Image coding based on a morphological representation of wavelet data

Edge-based perceptual image coding

We develop a novel psychovisually motivated edge-based low-bit-rate image codec. It offers a compact description of scale-invariant second-order statistics of natural images, the preservation of which is crucial to the perceptual quality of coded images. Although being edge based, the codec does not explicitly code the edge geometry. To save bits on edge descriptions, a background layer of the image is first coded and transmitted, from which the decoder estimates the trajectories of significant edges. The edge regions are then refined by a residual coding technique based on edge dilation and sequential scanning in the edge direction. Experimental results show that the new image coding technique outperforms the existing ones in both objective and perceptual quality, particularly at low bit rates.

AN IMPROVED EMBEDDED ZEROTREE WAVELET IMAGE CODING METHOD BASED ON COEFFICIENT PARTITIONING USING MORPHOLOGICAL OPERATION

In recent years, wavelets have attracted great attention in both still image compression and video coding, and several novel wavelet-based image compression algorithms have been developed so far, one of which is Shapiro's embedded zerotree wavelet (EZW) image compression algorithm. However, there are still some deficiencies in this algorithm. In this paper, after the analysis of the deficiency in EZW, a new algorithm based on quantized coefficient partitioning using morphological operation is proposed. Instead of encoding the coefficients in each subband line-by-line, regions in which most of the quantized coefficients are significant are extracted by morphological dilation and encoded first. This is followed by using zerotrees to encode the remaining space which has mostly zeros. Experimental results show that the proposed algorithm is not only superior to the EZW, but also compares favorably with the most efficient wavelet-based image compression algorithms reported so far.

Detection of ECG Signal Based on Multi-resolution Sub-band Filter

A high noisy environment severely contaminates the ECG signal. In this paper, the use of a wavelet transform domain filtering technique as an adaptive de-noising tool, implemented in ECG signal analysis, is presented. The multi-resolution representations of the signal, produced by wavelet transform (WT), are used for signal structure extraction. Experimental results have shown that the implementation of this wavelet-based filter in ECG signal analysis results in an efficient reduction of the high noisy environment, producing an almost noise-free output signal. Due to its simplicity and its fast implementation the method can easily be used in clinical medicine.

Noise Reduction in ECG Signal Based on Adaptive Wavelet Transform

Noise always influences on the result of signal-detection, therefore it is a hot topic to detect signal under the low signal-to-noise ratio (SNR) in current detection field. However, it is an intractable problem of signal-detection to extract weak signal under a high noisy environment. Adaptation filter provides a simple and useful way to detect signal. Through measuring and studying, it is possible to carry out the best combination of weak signal under the condition of weak signal. In this paper, we propose a novel mechanism to detect the ECG signal based on adaptation wavelet transform (WT). We adopt the sub-strap coded theory of WT and restore post-combination weak signal through adaptation matching of multi sub-straps' weights. The simulation results show that the proposed method can further improve the ability to detect signal, which is a very effective scheme to detect the property of weak signal and improve SNR.

Curved wavelet transform for image coding

The conventional two-dimensional wavelet transform used in existing image coders is usually performed through one-dimensional (1-D) filtering in the vertical and horizontal directions, which cannot efficiently represent edges and lines in images. The curved wavelet transform presented in this paper is carried out by applying 1-D filters along curves, rather than being restricted to vertical and horizontal straight lines. The curves are determined based on image content and are usually parallel to edges and lines in the image to be coded. The pixels along these curves can be well represented by a small number of wavelet coefficients. The curved wavelet transform is used to construct a new image coder. The code-stream syntax of the new coder is the same as that of JPEG2000, except that a new marker segment is added to the tile headers. Results of image coding and subjective quality assessment show that the new image coder performs better than, or as well as, JPEG2000. It is particularly efficient for images that contain sharp edges and can provide a PSNR gain of up to 1.67 dB for natural images compared with JPEG2000.

Mutual information-based analysis of JPEG2000 contexts

Context-based arithmetic coding has been widely adopted in image and video compression and is a key component of the new JPEG2000 image compression standard. In this paper, the contexts used in JPEG2000 are analyzed using the mutual information, which is closely related to the compression performance. We first show that, when combining the contexts, the mutual information between the contexts and the encoded data will decrease unless the conditional probability distributions of the combined contexts are the same. Given I, the initial number of contexts, and F, the final desired number of contexts, there are S(I, F) possible context classification schemes where S(I, F) is called the Stirling number of the second kind. The optimal classification scheme is the one that gives the maximum mutual information. Instead of using an exhaustive search, the optimal classification scheme can be obtained through a modified generalized Lloyd algorithm with the relative entropy as the distortion metric. For binary arithmetic coding, the search complexity can be reduced by using dynamic programming. Our experimental results show that the JPEG2000 contexts capture the correlations among the wavelet coefficients very well. At the same time, the number of contexts used as part of the standard can be reduced without loss in the coding performance.

Embedded image compression based on wavelet pixel classification and sorting

The method of modeling and ordering in wavelet domain is very important to design a successful algorithm of embedded image compression. In this paper, the modeling is limited to "pixel classification," the relationship between wavelet pixels in significance coding. Similarly, the ordering is limited to "pixel sorting," the coding order of wavelet pixels. We use pixel classification and sorting to provide a better understanding of previous works. The image pixels in wavelet domain are classified and sorted, either explicitly or implicitly, for embedded image compression. A new embedded image code is proposed based on a novel pixel classification and sorting (PCAS) scheme in wavelet domain. In PCAS, pixels to be coded are classified into several quantized contexts based on a large context template and sorted based on their estimated significance probabilities. The purpose of pixel classification is to exploit the intraband correlation in wavelet domain. Pixel sorting employs several fractional bit-plane coding passes to improve the rate-distortion performance. The proposed pixel classification and sorting technique is simple, yet effective, producing an embedded image code with excellent compression performance. In addition, our algorithm is able to provide either spatial or quality scalability with flexible complexity.

Information-theoretic analysis of interscale and intrascale dependencies between image wavelet coefficients

This paper presents an information-theoretic analysis of statistical dependencies between image wavelet coefficients. The dependencies are measured using mutual information, which has a fundamental relationship to data compression, estimation, and classification performance. Mutual information is computed analytically for several statistical image models, and depends strongly on the choice of wavelet filters. In the absence of an explicit statistical model, a method is studied for reliably estimating mutual information from image data. The validity of the model-based and data-driven approaches is assessed on representative real-world photographic images. Our results are consistent with empirical observations that coding schemes exploiting inter- and intrascale dependencies alone perform very well, whereas taking both into account does not significantly improve coding performance. A similar observation applies to other image processing applications.

Multiple description wavelet based image coding

We consider the problem of coding images for transmission over error-prone channels. The impairments we target are transient channel shutdowns, as would occur in a packet network when a packet is lost, or in a wireless system during a deep fade: when data is delivered it is assumed to be error-free, but some of the data may never reach the receiver. The proposed algorithms are based on a combination of multiple description scalar quantizers with techniques successfully applied to the construction of some of the most efficient subband coders. A given image is encoded into multiple independent packets of roughly equal length. When packets are lost, the quality of the approximation computed at the receiver depends only on the number of packets received, but does not depend on exactly which packets are actually received. When compared with previously reported results on the performance of robust image coders based on multiple descriptions, on standard test images, our coders attain similar PSNR values using typically about 50-60% of the bit rate required by these other state-of-the-art coders, while at the same time providing significantly more freedom in the mechanism for allocation of redundancy among descriptions.