Lossless and low-cost integer-based lifting wavelet transform

Discrete wavelet transform (DWT) is a powerful tool for analyzing real-time signals, including aperiodic, irregular, noisy, and transient data, because of its capability to explore signals in both the frequency- and time-domain in different resolutions. For this reason, they are used extensively in a wide number of applications in image and signal processing. Despite the wide usage, the implementation of the wavelet transform is usually lossy or computationally complex, and it requires expensive hardware. However, in many applications, such as medical diagnosis, reversible data-hiding, and critical satellite data, lossless implementation of the wavelet transform is desirable. It is also important to have more hardware-friendly implementations due to its recent inclusion in signal processing modules in system-on-chips (SoCs). To address the need, this research work provides a generalized implementation of a wavelet transform using an integer-based lifting method to produce lossless and low-cost architecture while maintaining the performance close to the original wavelets. In order to achieve a general implementation method for all orthogonal and biorthogonal wavelets, the Daubechies wavelet family has been utilized at first since it is one of the most widely used wavelets and based on a systematic method of construction of compact support orthogonal wavelets. Though the first two phases of this work are for Daubechies wavelets, they can be generalized in order to apply to other wavelets as well. Subsequently, some techniques used in the primary works have been adopted and the critical issues for achieving general lossless implementation have solved to propose a general lossless method. The research work presented here can be divided into several phases. In the first phase, low-cost architectures of the Daubechies-4 (D4) and Daubechies-6 (D6) wavelets have been derived by applying the integer-polynomial mapping. A lifting architecture has been used which reduces the cost by a half compared to the conventional convolution-based approach. The application of integer-polynomial mapping (IPM) of the polynomial filter coefficient with a floating-point value further decreases the complexity and reduces the loss in signal reconstruction. Also, the “resource sharing” between lifting steps results in a further reduction in implementation costs and near-lossless data reconstruction. In the second phase, a completely lossless or error-free architecture has been proposed for the Daubechies-8 (D8) wavelet. Several lifting variants have been derived for the same wavelet, the integer mapping has been applied, and the best variant is determined in terms of performance, using entropy and transform coding gain. Then a theory has been derived regarding the impact of scaling steps on the transform coding gain (GT). The approach results in the lowest cost lossless architecture of the D8 in the literature, to the best of our knowledge. The proposed approach may be applied to other orthogonal wavelets, including biorthogonal ones to achieve higher performance. In the final phase, a general algorithm has been proposed to implement the original filter coefficients expressed by a polyphase matrix into a more efficient lifting structure. This is done by using modified factorization, so that the factorized polyphase matrix does not include the lossy scaling step like the conventional lifting method. This general technique has been applied on some widely used orthogonal and biorthogonal wavelets and its advantages have been discussed. Since the discrete wavelet transform is used in a vast number of applications, the proposed algorithms can be utilized in those cases to achieve lossless, low-cost, and hardware-friendly architectures

Wavelet-Based Embedded Rate Scalable Still Image Coders: A review

Embedded scalable image coding algorithms based on the wavelet transform have received considerable attention lately in academia and in industry in terms of both coding algorithms and standards activity. In addition to providing a very good coding performance, the embedded coder has the property that the bit stream can be truncated at any point and still decodes a reasonably good image. In this paper we present some state-of-the-art wavelet-based embedded rate scalable still image coders. In addition, the JPEG2000 still image compression standard is presented.

Custom Lossless Compression and High-Quality Lossy Compression of White Blood Cell Microscopy Images for Display and Machine Learning Applications

This master's thesis investigates both custom lossless compression and high-quality lossy compression of microscopy images of white blood cells produced by CellaVision's blood analysis systems. A number of different compression strategies have been developed and evaluated, all of which are taking advantage of the specific color filter array used in the sensor in the cameras in the analysis systems. Lossless compression has been the main focus of this thesis. The lossless compression method, of those developed, that gave best result is based on a statistical autoregressive model. A model is constructed for each color channel with external information from the other color channels. The difference between the predictions from the statistical model and the original is further Huffman coded. The method achieves an average bit-rate of 3.0409 bits per pixel on the test set consisting of 604 images. The proposed lossy method is based on taking the difference between the image compressed with an ordinary lossy compression method, JPEG 2000, and the original image. The JPEG 2000 image is saved, as well as the differences at the foreground (i.e. locations with cells), in order to keep the cells identical to the cells in the original image, but allow loss of information for the, not so important, background. This method achieves a bit-rate of 2.4451 bits per pixel, with a peak signal-to-noise-ratio (PSNR) of 48.05 dB

The JPEG2000 still image compression standard

The development of standards (emerging and established) by the International Organization for Standardization (ISO), the International Telecommunications Union (ITU), and the International Electrotechnical Commission (IEC) for audio, image, and video, for both transmission and storage, has led to worldwide activity in developing hardware and software systems and products applicable to a number of diverse disciplines [7], [22], [23], [55], [56], [73]. Although the standards implicitly address the basic encoding operations, there is freedom and flexibility in the actual design and development of devices. This is because only the syntax and semantics of the bit stream for decoding are specified by standards, their main objective being the compatibility and interoperability among the systems (hardware/software) manufactured by different companies. There is, thus, much room for innovation and ingenuity. Since the mid 1980s, members from both the ITU and the ISO have been working together to establish a joint international standard for the compression of grayscale and color still images. This effort has been known as JPEG, the Join

Astronomical Image Compression Techniques Based on ACC and KLT Coder

This paper deals with a compression of image data in applications in astronomy. Astronomical images have typical specific properties — high grayscale bit depth, size, noise occurrence and special processing algorithms. They belong to the class of scientific images. Their processing and compression is quite different from the classical approach of multimedia image processing. The database of images from BOOTES (Burst Observer and Optical Transient Exploring System) has been chosen as a source of the testing signal. BOOTES is a Czech-Spanish robotic telescope for observing AGN (active galactic nuclei) and the optical transient of GRB (gamma ray bursts) searching. This paper discusses an approach based on an analysis of statistical properties of image data. A comparison of two irrelevancy reduction methods is presented from a scientific (astrometric and photometric) point of view. The first method is based on a statistical approach, using the Karhunen-Loeve transform (KLT) with uniform quantization in the spectral domain. The second technique is derived from wavelet decomposition with adaptive selection of used prediction coefficients. Finally, the comparison of three redundancy reduction methods is discussed. Multimedia format JPEG2000 and HCOMPRESS, designed especially for astronomical images, are compared with the new Astronomical Context Coder (ACC) coder based on adaptive median regression

WAVELET BASED DATA HIDING OF DEM IN THE CONTEXT OF REALTIME 3D VISUALIZATION (Visualisation 3D Temps-Réel à Distance de MNT par Insertion de Données Cachées Basée Ondelettes)

The use of aerial photographs, satellite images, scanned maps and digital elevation models necessitates the setting up of strategies for the storage and visualization of these data. In order to obtain a three dimensional visualization it is necessary to drape the images, called textures, onto the terrain geometry, called Digital Elevation Model (DEM). Practically, all these information are stored in three different files: DEM, texture and position/projection of the data in a geo-referential system. In this paper we propose to stock all these information in a single file for the purpose of synchronization. For this we have developed a wavelet-based embedding method for hiding the data in a colored image. The texture images containing hidden DEM data can then be sent from the server to a client in order to effect 3D visualization of terrains. The embedding method is integrable with the JPEG2000 coder to accommodate compression and multi-resolution visualization. Résumé L'utilisation de photographies aériennes, d'images satellites, de cartes scannées et de modèles numériques de terrains amène à mettre en place des stratégies de stockage et de visualisation de ces données. Afin d'obtenir une visualisation en trois dimensions, il est nécessaire de lier ces images appelées textures avec la géométrie du terrain nommée Modèle Numérique de Terrain (MNT). Ces informations sont en pratiques stockées dans trois fichiers différents : MNT, texture, position et projection des données dans un système géo-référencé. Dans cet article, nous proposons de stocker toutes ces informations dans un seul fichier afin de les synchroniser. Nous avons développé pour cela une méthode d'insertion de données cachées basée ondelettes dans une image couleur. Les images de texture contenant les données MNT cachées peuvent ensuite être envoyées du serveur au client afin d'effectuer une visualisation 3D de terrains. Afin de combiner une visualisation en multirésolution et une compression, l'insertion des données cachées est intégrable dans le codeur JPEG 2000