Image Compression using Wavelet and SPIHT

Encoding Algorithm

Syed Abdul Rahim, Assoc. Professor, ECE

CH.Manjeeth1, CH. Mounika2 , G.Vishnu Priya3, I. Uday Babu4

Department Of Electronics And Communication Engineering

Rise Krishna Sai Prakasam Group Of Institutions , Vallur , Ongole: 523272,

Andhra Pradesh , India

Abstract:-Image compression is nothing but reducing the amount of data required to represent an

image. To compress an image efficiently we use various techniques to decrease the space and to increase

the efficiency of transfer of the images over network for better access. But these methods have been

replaced by digital wavelet transform based compression method as these methods have high speed, low

memory requirements and complete reversibility. Now in this work we are considering SPIHT as a

placement for wavelet compression methods. SPIHT gives better simplicity and better compression

compared to the other techniques. We are comparing it with wavelet encoding scheme and comparing the

final results in terms of bit error rate, PSNR and MSE.

Keywords: - Wavelet transform Scalability, SPIHT, PSNR, MSE.

1. INTRODUCTION

Compression is the process of reducing large data

files into smaller files for efficiency of storage and

transmission.

Data compression techniques are:

a. Lossless data compression

b. Lossy data compression

Lossless data compression is nothing but the

original data can be reconstructed exactly from

compressed data.

Lossy data compression in which data after

compression and then decompression retrieves a file

that is not exactly as the original data as there will

be loss of data.

1.1. Wavelets Definition Wavelets are mathematical functions that cut up

data into different frequency components. The

fundamental idea behind wavelets is to analyze the

signal at different scales or resolutions, which is

called multiresolution.

1.2. Wavelet Transform The most important feature of wavelet transform is

it allows multiresolution decomposition. An image

that is decomposed by wavelet transform can be

reconstructed with desired resolution. The

procedure for this is a low pass filter and a high

pass filter is chosen, such that they exactly halve

thefrequency range between themselves. This filter

pair is called the Analysis Filter pair. First of all, the

low pass filter is applied for each row of data, and

then we obtain low frequency components of the

row. As the LPF is a half band filter, the output data

consists of frequencies only in the first half of the

original frequency range. By Shannon's Sampling

Theorem, they can be sub sampled by two, so that

the output data contains only half the original

number of samples, similarly the high pass filter is

applied for the same row of data, and now the high

pass components are separated, and placed by the

side of the low pass components. This procedure is

done for all rows.

1.3. wavelet decomposition

LL HL

LH HH

1st level

LL HL HL

LH HH

LH HH

2nd level

LL HL HL

HL

LH HH

LH HH

LH HH

3rd level

Fig:-wavelet decomposition

2. SPIHT ALGORITHM Set Portioning in Hierarchical Trees (SPIHT) is a wavelet based Image compression method SPIHT introduces three lists:

a. List of Significant Pixels (LSP), b. List of Insignificant Pixels (LIP) and

c. List of Insignificant Sets (LIS).

The SPIHT algorithm partitions the decomposed

wavelet into significant and insignificant partitions

based on

the following function:

---(1)

Here Sn(T) is the significance of a set of coordinates

T, and Ci,j is the coefficient value at coordinate (i,

j).

There are two passes in the algorithm- the sorting

pass and the refinement pass. The SPIHT encoding

process utilizes three lists,

LIP (List of Insignificant Pixels) – It contains

individual coefficients that have magnitudes smaller

than the thresholds.

LIS (List of Insignificant Sets) – It contains set of

wavelet coefficients that are defined by tree

structures and are found to have magnitudes smaller

than the threshold.

LSP (List of Significant Pixels) – It is a list of pixels

found to have magnitudes larger than the threshold

(significant).

The sorting pass is performed on the above three

lists. The maximum number of bits required to

represent the largest coefficient in the spatial

orientation tree is obtained and represented by nmax,

which is

---(2)

To find the number of passes we use above the

formula First initialization is done, and then algorithm takes two stages for each level of threshold 1. The sorting pass (in which lists are organized) and

2. The refinement pass.

Original Wavelet Sorting

Image transform pass

Transmission Entropy Refinement

coding pass

Fig -6: Block diagram of SPIHT

We find initial threshold as T0=2n.

During the sorting pass, those coordinates of the

pixels which

Remain in the LIP are tested for significance by

using equation 1, The result is sent to the output and

out of it the significant will be transferred to the

LSP as well as having their sign bit output. Sets in

the LIS will get their significance tested too and if

found significant, will be removed and partitioned

into subsets. Subsets with only one coefficient and

found to be significant, will be eliminated and

divided into subsets.

Subsets having only one coefficient and found to be

significant will be inserted to the LSP; otherwise

they will be inserted to the LIP.

In the refinement pass, the nth MSB of the

coefficients in the LSP is the final output. The value

of n is decremented and the sorting and refinement

passes are applied again.

These passes will keep on continuing until either the

desired rate is reached or n =0, and all nodes in the

LSP have all their bits output. The latter case will

give an almost exact reconstruction since all the

coefficients have been processed completely.

(a)Original Image (b)Reconstructed Image through DCT

(c) Reconstructed Image through SPIHT

%psnr_dct=10*log10(psnr_num/psnr_den);

%mse_dct = (mseR + mseG + mseB)/3;

MSE=sum(sum((double(img_spiht)-

double(Orig_I)).^2))/nRow / nColumn;

Psnr of SPIHT =10*log10(Q*Q/MSE)

3.RESULTS

For Lena Image

DCT SPIHT

MSE 54.00 6.72

PSNR 30.81 39.85

So from the above table it is clear that SPIHT is a

better method as it demonstrates low error (lower

value of MSE) and higher fidelity (higher peak to

signal ratio).

4. FUTURE VIEW

1. In future this work may extend for the color

image and video compression.

2.For Achieving higher compression

rates SPIHT for coding followed by CABAC

(Context Based Adaptive Binary Arithmetic

Coding) may be employed.

5. CONCLUSIONS

In this paper Image is considered and wavelet

transform is applied on the image and wavelet

decomposition is done. By using SPIHT algorithms

in terms memory spacing, size, compression ratio,

mean square error, peak signal to noise ratio are

analysed. So this paper presents comparative

analysis between compression algorithms. In this

work we have provided the basics of wavelet

transform and comparisons of different algorithms

used for an image. Finally we get reduced bit stream

and better scalability.

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