Source-linked AI summary
Haar Wavelet Based Approach for Image Compression and Quality Assessment of Compressed Image
Kamrul Hasan Talukder, Koichi Harada
TL;DR
The paper addresses efficient storage and transmission of image data while preserving acceptable image quality. It presents a low-complexity 2D Haar-wavelet compression method with thresholding and evaluates reconstructed images using compression and quality metrics. The reported results include CR 14.375 for universal thresholding and PSNR 24.875 for the universal method.
Problem
Growing digital-image data creates substantial storage and transmission demands, motivating efficient compression with acceptable reconstructed-image quality.
Method
The paper applies a 2D Haar discrete wavelet transform, thresholds detail coefficients, reconstructs images, and evaluates them with CR, PSNR, MOS, and PQS.
Results
CR is 14.375 for universal thresholding, while PSNR is 24.875 for the universal method; soft thresholding performs better than hard thresholding for PSNR.
Takeaways & Limitations
Threshold selection controls the tradeoff between compression and image quality, while perceptual measures are used because PSNR alone is not adequate for picture quality.
Abstract
from arXiv · showhide
With the increasing growth of technology and the entrance into the digital age, we have to handle a vast amount of information every time which often presents difficulties. So, the digital information must be stored and retrieved in an efficient and effective manner, in order for it to be put to practical use. Wavelets provide a mathematical way of encoding information in such a way that it is layered according to level of detail. This layering facilitates approximations at various intermediate stages. These approximations can be stored using a lot less space than the original data. Here a low complex 2D image compression method using wavelets as the basis functions and the approach to measure the quality of the compressed image are presented. The particular wavelet chosen and used here is the simplest wavelet form namely the Haar Wavelet. The 2D discret wavelet transform (DWT) has been applied and the detail matrices from the information matrix of the image have been estimated. The reconstructed image is synthesized using the estimated detail matrices and information matrix provided by the Wavelet transform. The quality of the compressed images has been evaluated using some factors like Compression Ratio (CR), Peak Signal to Noise Ratio (PSNR), Mean Opinion Score (MOS), Picture Quality Scale (PQS) etc.
I. INTRODUCTION
Image compression addresses the storage and transmission demands created by growing digital-image use. The introduction motivates transform and wavelet-based methods, highlighting wavelets' compression and transmission advantages.
- Motivation: Digital images require substantial storage capacity and transmission bandwidth, challenging current technologies and multimedia applications.The paper cites teleconferencing, HDTV, satellite communications, and digital movie storage as applications requiring high compression.
- Motivation: Image compression removes redundant information to reduce file size while maintaining acceptable visual quality.Smaller files require less storage and can be transmitted or downloaded more quickly.
- Transform Coding: DCT transforms image data into a frequency domain where fewer coefficients can represent typical image blocks efficiently.For typical 8x8 blocks, many spatial-frequency coefficients are zero or near zero.
- Wavelet Compression: Wavelet-based algorithms are prominent contenders in the JPEG-2000 standard.
- Wavelet Compression: Wavelet-based compression avoids blocking artifacts, supports scalability and progressive transmission, and can achieve high compression ratios.The introduction also associates wavelets with human-visual-system characteristics and robustness to transmission and decoding errors.
II. BACKGROUND
The paper introduces image-compression background covering compression principles, compression-method classifications, general image-coder structure, and wavelets for image compression.
- Background: The background section surveys image-compression principles, method classifications, general image-coder frameworks, and wavelets.
A. Principles of Image Compression
Image compression exploits redundancy and irrelevancy in images to create less-correlated representations. Redundancy reduction removes duplication, while irrelevancy reduction omits information not noticed by the human visual system.
- Compression Principles: Neighboring pixels are correlated, so a primary compression task is finding a less-correlated image representation.
- Compression Principles: Compression combines redundancy reduction, which removes duplication, with irrelevancy reduction, which omits information not noticed by the HVS.HVS denotes the Human Visual System.
- Compression Principles: Spatial redundancy or correlation is identified as one type of redundancy in images.
B. Classification of Compression Technique
Compression techniques are classified along two dimensions: lossless versus lossy and predictive versus transform coding. These categories differ in reconstruction fidelity and how image information is encoded.
- Lossless versus Lossy: Lossless compression reconstructs an image numerically identical to the original but generally achieves only modest compression.
- Lossless versus Lossy: Lossy compression permits degradation relative to the original, often by discarding redundant information.
- Predictive versus Transform Coding: Predictive coding uses available information to predict future values and codes the difference in the spatial domain.DPCM is identified as one example of predictive coding.
- Predictive versus Transform Coding: Transform coding encodes image information after transforming it from the spatial domain.The supplied passage introduces transform coding but truncates its further explanation.
C. Framework of General Image Compression Method
A typical lossy image compression system combines source transformation, quantization, and entropy encoding to reduce image data. The source encoder decorrelates data, the quantizer reduces coefficient precision, and the entropy encoder further compresses quantized values losslessly.
- A typical lossy image compression system contains a source encoder, quantizer, and entropy encoder.These components work together as the encoder framework.
- Source Encoder (Linear Transformer): The source encoder applies a linear transform such as DFT, DCT, or DWT to decorrelate image data.Each transform has different advantages and disadvantages.
- Quantizer: The quantizer reduces storage bits by lowering transformed-coefficient precision through a lossy many-to-one mapping.Scalar and vector quantization are possible, using uniform or non-uniform quantizers depending on the problem.
- Entropy Encoder: The entropy encoder losslessly compresses quantized values by modeling their probabilities and assigning appropriate codes.Its output code stream can be smaller than the input stream.
- Best compression requires an optimum signal transformation together with properly designed quantization and entropy encoding.
D. Wavelets for image compression
Wavelet transforms represent image data across spatial and frequency information using scaled and shifted mother wavelets. Their multiresolution structure supports processing at different detail scales, progressive transmission, and image zooming without extra storage.
- Wavelet transforms exploit spatial and frequency correlations through dilations and translations of a mother wavelet.
- Multiresolution analysis allows wavelet transforms to operate at different scales according to the required image details.
- Wavelet representations support progressive image transmission and zooming without requiring extra storage.
A. Haar Wavelet Transform
The Haar wavelet transform represents images through recursively averaged coefficients and detail coefficients, enabling reconstruction and compression by thresholding small details.
- A. Haar Wavelet Transform: The one-dimensional Haar transform recursively averages and differences coefficients, producing a lower-resolution representation plus detail coefficients that support reconstruction.For the four-pixel example, the transform is [6 2 1 - 1].
- A. Haar Wavelet Transform: The Haar multiresolution framework uses nested spaces V0⊂ V1⊂ V2⊂ …, where each space represents piecewise-constant functions at a different resolution.The associated scaling and wavelet functions generate the one-dimensional basis used to construct the 2D transform.
- A. Haar Wavelet Transform: The 2D Haar DWT uses one scaling function and three wavelet functions to capture horizontal, vertical, and diagonal details.These functions are formed by multiplying one-dimensional scaling and wavelet functions.
- A. Haar Wavelet Transform: The 2D transform applies the one-dimensional transform across rows and then columns, recursively operating on the quadrant containing averages.This produces one overall average coefficient and detail coefficients at multiple resolution levels.
- A. Haar Wavelet Transform: Thresholding detail coefficients whose magnitudes are at most ε increases zeros and compression, while ε=0 preserves lossless reconstruction.The paper uses hard, soft, and universal thresholding, with image quality depending on the tradeoff between ε and compression.
IV. QUALITY MEASUREMENT
The study evaluates compressed grayscale images using compression ratio, PSNR, MOS, and PQS. It reports thresholding-dependent compression and PSNR results, while noting that perceptual measures complement PSNR.
- Experimental setup: Twenty 256×256 grayscale images were evaluated, with CR defined as the ratio of original to updated transformed nonzero elements.The experiment compares thresholding methods across compression settings.
- Compression ratio: 14.375 CR was reported for universal thresholding, while hard thresholding provided the best CR and soft thresholding depended on ε.The paper states that soft thresholding outperformed universal thresholding in CR under appropriate ε selection.
- PSNR: 24.875 PSNR was reported for universal thresholding, while soft thresholding performed better than hard thresholding.PSNR is defined from the mean squared error between the original and decompressed images.
- Perceptual quality: MOS and PQS were applied because PSNR was considered inadequate as a perceptually meaningful picture-quality measure.PQS combines distortion measures using regression with MOS, while MOS uses a five-grade impairment scale.
V. DISCUSSION
The discussion emphasizes that decomposition level and coefficient thresholding govern compression quality. It also limits the reported experiments to grayscale images while describing how the approach could extend to color components.
- Wavelet decomposition: A larger number of wavelet decompositions can better separate important DWT coefficients from less important coefficients.Decomposition level also determines the lowest resolution represented in the wavelet domain.
- Coefficient thresholding: Compression is performed by discarding wavelet coefficients below a threshold using hard, soft, or universal thresholding.The experiment supports fixed-compression operation by changing the threshold to reach the required compression ratio.
- Image scope: The experiments consider only grayscale images, although the transforms and compression techniques are described as applicable independently to color components.The discussion distinguishes luminance and chromatic components when describing a possible RGB-to-YIQ extension.
VI. CONCLUSION
The paper presents a low-complexity 2D Haar-wavelet image-compression method with compressed-image quality measurement. It identifies threshold selection, transformation level, and metric comparison as areas for further study.
- Conclusion: A low-complexity 2D image-compression method using Haar wavelets is presented together with compressed-image quality measurement.The conclusion frames the method as suitable for addressing storage and imaging-resource constraints.
- Future work: Future work includes studying the tradeoff between threshold ε and image quality and determining application-specific transformation levels.The conclusion also proposes more thorough comparisons of still-image quality-measurement algorithms.
- Quality assessment: The reported metrics performed well in estimating perceptual error, but no decisive advantage of one algorithm over another could be concluded.The paper notes that published algorithms sometimes leave implementation parameters unspecified, for which it provides estimates.