Application In Image Coding Research Articles

Three-dimensional Epanechnikov mixture regression in image coding

Kernel methods have been studied extensively in recent years. We propose a three-dimensional (3-D) Epanechnikov Mixture Regression (EMR) based on our Epanechnikov Kernel (EK) and realize a complete framework for image coding. In our research, we deduce the covariance-matrix form of 3-D Epanechnikov kernels and their correlated statistics to obtain the Epanechnikov mixture models. To apply our theories to image coding, we propose the 3-D EMR which can better model an image in smaller blocks compared with the conventional Gaussian Mixture Regression (GMR). The regressions are all based on our improved Expectation-Maximization (EM) algorithm with mean square error optimization. Finally, we design an Adaptive Mode Selection (AMS) algorithm to realize the best model pattern combination for coding. Our recovered image has clear outlines and superior coding efficiency compared to JPEG below 0.25bpp. Our work realizes an unprecedented theory application by: (1) enriching the theory of Epanechnikov kernel, (2) improving the EM algorithm using MSE optimization, (3) exploiting the EMR and its application in image coding, and (4) AMS optimal modeling combined with Gaussian and Epanechnikov kernel.

Polarization state and image rotation via spontaneously generated coherence in a spinning fast light medium

In this article we propose a four-level rubidium (Rb87) atomic system for observing interesting features of polarization state rotation in a fast light medium. We investigate spontaneously generated coherence (SGC) for a spinning medium. We show how SGC can affect different spectral profiles of the polarization state and images in this suggested model. We observe a 0.5 radian rotation and 2.5 microsecond time advancement in our proposed system. Our precise results will provide a new platform for researchers in quantum optics due to its applications in image coding, telecommunications and cloaking technology.

Optical activity and excitation of surface plasmon polaritons with electromagnetically induced chiral media

Chiral materials possess some unusual properties for which they have attracted tremendous interest in recent research. In this paper, we discuss the interaction of electromagnetic fields with an initially isotropic material, making it anisotropic chiral by inducing magnetoelectric cross coupling. We consider a four-level double Λ -type configuration of an atomic ensemble, which is simultaneously sensitive to relative phase of the applied fields due to its closed-loop nature, providing an extra degree of freedom for controlling the birefringent nature of the medium. We show that the material splits a linearly polarized probe field into left- (LCP) and right-circularly polarized (RCP) components, and their angular divergence can be related to the optical activity of the medium. This leads to efficient modulation of the probe field, which may be helpful in accurate position detection of the transmitted beams and images. Next, we demonstrate that such a medium can be used to couple incident light with surface plasmons (SPs) in two ways: (1) as a prism-like coupler, in either Otto- or Kretschmann-type geometry, where excitation of SPs can be achieved beyond a certain incident angle of the interacting pulse in a plasmonic waveguide placed closed to it; and (2) direct excitation of SPs by a LCP or RCP beam from the chiral medium in a particular slit-type plasmonic waveguide. We find that the coupled modes in the latter case are unidirectional and highly tunable. Further, we show that the birefringent nature of the medium as well as the plasmonic field intensities can be efficiently manipulated with a number of controlling parameters. Our results may find applications in image coding, plasmonic sensors, and bio-photonics.

All Phase Inverse Discrete Sine Biorthogonal Transform and Its Application in Image Coding

All Phase Inverse Discrete Sine Biorthogonal Transform and Its Application in Image Coding

Embedding Binary Image Watermark in DC Components of All Phase Discrete Cosine Biorthogonal Transform

Watermarking technique provides the possibility for copyright protection. Discrete cosine transform (DCT) is the most popular tool used in watermarking algorithm. But the watermarking algorithm based on DCT is not the most ideal choice in terms of the complexity and robustness. All phase discrete cosine biorthogonal transform (APDCBT) owns the characteristics of high frequency attenuation and good applications in image coding, image denoising and other fields of digital image processing, which provides an efficient method for watermarking. In this paper, a new watermarking algorithm based on APDCBT is proposed. Besides, the binary image watermark is scrambled by Arnold transform to enhance its privacy and robustness greatly in our algorithm. The watermark information is embedded in direct-current (DC) components considering DC components have much larger perceptual capacity. Compared with the DCT algorithm, the proposed algorithm has stronger robustness in embedding and extracting the watermark. Experimental results show that our algorithm can satisfy the imperceptibility and robustness very well. Furthermore, our algorithm is tested against four kinds of attacks: JPEG compression, Gaussian noise, salt & pepper noise and rotation.

Structural similarity index measurement-noise shaping algorithm and its application in image coding and transmission

Structural similarity index measurement-noise shaping algorithm and its application in image coding and transmission

Adaptive Golomb Code for Joint Geometrically Distributed Data and Its Application in Image Coding

This paper proposes joint-probability-based adaptive Golomb coding (JPBAGC) to improve the performances of the Golomb family of codes, including Golomb coding (GC), Golomb–Rice coding (GRC), exp-Golomb coding (EGC), and hybrid Golomb coding (HGC), for image compression. The Golomb family of codes is ideally suited to the processing of data with geometric distribution. Since it does not require a coding table, it has higher coding efficiency than Huffman coding. In this paper, we find that there are many situations in which the probability distribution of data is not only geometric, but also depends on the probability distribution of the other data. Accordingly, we used the joint probability of generalizing the Golomb family of codes and exploiting the dependence between neighboring image data. The proposed JPBAGC improves the efficiency of many image and video compression standards, such as the joint photographic experts group (JPEG) compression scheme and the H.264-intra JPEG-based image coding system. Simulation results demonstrate the superior coding efficiency of the proposed scheme over those of Huffman coding, GC, GRC, EGC, and HGC.

Robust optimal post-filter in oversampled lapped transform: Theory and application in image coding

Time domain oversampled lapped transforms (TDOLTs) with lattice structure can guarantee linear phase and perfect reconstruction and have the advantage of improving coding efficiency and reducing blocking effects which usually exist in DCT transforms. The post-filter is not unique in TDOLTs for a fixed pre-filter. In this paper, we propose a method to design the optimal post-filter for TDOLTs and partial TDOLTs with known noises. We also study the worst-case design of post-filters when the spectrum of noises are unknown. The obtained optimal post-filter is applied to JPEG codec. The performance in reducing the blocking artifacts and effectiveness of the proposed methods are demonstrated by various examples.

Linear-attenuated Discrete Cosine Biorthogonal Transform and Its Application in Image Coding

Linear-attenuated Discrete Cosine Biorthogonal Transform and Its Application in Image Coding

Shape Adaptive All Phase Biorthogonal Transform and Its Application in Image Coding

Abstract —In this paper shape adaptive all phase biorthogonal transform (SA-APBT) for coding arbitrarily shaped image segments is proposed. The proposed transform can be used in region-based image compression instead of the shape adaptive discrete cosine transform (SA-DCT). Region-based image coding method is made up of three procedures: image segmentation, contour coding and texture coding. An image is divided into region-of-interest (ROI) and background area by image segmentation. Both areas are encoded and decoded independently. Experimental results on test images show that compared with SA-DCT at the same bit rates, the PSNRs and visual effects of reconstructed images based on SA-APBT are comparable to the one based on SA-DCT especially at low bit rates. And the SA-APBT transform coefficients are quantized uniformly, while the SA-DCT transform coefficients are quantized according to different quantization steps in the quantization table. So the quantization based on SA-APBT is simpler and computational complexity is reduced.

Stabilization and optimization of PLUS factorization and its application in image coding

A recently developed PLUS factorization holds great promise in image coding due to its simplicity and integer reversibility. However, existing PLUS factorizations did not consider stability and optimality. To address these problems, we propose methodologies to design stable and optimal PLUS factorization algorithms. Firstly, we propose three stable PLUS factorization algorithms, prove the stability theorem under no perturbation and analyze stability under perturbation. Furthermore, we obtain a closed-form formula for transform error, and use the formula to design an algorithm for optimal PLUS factorization. Then, we apply the PLUS factorization to image coding. The integer DCTs implemented with the optimal PLUS factorizations found by our algorithms outperform the integer DCT with expansion factors in terms of entropy. The optimal PLUS factorizations are superior to the lifting factorization in JPEG-XR. The experimental results agree with analytical results of PLUS factorization, and show superior performance of our algorithms in image coding.

Optimal Design of FIR Triplet Halfband Filter Bank and Application in Image Coding

This correspondence proposes an efficient semidefinite programming (SDP) method for the design of a class of linear phase finite impulse response triplet halfband filter banks whose filters have optimal frequency selectivity for a prescribed regularity order. The design problem is formulated as the minimization of the least square error subject to peak error constraints and regularity constraints. By using the linear matrix inequality characterization of the trigonometric semi-infinite constraints, it can then be exactly cast as a SDP problem with a small number of variables and, hence, can be solved efficiently. Several design examples of the triplet halfband filter bank are provided for illustration and comparison with previous works. Finally, the image coding performance of the filter bank is presented.

Low memory implementation of generic hierarchical transforms for parent–children tree (PCT) production and its application in image compression

This paper presents a unified approach for low-memory and on-the-fly implementation of generic hierarchical transforms (GHTs) suited for parent–children tree (PCT) production, called the stripe-based hierarchical transform (SBHT). Here, the term “generic” means that totally different FBs may appear in different decomposition levels. This approach generates the exactly same subband coefficients as the traditional global implementation of GHTs with a low memory budget that is unrelated to the input signal length and only dependent on the GHT. The SBHT lends itself to the PCT-based image coding algorithm in the sense that the basic data unit generated by the SBHT is row-based collections of PCT structures, the most widely used data entity in subband coding. To demonstrate the SBHT's application in image coding, a PCT coder based on the LLEC is proposed to encode the PCTs generated by the SBHT. No intermediate buffering is needed between the SBHT and the codec. The experiments show that when the GHT is configured appropriately, the proposed coder provides competitive coding efficiency relative to the SPIHT and JPEG2000 with a very low memory budget and low computation complexity.

Implementational Aspects of the Contourlet Filter Bank and Application in Image Coding

This paper analyzed the implementational aspects of the contourlet filter bank (or the pyramidal directional filter bank (PDFB)), and considered its application in image coding. First, details of the binary tree-structured directional filter bank (DFB) are presented, including a modification to minimize the phase delay factor and necessary steps for handling rectangular images. The PDFB is viewed as an overcomplete filter bank, and the directional filters are expressed in terms of polyphase components of the pyramidal filter bank and the conventional DFB. The aliasing effect of the conventional DFB and the Laplacian pyramid to the directional filters is then considered, and the conditions for reducing this effect are presented. The new filters obtained by redesigning the PDFBs satisfying these requirements have much better frequency responses. A hybrid multiscale filter bank consisting of the PDFB at higher scales and the traditional maximally decimated wavelet filter bank at lower scales is constructed to provide a sparse image representation. A novel embedded image coding system based on the image decomposition and a morphological dilation algorithm is then presented. The coding algorithm efficiently clusters the significant coefficients using progressive morphological operations. Context models for arithmetic coding are designed to exploit the intraband dependency and the correlation existing among the neighboring directional subbands. Experimental results show that the proposed coding algorithm outperforms the current state-of-the-art wavelet-based coders, such as JPEG2000, for images with directional features.

On minimal lattice factorizations of symmetric-antisymmetric multifilterbanks

This paper introduces two minimal lattice structures for symmetric-antisymmetric multiwavelets (SAMWTs) and symmetric-antisymmetric multifilterbanks (SAMFBs). First, by exploring the relation of the symmetric-antisymmetric property in multifilterbanks and the linear-phase property in traditional scalar filterbanks, we show that the implementation and design of an SAMFB can be converted into that of a four-channel scalar linear-phase perfect reconstruction filterbank (LPPRFB). Then, based on the lattice factorization for LPPRFBs, we propose two fast, modular, minimal structures for SAMFBs. To demonstrate the effectiveness of the proposed lattice structures, several rational or dyadic-coefficient SAMWT design examples are presented along with their application in image coding.

Time-Domain Oversampled Lapped Transforms: Theory, Structure, and Application in Image Coding

This paper generalizes time-domain lapped transforms (TDLTs) proposed by Tran et al. to oversampled systems, thus leading to time-domain oversampled lapped transforms (TDOLTs). These new transforms correspond to a subclass of oversampled linear-phase perfect reconstruction filterbanks (OLPPRFBs), which can be implemented by adding a prefilter before the discrete cosine transform (DCT) and a post-filter after the inverse discrete cosine transform (IDCT). Structures of the pre- and post-filters are developed, and the frame-theoretic properties of TDOLTs are analyzed. A new parameterization of lattice matrices through the Givens-QR factorization is proposed for unconstrained optimization. Comparisons with other parameterization methods are also included. Several design examples, along with some image coding results, are presented to demonstrate the validity of the theory and the potential of TDOLTs in image coding, especially in error-resilient coding.

A class of regular biorthogonal linear-phase filterbanks: theory, structure, and application in image coding

This paper discusses a method of regularity imposition onto biorthogonal linear-phase M-band filterbanks using the lattice structure. A lifting structure is proposed for lattice matrix parameterization where regularity constraints can be imposed. The paper focuses on cases with analysis and synthesis filterbanks having up to two degrees of regularity. Necessary and sufficient conditions for regular filterbanks in terms of the filter impulse response, frequency response, scaling function, and wavelets are revisited and are derived in terms of the lattice matrices. This also leads to a constraint on the minimum filter length. Presented design examples are optimized for the purpose of image coding, i.e., the main objectives are coding gain and frequency selectivity. Simulation results from an image coding application also show that these transforms yield improvement in the perceptual quality in the reconstruction images. The approach has also been extended to the case of integer/rational lifting coefficients, which are desirable in many practical applications.

General construction of wavelet filters via a lifting scheme and its application in image coding

By using a lifting scheme, we present a technique to construct compactly supported wavelets whose coefficients are composed of free variables that lie in an interval. By selecting the coefficients of the 9 to 7 wavelet filter and associated lifting scheme, an efficient approach via wavelets for image compression is developed. Furthermore, the rationalized coefficients wavelet filter that can be implemented with simple integer arithmetic is achieved, and its characteristic is close to the well-known original irrational coefficients 9 to 7 wavelet filters developed by Cohen, Daubechies, and Feauveau. Software and hardware simulations show that the new method has very low complexity, and simultaneously preserves a high quality of a compressed image.

Linear transform for simultaneous diagonalization of covariance and perceptual metric matrix in image coding

Two types of redundancies are contained in images: statistical redundancy and psychovisual redundancy. Image representation techniques for image coding should remove both redundancies in order to obtain good results. In order to establish an appropriate representation, the standard approach to transform coding only considers the statistical redundancy, whereas the psychovisual factors are introduced after the selection of the representation as a simple scalar weighting in the transform domain. In this work, we take into account the psychovisual factors in the definition of the representation together with the statistical factors, by means of the perceptual metric and the covariance matrix, respectively. In general the ellipsoids described by these matrices are not aligned. Therefore, the optimal basis for image representation should simultaneously diagonalize both matrices. This approach to the basis selection problem has several advantages in the particular application of image coding. As the transform domain is Euclidean (by definition), the quantizer design is highly simplified and at the same time, the use of scalar quantizers is truly justified. The proposed representation is compared to covariance-based representations such as the DCT and the KLT or PCA using standard JPEG-like and Max-Lloyd quantizers.

Region-of-interest coding based on set partitioning in hierarchical trees

In many image-coding applications such as Web browsing, image databases, and telemedicine, it is useful to reconstruct only a region of interest (ROI) before the rest of the image is reconstructed. In this paper, an ROI coding functionality is incorporated with the set partitioning in hierarchical trees (SPIHT) algorithm for wavelet-based image coding. By placing a higher emphasis on the transform coefficients pertaining to the ROI, the ROI is coded with higher fidelity than the rest of the image in earlier stages of progressive coding. The general thrust of this research is to identify necessary coefficients in the wavelet-transform domain for the decoder to reconstruct the desired region. This new method provides better performance than the previously presented methods.