact computation (albeit new and efficient inexact
adder cells are utilized in this manuscript). As a
result, the significance of this text may be found in
the combined consequences of these three levels. The
suggested framework has been thoroughly examined
and appraised. For picture compression as an
application of inexact computing, simulation and
error analysis demonstrate remarkable consistency in
findings. To prevent misunderstanding, the term
"approximate" refers specifically to DCT methods,
while the term "inexact" refers to circuits and designs
that employ non-exact hardware to compute the DCT.
2. REVIEW OF DCT For manuscript completeness,
preliminaries to approximate DCT and a review
of relevant topics are presented next.
2.1. Discrete Cosine Transform (DCT) To obtain the
ith and jth DCT transformed elements of an
image block (represented by a matrix p of size
N), the following equation is used:
Where is the element of the image. This
equation calculates one entry of the
Transformed image from the pixel values of the
original image matrix. For the commonly used
Block for JPEG compression, N is equal to 8 and
from . Therefore is also given
By the following equation:
For matrix calculations, the SCT matrix is obtained
from the following:
So, DCT is computation intensive and may require
floating-point operations for processing, Unless an
approximate algorithm is utilized.
2.2. Joint Photographic Experts Group (JPEG)
The JPEG processing is first initiated by
transforming an image to the frequency domain
using the DCT; this separates images into parts
of differing frequencies. Then, the quantization is
performed such that frequencies of lesser
importance are discarded. This reflects the
capability of humans to be reasonably good at
seeing small differences in brightness over a
relatively large area, but they The precise degree
of a quickly fluctuating brightness change is
frequently indistinguishable. During this
quantization stage, each frequency domain
component is split by a constant and then
rounded to the closest integer to compress it. As
a consequence, many high frequency
components have extremely tinyor probable zero
values, at best negligible values. The picture is
then recovered during the decompression
process, which is carried out with just the
necessary frequencies kept. The following
actions must be taken before JPEG processing
can begin:

1. An picture (in color or grayscale) is first
segmented into kxk pixel blocks (k = 8 is typical).
2. The DCT is then applied to each block from left
to right and top to bottom.
3. This produces kxk coefficients (so 64 for k = 8)
which are quantized to minimize the magnitudes.
4. The compressed picture, i.e., the stored or
communicated image, is represented by the
resultant array of compressed blocks. 5. To obtain
the picture, decompress the compressed image
(array of blocks) using Inverse DCT (IDCT).
3. INEXACT ADDITION AND
APPROXIMATE DCT
Arithmetic circuits are particularly adapted to inexact
computation; also, they have been widely studied in
the technical literature.
Literature and is an essential arithmetic operation in
many inexact computer applications. A decrease in
circuit complexity at the transistor level of an adder
circuit frequently results in a significant reduction in
power dissipation, which is often more than that
provided by standard low power design approaches
[10]. In [12], inexact adder designs were evaluated:
inexact operation was introduced by either replacing
the accurate cell of a modular adder design with a
reduced circuit complexity approximation cell, or by
changing the production and propagation of the carry
in the addition process. Three novel inexact adder cell
designs (denoted as InXA1, InXA2, and InXA3) are
reported in [14]; these cells have both electrical and
error properties that are particularly advantageous for
approximation computation. These adder cells, as
shown in Table 1, offer the following advantages over
prior designs [10], [13]: I a limited number of
transistors; (ii) a small number of erroneous outputs at
the two outputs (Sum and Carry); and (iii) reduced
switching capacitances (represented in Cgn gate
capacitance of minimal size NMOS), resulting in a
significant decrease in both delay and energy
dissipation (Table 3). (and their product as combined
metric). Table 1 displays metrics such as latency,
energy wasted, and EDP (energy delay product) of
inexact cells for both average and worst instances.
InXA1 is the least average and lowest performing
inexact cell. case InXA2 incurs delays in the least
average and worst case power dissipations, as well as
the least average EDP. Extensive modeling was used
to establish the average and worst-case latency and
energy dissipation of the adder cells. The delay for
each input signal is recorded when the output reaches
90% of its maximum value, whereas the energy
wasted in all transistors is measured when the output
reaches 90%. Based on these benefits, InXA1 and
InXA2 based adders are being explored for the DCT
application, which will be discussed more below.
4. APPROXIMATE FRAMEWORKS
PROPOSED
This research introduces a novel picture compression
framework with three layers of approximation, as
seen below.
Level 1 represents the multiplier-less DCT
transformation, Level 2 represents high frequency
filtering, and Level 3 represents inexact calculation.
Levels 1 and 3 have already been discussed. Although
high frequency filtering (Level 2) is not a novel idea,
it is worth describing it for completeness' sake since it
adds to the proposed framework's execution time and
energy savings. As a consequence, rather than
executing the quantization process on all resultant
DCT transformation coefficients, the operation is
only conducted on the set of coefficients for the
changed block's low frequency components.
4.1. High Frequency Filtration
Filtering the high frequencies results in a picture that
is hardly discernible by the human eye (as only
sensitive to low frequency contents).
This functionality allows you to compress a picture.
As previously stated, a DCT changes the picture in
the frequency domain such that the coefficients that
represent the high frequency components (and so are
not visible to the human eye) may be ignored while
the other coefficients are retained. When used to
picture compression applications, different amounts
of retained coefficients are investigated; it has been
proved that just 0.34-24.26 percent of 92112 DCT
coefficients are adequate in high speed face
recognition applications.
Image compression using a supporting vector
machine that only considers the top 8-16 coefficients,
As suggested an image reconstruction approach based
only on three coefficients. Evaluation and comparison
of several picture compression algorithms using just
ten coefficients, as described in [25].

4.2. DCT Implementation Estimate
Unlike the approximate DCT techniques shown in
Table 1, all needed computations (addition and
subtraction) are then executed at the bit level
using the associated logic functions. The length of
all operators is 32 bits, and MATLAB simulates
implementations using their Boolean logical
functions.
Selected approximation DCT techniques are
simulated for the Lena picture, and the results are
presented in Fig. 1, where the Power Signal to
Noise Ratio (PSNR) of all methods is plotted
against the number of Retained Coefficients (RC)
utilized in the compression's quantization step.
The PSNR is derived as follows from the Mean
Square Error (MSE):Mean Square Error (MSE):
Where p (j,k) is the image's correct pixel value at
row x and column y, p (x,y) is the approximation
value of the same pixel, and m and n are the
image's dimensions (rows and columns
respectively). Peak Signal to Noise Ratio (PSNR):
Except for the non-orthogonal SDCT approach, the
data reveal that compression utilizing CB11 delivers
the best PSNR values. There are three categories of
behavior noticed. Increasing output quality as the
number of retained increases coefficients (RC). This
By raising the RC for CB11, BAS08, BAS09, and
BAS11 (a = 0 and a = 1), a virtually constant PSNR is
obtained. This happens with BC12 and PEA14,
resulting in a decrease in output quality as the RC
increases. This happens with both BAS11 (a = 2) and
PEA12. Two additional metrics, the Average
Difference (AD) and the Maximum Absolute
Difference (MAD), are employed to get a better
understanding of the resultant quality (MD). These
metrics are defined as follows: Average Difference
(AD):
Maximum Absolute Difference (MD):
Figs. 2 shows the resulting AD and MD for all
methods; the average difference between the
uncompressed and inexact-compressed images
become smaller as RC increases except for BAS11(a
=2) and PEA12 (further confirming the PSNR results
Fig1: Compression of an image using
approximate DCT and bit-level exact computing.
Fig2: Maximum absolute difference (MD) for
compression of an image using approximate
DCT
Fig3: Approximate DCT compression of an
image using inexact adders with different NAB
values; (Number of Approximate bits) NAB =3

values; NAB =4
values; NAB =5
values; NAB =6
In Fig. 1). Fig. 2 shows that the MD between the
uncompressed and inexact-compressed image
pixels is reduced as more retained coefficients are
used, the exceptions are PEA12 and BAS11 (a =2).
This further confirms the previous results.
Fig. 4 depicts the compressed Lena image using the
most accurate CB11 method for three RC values, i.e.,
4, 10 and 16 retained coefficients. This figure also
shows for comparison purpose the exact DCT
compression results with RC = 16.
4.3 Approximate DCT Using Inexact Computing
Consider next the approximate DCT compression of
Lena using inexact adders; as previously, the value of
the NAB is increased from 3 to 6. The PSNR results
are shown in Fig. 3,4,5,6 versus RC; the PSNR of the
Compressed pictures (a measure of quality) are
displayed by running all approximation DCT
algorithms with just one inexact adder (for example,
AMA1 as the inexact adder in the top row). Each
column depicts the compressed picture quality by
running all approximation DCT algorithms with just
inexact adders (for a NAB value). The leftmost
column, for example, is for NAB = 3. The PSNR
degrades as the NAB grows, as predicted (an
acceptable level of PSNR is obtained at a NAB value
of 4). 4.4 Truncation Truncation is one of the inexact
computing strategies that may be used; truncation
outcomes are also displayed. The employment of
inexact adders yields more precise results (truncation
is performed at values of 3 and 4 bits).
5. CONCLUSION
This research introduced a novel method for
compressing pictures by employing the Discrete
Cosine Transform (DCT) algorithm. The suggested
method consists of a three-level structure in which a
multiplier-less DCT transformation (containing just
adds and shift operations) is performed first, followed
by high frequency component (coefficient) filtering
and calculation utilizing inexact adders. It has been
shown that by employing 8 x 8 picture blocks, each
level contributes to an approximation in the
compression process while still producing a very
good quality image at the end. The findings of this
publication suggest that the combined impacts of
these three levels are well known; simulation and
error analysis have shown a remarkable agreement in
results for picture compression as an application of
inexact computing.
Because the suggested framework has been shown to
be successful for a DCT approach incorporating
approximation at all three recommended levels, the
following particular discoveries have been discovered
and proven in this paper via simulation and analysis.
analysis of errors When employing precise 16 bit

adders, CB11 delivers the greatest quality
compression (highest PSNR values) of any
approximation DCT approach (Fig. 1). Other quality
indicators for image manipulation (AD and MD)
PSNR findings were verified. Figures 1 and 2
Methods The next best approaches are BAS08,
BAS11 with a = 0 and BAS11 with a = 1. InXA2 has
been determined to perform the best among the
inexact adders studied [14]. When using inexact
adders. Non-truncation based approaches give
superior results than related truncation schemes when
implementing approximation DCT JPEG
compression, particularly when considering greater
NABs. (Figures 3, 4, and 6) When diverse pictures
are utilized, the DCT calculated with inexact adders
produces consistent results. In general, NAB values
up to 4 provide sufficient compression. Then it was
shown that using bigger NAB values reduces the
quality of the findings significantly. Utilizing four
picture benchmarks, the BC12 and PEA14 techniques
require the least amount of execution time and energy
to compress an image when compared to using an
exact adder. When it comes to the greatest PSNR as a
measure of picture quality, the approximate DCT
technique CB11 delivers the highest value;
nevertheless, when both execution time and energy
savings are considered, the best approximate DCT
method is BAS09.
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