An Enhanced Image Compression Codec using Spline-based Directional

Lifting Wavelet Transform and an Improved SPIHT Algorithm

Rania Boujelbene and Yousra Ben Jemaa

University of Tunis-El Manar, L3S Laboratory, ENIT, Tunis, Tunisia

Keywords:

Image Compression, Spline-wavelet Transform, Directional Lifting, Improved SPIHT.

Abstract:

A novel lossy image-compression scheme is proposed in this paper. A two-step structure is embedded in this

codec. A spline-based directional lifting wavelet transform is used to decorrelate the image data in the ﬁrst

step. Then in the second step, an improved Set Partitioning in Hierarchical Trees (SPIHT) algorithm based on

binary tree is developed to code the wavelet coefﬁcients. The numerical results demonstrated the efﬁciency of

the proposed approach to achieve signiﬁcant gains in terms of PSNR, BD-PSNR and SSIM for all test images.

It offers better results compared to the existing ones.

1 INTRODUCTION

Image compression is important for many applica-

tions that imply enormous data storage, transmission

and retrieval such as for multimedia (SerElkhetm and

Heshmat, 2020), video conferencing (Wang et al.,

2018), medical imaging (Kumar and Parmar, 2020)

and so on.

During the past few years, several lossy image com-

pression schemes have been developed. Usually, a

three processing steps known as decorrelation, quan-

tization and entropy coding (specially the arithmetic

coding) are embedded in these schemes.

In the ﬁrst step, the Discrete wavelet transform

(DWT) has been successfully used in image-

processing applications (Wu, 1997) ever since Mal-

lat proposed the multiresolution representation of sig-

nals based on wavelet decomposition. The advan-

tage of DWT over other transformations is that it

performs multiresolution analysis with localization in

both time and frequency (Saroya and Kaur, 2014).

DWT has traditionally been implemented by convo-

lution structure. However, this method requires both

far more computations and large storage features that

are not desirable for either high speed or low power

image processing applications. Hence, the lifting

based DWT (Daubechies and Sweldens, 1998) was

proposed and it has become popular with less cost

of computation, more efﬁcient performance and eas-

ier hardware implementability. In (Boujelbene et al.,

2016), a new biorthogonal wavelet transforms using

splines performed in a lifting manner is proposed .

Unlike conventional approaches which are limited to

a few orders of splines, the proposed method uses

several orders of ﬁlters in order to converge towards

an optimal transformation. However, this approach

does not faithfully represent the detailed information

of the image. To adjust much better to the image

orientation characteristics, a new kinds of wavelet-

like transforms have been proposed such as grou-

plets (Mallat, 2009), tetrolets (Krommweh, 2010) and

so on. These transforms require an edge-detection

step and an adaptive decomposition (Saha et al.,

2020). However, the edge-detection stage is gener-

ally a computationally-requiring process. Another se-

ries of methods (Chang and Girod, 2007) (Boujel-

bene and Jemaa, 2020) using the lifting scheme to em-

brace the ﬂexibility of arbitrary directional transform

e.g. adaptive directional lifting (ADL) have been pro-

posed. These methods achieve higher compression

performance.

After the image decomposition, an existing coding

algorithm, such as EZW, SPIHT or SPECK, is usually

followed directly. Some improved coding method like

(Huang and Dai, 2012; Ke-kun, 2012; Jiang et al.,

2018; Mander and Jindal, 2017) can be also used.

Indeed, in (Huang and Dai, 2012), a scan method

based on binary tree coding with adaptive scanning

order (BTCA) is proposed. This algorithm has qual-

ity, position, and resolution scalability. However, it

is only a little slower than SPIHT without arithmetic

coding. In (Jiang et al., 2018), an image coding algo-

rithm called SLCCA Plus which uses Non-Uniform

Quantization, Extended Cluster Filtering, and Signi-

Boujelbene, R. and Ben Jemaa, Y.

An Enhanced Image Compression Codec using Spline-based Directional Lifting Wavelet Transform and an Improved SPIHT Algorithm.

DOI: 10.5220/0010549306310638

In Proceedings of the 16th International Conference on Software Technologies (ICSOFT 2021), pages 631-638

ISBN: 978-989-758-523-4

631

ﬁed Shared-Zerois is proposed. Although it raises the

coding gain, this method requires more time. In order

to speed up the encoding time, an improved SPIHT

algorithm based on binary tree (Ke-kun, 2012) which

raises the coding efﬁciency is proposed.

Unlike exsiting approachs which can have limited

performance by considering only one compression

stage either of decorrelation or coding, and in order to

provide a good compression scheme, both the process

of image decomposition and coding are considered in

this paper. First, we employ a new spline wavelet

transform based on directional lifting (ADL-SWT),

which aims at further reducing the magnitude of the

high-frequency wavelet coefﬁcients. Then, after the

ADL-SWT transform, an improved SPIHT coding al-

gorithm based on binary tree (TSPIHT) is used, which

can provide good coding performance with low com-

plexity.

The remainder of this paper is organized as fol-

lows: In Section 2, the block diagram for the pro-

posed codec is presented in detail. Here, we de-

scribe the principle of the spline-based directional lift-

ing wavelet transform and the different steps of the

TSPIHT coding algorithm. The experimental results

are presented in Section 3, followed ﬁnally by a con-

clusion in Section 4.

2 PROPOSED CODEC SCHEME

FOR WAVELET IMAGE

COMPRESSION

We present here the block diagram of the proposed

wavelet image compression scheme which is com-

posed of two connected blocs as shown in Figure 1.

Figure 1: Block diagram for optimal codec.

A Spline wavelet transform based on adaptive di-

rectional lifting (ADL-SWT) represents the transform

which combines the spline ﬁlter of order 5 with the

adaptive directional lifting (ADL).

After the wavelet transform step, we try to get a way

to code the wavelet coefﬁcients into an effective result

by taking into account the storage space , the redun-

dancy and the speed. An improved SPIHT based on

binary tree (TSPIHT) image coding is the best way

which allows to raise the coding efﬁciency with de-

creasing the encoding time. In addition, this algo-

rithm does not require arithmetic coding to improve

its performance.

Once the input image has been coded, it is saved or

sent through the communication channel to the re-

ceiver who needs to use this code in order to recon-

struct the input image. This is the decoding process

which consists of the TSPIHT decoding and the in-

verse ADL-SWT.

2.1 ADL-SWT

Instead of alternately using the lifting-based predic-

tion in the horizontal or vertical direction, the ADL

performs the prediction in windows of high pixel

correlation. For lossy image compression, unlike

conventional methods that use the ADL with the

biorthogonal 9/7 ﬁlter, this technique mixes ADL

with a spline wavelet ﬁlter. In fact, we have concen-

trated on the polynomial spline for the calculation of

the ﬁlter taps. Lately, it was shown in (Boujelbene

et al., 2016; Boujelbene et al., 2017) that the poly-

nomial spline wavelet ﬁlter of ﬁfth order provides the

best performance as compared to the most efﬁcient

existing ﬁlters such as the biorthogonal 9/7.

Hence, to construct this performed scheme, the best

spline ﬁlter of ﬁfth order is combined with the ADL

by incorporating the coefﬁcients calculated by this ﬁl-

ter into the ADL. Thus, the proposed ADL-SWT is

employed as the representation of our image compres-

sion system. The proposed 2-D ADL-SWT involves

two separable transforms. The schematic representa-

tion of this transform is shown in Figure 2.

Let X[m,n] be a 2-D signal, where m and n repre-

sent the row and column indices, respectively. Firstly,

carry out 1-D ADL-SWT on each image column, pro-

ducing a vertical low-pass subband (L) and a vertical

high-pass subband (H). Secondly, carry out 1-D ADL-

SWT on each row of L and H.

After one-level decomposition, one low-pass subband

(LL) and three high-pass subbands (LH,HL and HH)

are generated. In other words, the subband decompo-

sition structure of 2-D ADL-SWT is the same that of

2-D DWT. The decomposition process of ADL-SWT

can be extended to any desired level

For ADL-SWT, unlike DWT which does transform

along the ﬁxed direction, the selected ﬁltering need

to be encoded as side information. So, to reduce the

overhead bits for the direction information, the image

is divided into regions of approximately uniform edge

orientations. All the pixels in the local region are pre-

dicted and updated along the uniform direction which

is chosen in a rate-distortion optimal sense.

ICSOFT 2021 - 16th International Conference on Software Technologies

632

Figure 2: 2-D Adaptive Directional Lifting Spline Wavelet Transform.

The main steps of the ADL-SWT transform are illus-

trated by Algorithm 1.

Algorithm 1: ADL-SWT transform.

1: The image is adaptively divided into blocks of variable

sizes based on hierarchical quadtree segmentation.

2: Each block of 16x16 can be divided into three modes

(16x16, 8x8 and 4x4).

3: Perform the ADL of spline wavelet ﬁlter on these

modes

4: if The enegry metric (sum of absolute coefﬁcients in

high frequency subband) related to one of these block

modes is smaller than the other then

5: Select this mode

6: end if

7: The output is divided to variable-size regions based on

hierarchical quadtree segmentation.

8: Each block of 16x16 can be divided into three modes

(16x16, 8x8 and 4x4).

9: Perform the ADL of spline wavelet ﬁlter on these

modes

10: if The enegry metric related to one of these block

modes is smaller than the other then

11: Select this mode

12: end if

13: The inverse transform is performed to reconstruct the

image by giving the optimal lifting direction as side

information

2.2 TSPIHT Algorithm

Set Partitioning In Hierarchical Tree algorithm

(SPIHT) (Said and Pearlman, 1996) is one of the

most most powerful and efﬁcient algorithms for im-

age compression available. It is based on the same

concepts: a progressive coding is applied, processing

the image respectively to a lowering threshold. The

difference is in the concept of zero trees : in SPIHT,

a spatial orientation trees is used. This is an idea that

takes into account bounds between coefﬁcients across

sub bands at different levels. The main steps of the

SPIHT algorithm are as follows:

1. If there is a coefﬁcient at the highest level of the

wavelet transform in a certain subband which con-

sidered insigniﬁcant against a certain threshold, it

is very probable that its descendants in lower lev-

els will be insigniﬁcant too. So, we can code quite

a large group of coefﬁcients with one symbol.

2. Put the wavelet coefﬁcients into a sorting pass

that ﬁnds the signiﬁcance coefﬁcients in all coef-

ﬁcients and encodes the sign of these signiﬁcance

coefﬁcients.

3. The signiﬁcance coefﬁcients that can be found in

the sorting pass are put into the reﬁnement pass

that uses two bits to exact the reconstruct value

for approaching to real value.

4. The threshold T is halved and the coding process

will be repeated until the target is met or all the

coefﬁcients are coded.

In order to raise the performance of SPIHT algorithm

and the encoding speed, a TSPIHT coding algorithm

(Ke-kun, 2012) is used and incorporated in our com-

pression codec. In this algorithm, the four coefﬁ-

cients splited by D-type sets (set of coordinates of

all descendants of a node) are coded by binary tree.

Through coding the signiﬁcance of L-type (all de-

scendants except the offspring) sets ﬁrst, the algo-

rithm can determine the signiﬁcance of the root of the

binary tree in advance with high probability, in a way

to improve the coding efﬁciency.

3 EXPERIMENTAL RESULTS

To assess the efﬁciency of the proposed approach,

a number of numerical experiments have been per-

formed on a number of natural images using several

performance measures.

For a fair comparison, the proposed codec has been

compared with the codecs presented in (Boujelbene

et al., 2017) and (Boujelbene and Jemaa, 2020) ﬁrstly

and with the JPEG2000 standard secondly.

3.1 Test Images

The standard Waterloo 8-bit gray-scale image set con-

taining twelve images (Lena: 512 × 512, Barbara:

512 × 512, Boat: 512 × 512, Mandrill: 512 × 512,

An Enhanced Image Compression Codec using Spline-based Directional Lifting Wavelet Transform and an Improved SPIHT Algorithm

633

Zelda: 512 × 512, Goldhill: 512 × 512, Peppers:

512 × 512, House: 512 × 512, Washsat: 512 × 512,

France: 256 × 256, Montage: 256 ×256 and Library:

256×256) of different sizes, ranging from 256 to 512,

has been considered to perform the required tests.

3.2 Performance Criteria

Peak Signal to Noise Ratio (PSNR), Structural Sim-

ilarity Index Measure (SSIM) and Bjøntegaard Delta

PSNR (BD-PSNR) were used in our experiments as a

set of performance criteria.

The PSNR is deﬁned as follows:

PSNR(dB) = 10log

[

(Peak)

MSE

], (1)

where Peak is equal to 255 for the images in 8 bits per

pixel (bpp) and

MSE =

M × N

∑

( f (i, j) −

f (i, j))

, (2)

where f ,

f and M × N represent the original image,

the reconstructed image and the total number of pixels

in the image, respectively.

Besides PSNR, to further evaluate the quality and

the distortion for the reconstructed image using the

presented techniques, we use SSIM which is consid-

ered to be correlated with the quality perception of

the human visual system (HVS). The SSIM is a deci-

mal value between 0 (zero correlation with the origi-

nal image) and 1 (exact same image). It is deﬁned as

follows:

SSIM = [l( f ,

f )]

[c( f ,

f )]

[s( f ,

f )]

(3)

where: ( f ,

f ), l( f ,

f ), c( f ,

f ) and s( f ,

f ) represent

respectively two images, luminance comparison, con-

trast comparison and structural comparison between

two images.

α > 0, β > 0 and σ > 0 are used to adjust the impor-

tance of the three parameters.

To calculate the coding efﬁciency between dif-

ferent codecs based on PSNR measurements, a

Bjøntegaard model was proposed by Gisle Bjntegaard

(Bjontegaard, 2001). It is used to calculate the av-

erage PSNR and bit rate differences between two

rate-distortion (R-D) curves obtained from the PSNR

measurement when encoding a content at different

bit rates. The Bjøntegaard delta PSNR (BD-PSNR),

which corresponds to the average PSNR difference in

dB for the same bit rate is used in our experiments.

3.3 Performance Results

A comparison between the proposed codec and the

existing ones is presented in this section. Firstly, we

have analysed and compared its performance to its ob-

tained by the codecs 1 and 2.

The codec 1 which is presented in (Boujelbene et al.,

2017), is constructed by the optimal spline wavelet

transform (OSWT) with the TSPIHT algorithm. In-

deed, OSWT is the optimal spline wavelet transform

using conventional lifting and generated by a poly-

nomial spline ﬁlter of order 5. On the other hand,

the codec 2 which is presented in (Boujelbene and Je-

maa, 2020), is constructed by the ADL-SWT trans-

form with the SPIHT algorithm. As mentioned in the

previous section, ADL-SWT is the proposed wavelet

transform using directional lifting and a polynomial

spline ﬁlter of order 5.

We present in Table 1 the PSNR and SSIM results

of all the test images at different bitrates.

Obviously, Table 1 shows that the PSNR results ob-

tained by the proposed codec for all test images are

better than those obtained by the two codecs in most

cases, and the improvement in PSNR is around 0.02-

1.64 dB for all test images when compared to codec 1

and up to 0.43 dB when compared to codec 2.

Also, it is observed from Table 1 that the proposed

codec produces high SSIM values when compared to

the existing ones.

In addition, the coding efﬁciency was evaluated

using the BD-PSNR gain measure. According to the

simulation results shown in Table 2, we conclude

that the proposed codec outperforms the two existing

codecs for different test images. Indeed, the average

PSNR gain against codecs 1 and 2 reaches 0.421 dB

and 0.189 dB, respectively.

All these results justify the efﬁciency of the

TSPIHT used in codec 1 as compared to the SPIHT

coding algorithm as well as the efﬁciency of the trans-

form using ADL employed in codec 2 over the one

using the conventional lifting.

Moreover, in order to further evaluate the perfor-

mance of the proposed codec, we compare its robust-

ness with the JPEG2000 standard.

Figure 3 illustrates the results in terms of PSNR pro-

vided by the two codecs, and assessed at the same

bitrates. Based on Figure 3, we can conclude that the

results obtained by the proposed codec are better in

most cases to those obtained by JPEG2000.

The performance, reported in Table 3, are com-

puted in terms of BD-PSNR gain. It can be observed

that for all images the proposed codec performs better

than the JPEG2000 standard and the average PSNR

gain can achieve up to 1.185 dB against JPEG2000.

ICSOFT 2021 - 16th International Conference on Software Technologies

634

Table 1: Comparison of the coding performance between the proposed and the existing codecs.

Image Bitrate

Methods

Proposed codec Codec 1 Codec 2

PSNR(dB) SSIM PSNR(dB) SSIM PSNR(dB) SSIM

Lena

0.25 34.16 0.9701 34.08 0.9549 34.06 0.967

0.5 37.52 0.989 37.2 0.9775 37.41 0.981

0.75 39.38 0.993 38.99 0.985 39.25 0.989

1 40.8 0.999 40.2 0.9897 40.62 0.997

Barbara

0.25 29.14 0.919 27.5 0.8933 29.03 0.912

0.5 33.27 0.975 31.69 0.9542 33.14 0.969

0.75 35.81 0.9829 34.59 0.9746 35.62 0.9815

1 37.85 0.996 36.62 0.9848 37.77 0.994

Boat

0.25 30.63 0.9421 29.65 0.903 30.5 0.939

0.5 33.91 0.671 33.01 0.9589 33.82 0.9698

0.75 35.89 0.9861 35.1 0.9765 35.81 0.9856

1 37.96 0.9981 36.5 0.9834 37.89 0.997

Mandrill

0.25 23.45 0.791 23 0.7894 23.21 0.7901

0.5 25.46 0.8822 25.31 0.88 25.34 0.8812

0.75 27.66 0.933 27.4 0.9227 27.59 0.9322

1 28.95 0.9721 28.87 0.9471 28.91 0.971

Zelda

0.25 37.57 0.976 37.55 0.9755 37.52 0.9601

0.5 39.76 0.9875 39.71 0.9866 39.71 0.977

0.75 41.15 0.9921 41.01 0.9916 41.01 0.9901

1 42.1 0.9946 42.02 0.9937 41.98 0.9931

Goldhill

0.25 30.61 0.9132 30.3 0.905 30.39 0.8215

0.5 33.06 0.9641 32.83 0.9523 32.96 0.934

0.75 34.97 0.972 34.77 0.9719 34.88 0.9486

1 36.44 0.9832 36.23 0.9807 36.21 0.9629

Peppers

0.25 33.23 0.9621 33.15 0.951 33.07 0.9588

0.5 36.21 0.9747 35.7 0.9728 35.81 0.9733

0.75 37.41 0.9844 36.85 0.981 37.29 0.9822

1 38.78 0.9891 38.1 0.9851 38.43 0.9885

House

0.25 23.49 0.8256 23.41 0.8175 23.31 0.8091

0.5 26.2 0.9178 26.13 0.9059 26.04 0.909

0.75 28.64 0.9513 28.59 0.9452 28.58 0.9448

1 30.3 0.963 30.28 0.9621 30.17 0.9626

Washsat

0.25 33.78 0.8972 33.66 0.8965 33.66 0.8953

0.5 35.99 0.9478 35.75 0.9458 35.91 0.9301

0.75 37.93 0.9719 37.26 0.965 37.63 0.9715

1 38.72 0.98 38.65 0.9787 38.59 0.98

France

0.25 23.36 0.7289 23.21 0.728 23.1 0.7093

0.5 26.49 0.8438 26.01 0.8437 26.32 0.8331

0.75 29.31 0.9119 29.16 0.9111 29.12 0.8899

1 31.4 0.941 31.33 0.9399 31.29 0.9302

Montage

0.25 29.87 0.8899 29.75 0.8894 29.53 0.8721

0.5 35.1 0.9567 34.99 0.9494 34.67 0.9423

0.75 39.02 0.971 38.91 0.971 38.68 0.9688

1 41.94 0.984 41.88 0.9812 41.59 0.9849

Library

0.25 20.51 0.6101 20.45 0.605 20.46 0.5966

0.5 23.91 0.7488 23.39 0.7425 23.68 0.7452

0.75 26.01 0.8215 25.39 0.8113 25.78 0.8106

1 28.71 0.882 27.73 0.8675 27.98 0.8708

An Enhanced Image Compression Codec using Spline-based Directional Lifting Wavelet Transform and an Improved SPIHT Algorithm

635

0 , 2 5 0 , 5 0 0 , 7 5 1 , 0 0

3 4

3 5

3 6

3 7

3 8

3 9

4 0

4 1

P S N R ( d B )

B i t r a t e ( b p p )

P r o p o s e d c o d e c

J P E G 2 0 0 0

(a) Lena

0 , 3 0 , 4 0 , 5 0 , 6 0 , 7 0 , 8 0 , 9 1 , 0

2 8

3 0

3 2

3 4

3 6

3 8

P r o p o s e d c o d e c

J P E G 2 0 0 0

P S N R ( d B )

B i t r a t e ( b p p )

(b) Barbara

0 , 2 5 0 , 5 0 0 , 7 5 1 , 0 0

3 0

3 1

3 2

3 3

3 4

3 5

3 6

3 7

3 8

P r o p o s e d c o d e c

J P E G 2 0 0 0

P S N R ( d B )

B i t r a t e ( b p p )

0 , 3 0 , 4 0 , 5 0 , 6 0 , 7 0 , 8 0 , 9 1 , 0

2 4

2 6

2 8

P r o p o s e d c o d e c

J P E G 2 0 0 0

P S N R ( d B )

B i t r a t e ( b p p )

(d) Mandrill

0 , 3 0 , 4 0 , 5 0 , 6 0 , 7 0 , 8 0 , 9 1 , 0

3 6

3 8

4 0

4 2

P r o p o s e d c o d e c

J P E G 2 0 0 0

P S N R ( d B )

B i t r a t e ( b p p )

(e) Zelda

0 , 2 5 0 , 5 0 0 , 7 5 1 , 0 0

3 0

3 1

3 2

3 3

3 4

3 5

3 6

3 7

P r o p o s e d c o d e c

J P E G 2 0 0 0

P S N R ( d B )

B i t r a t e ( b p p )

(f) Goldhill

0 , 3 0 , 4 0 , 5 0 , 6 0 , 7 0 , 8 0 , 9 1 , 0

3 4

3 6

3 8

P r o p o s e d c o d e c

J P E G 2 0 0 0

P S N R ( d B )

B i t r a t e ( b p p )

(g) Peppers

0 , 3 0 , 4 0 , 5 0 , 6 0 , 7 0 , 8 0 , 9 1 , 0

2 2

2 4

2 6

2 8

3 0

P r o p o s e d c o d e c

J P E G 2 0 0 0

P S N R ( d B )

B i t r a t e ( b p p )

(h) House

0 , 3 0 , 4 0 , 5 0 , 6 0 , 7 0 , 8 0 , 9 1 , 0

3 4

3 6

3 8

P r o p o s e d c o d e c

J P E G 2 0 0 0

P S N R ( d B )

B i t r a t e ( b p p )

(i) Washsat

0 , 3 0 , 4 0 , 5 0 , 6 0 , 7 0 , 8 0 , 9 1 , 0

2 4

2 6

2 8

3 0

3 2

P r o p o s e d c o d e c

J P E G 2 0 0 0

P S N R ( d B )

B i t r a t e ( b p p )

(j) France

0 , 3 0 , 4 0 , 5 0 , 6 0 , 7 0 , 8 0 , 9 1 , 0

3 0

3 2

3 4

3 6

3 8

4 0

4 2

P r o p o s e d c o d e c

J P E G 2 0 0 0

P S N R ( d B )

B i t r a t e ( b p p )

(k) Montage

0 , 3 0 , 4 0 , 5 0 , 6 0 , 7 0 , 8 0 , 9 1 , 0

2 0

2 2

2 4

2 6

2 8

P r o p o s e d c o d e c

J P E G 2 0 0 0

P S N R ( d B )

B i t r a t e ( b p p )

(l) Library

Figure 3: PSNR (in dB) versus the bitrate (bpp) of the proposed and JPEG2000 codecs for all grayscale test images.

ICSOFT 2021 - 16th International Conference on Software Technologies

636

Table 2: BD-PSNR gain (dB) of the proposed codec against codecs 1 and 2 for all test images.

Image

BD-PSNR

codec 1-Proposed codec

BD-PSNR

codec 2-Proposed codec

Lena 0.327 0.12

Barbara 1.532 0.118

Boat 1.007 0.093

Mandrill 0.188 0.162

Zelda 0.05 0.062

Goldhill 0.24 0.142

Peppers 0.467 0.352

House 0.063 0.158

Washsat 0.192 0.095

France 0.357 0.175

Montage 0.103 0.402

Library 0.52 0.283

Average 0.421 0.189

Table 3: BD-PSNR gain of the proposed codec against

JPEG2000 for all grayscale test images.

Image BD-PSNR(dB)

Lena 0.24

Barbara 0.787

Boat 1.013

Mandrill 0.457

Zelda 0.618

Goldhill 0.255

Peppers 0.892

House 0.448

Washsat 0.277

France 0.655

Montage 1.185

Library 0.093

Average 0.577

To conclude, by analysing the results obtained, we

can notice that our proposed approach is consistently

more effective for all test images.

4 CONCLUSION

In this paper, a new wavelet image compression

scheme which is constructed with a new spline

wavelet transform based on adaptive directional lift-

ing and an improved coding algorithm is presented.

Experimental results have shown the superiority of

the proposed codec over the exiting ones in terms of

PSNR, BD-PSNR and SSIM for different test images.

In the future, we plan to ﬁnd a methodology for the

integration of the encryption schemes with our com-

pression codec.

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