Integer lapped transforms and their applications to image coding

This paper proposes new integer approximations of the lapped transforms, called the integer lapped transforms (ILT), and studies their applications to image coding. The ILT are derived from a set of orthogonal sinusoidal transforms having short integer coefficients, which can be implemented with simple integer arithmetic. By employing the same scaling constants in these integer sinusoidal transforms, integer versions of the lapped orthogonal transform (LOT), the lapped biorthogonal transform (LBT), and the hierarchical lapped biorthogonal transform (HLBT) are developed. The ILTs with 5-b integer coefficients are found to have similar coding gain (within 0.06 dB) and image coding performances as their real-valued counterparts. Furthermore, by representing these integer coefficients as sum of powers-of-two coefficients (SOPOT), multiplier-less lapped transforms with very low implementation complexity are obtained. In particular, the implementation of the eight-channel multiplier-less integer LOT (ILOT), LBT (ILBT), and HLBT (IHLBT) require 90 additions and 44 shifts, 98 additions and 59 shifts, and 70 additions and 38 shifts, respectively.     

Image coding using lapped biorthogonal transform

The wireless sensor network utilizes image compression algorithms like JPEG, JPEG2000, and SPIHT for image transmission with high coding efficiency. During compression, discrete cosine transform (DCT)–based JPEG has blocking artifacts at low bit-rates. But this effect is reduced by discrete wavelet transform (DWT)–based JPEG2000 and SPIHT algorithm but it possess high computational complexity. This paper proposes an efficient lapped biorthogonal transform (LBT)–based low-complexity zerotree codec (LZC), an entropy coder for image coding algorithm to achieve high compression. The LBT-LZC algorithm yields high compression, better visual quality with low computational complexity. The performance of the proposed method is compared with other popular coding schemes based on LBT, DCT and wavelet transforms. The simulation results reveal that the proposed algorithm reduces the blocking artifacts and achieves high compression. Besides, it is analyzed for noise resilience.     

A biorthogonal transform with overlapping and non-overlapping basis functions for image coding

The paper presents a novel design method of a biorthogonal lapped transform that consists of long (overlapping) and short (nonoverlapping) basis functions (VLLBT, variable-length function lapped biorthogonal transform), which can reduce annoying blocking artifacts and ringing. We formulate the VLLBT by extending conventional lapped transforms. Then, we provide the theory of the Karhunen-Loeve transform in a subspace (SKLT). Using the theory of the SKLT, we show that given the biorthogonal long basis functions of the VLLBT, the optimal short basis functions in the energy compaction sense are derived by solving an eigenvalue problem without iterative searching techniques. This leads to a desirable feature from a parameter optimization point of view since the degree of freedom for the VLLBT can be theoretically reduced by means of the SKLT. Moreover, the SKLT easily enables us to construct a two-dimensional (2D) VLLBT with nonseparable short basis functions. Experimental results show that, compared to the case where all parameters are optimized, the reduction of free parameters by using the SKLT causes no decline in coding gain for the AR(1) process, and the proposed transform provides promising performance in the efficiency of image coding.     

Extended lapped transform in image coding

A modulated lapped transform with extended overlap (ELT) is investigated in image coding with the objective of verifying its potential to replace the discrete cosine transform (DCT) in specific applications. Some of the criteria utilized for the performance comparison are reconstructed image quality (both objective and subjective), reduction of blocking artifacts, robustness against transmission errors, and filtering (for scalability). Also, a fast implementation algorithm for finite-length-signals using symmetric extensions is developed specially for the ELT with overlap factor 2 (ELT-2). This comparison shows that ELT-2 is superior to both DCT and the lapped orthogonal transform (LOT).     

New family of lapped biorthogonal transform via lifting steps

By scaling all discrete cosine transform (DCT) intermediate output coefficients of the lapped transform and employing the type-II and type-IV DCT based on lifting steps, a new family of lapped biorthogonal transform is introduced, called the IntLBT. When all the elements with a floating point of each lifting matrix in the IntLBT are approximated by binary fractions, the IntLBT is implemented by a series of dyadic lifting steps and provides very fast, efficient in-place computation of the transform coefficients, and all internal nodes have finite precision. When each lifting step in the IntLBT is implemented using the same nonlinear operations as those used in the well known integer-to-integer wavelet transform, the IntLBT maps integers to integers, so it can express lossless image information. As an application of the novel IntLBT to lossy image compression, simulation results demonstrate that the IntLBT has significantly less blocking artefacts, higher peak signal-to-noise ratio, and better visual quality than the DCT. More importantly, the IntLBT's coding performance is approximately the same as that of the much more complex Cohen-Daubechies-Feauveau (CDF) 9/7-tap biorthogonal wavelet with floating-point coefficients, and in some cases even surpasses that of the CDF 9/7-tap biorthogonal wavelet.     

双正交重叠变换的整数实现算法与图像压缩

本文利用提升原理,以二进制整数DCT为基础,提出了双正交重叠变换的整数实现算法,其计算只需要少量的移位和加法运算,因而软件实现和硬件实现都非常简单.实验结果表明,它是一种有效的图像压缩变换,压缩质量大大超过了运算量更多的近似二进制整数小波变换和DCT,与Daubechies 9/7小波也非常接近.     

Block classification for an adaptive 1-D/2-D DCT video coding

A classification scheme for an adaptive one- or two-dimensional discrete cosine transform (1-D/2-D DCT) technique is described and demonstrated to be a more appropriate strategy than the conventional 2-D DCT for coding motion compensated prediction error images. Two block-based classification methods are introduced and their accuracy in predicting the correct transform type discussed. The accuracy is assessed with a classification measure designed to ascertain the effectiveness of energy compaction when the predicted transform class is applied; vis-a-vis horizontally, vertically or two-dimensionally transformed blocks. Energy compaction is a useful property not only for efficient entropy coding but also for enhancing the resilience of the transform coder to quantisation noise. Improvements against the homogeneous 2-D DCT system both in terms of the peak signal to noise ratio and subjective assessments are achieved. Observable ringing artifacts along edges, which are usual in conventional transform coding, are reduced     

Linear phase paraunitary filter bank with filters of differentlengths and its application in image compression

In this paper, the theory, structure, design, and implementation of a new class of linear-phase paraunitary filter banks (LPPUFBs) are investigated. The novel filter banks with filters of different lengths can be viewed as the generalized lapped orthogonal transforms (GenLOTs) with variable-length basis functions. Our main motivation is the application in block-transform-based image coding. Besides having all of the attractive properties of other lapped orthogonal transforms, the new transform takes advantage of its long, overlapping basis functions to represent smooth signals in order to reduce blocking artifacts, whereas it reserves short basis functions for high-frequency signal components like edges and texture, thereby limiting ringing artifacts. Two design methods are presented, each with its own set of advantages: the first is based on a direct lattice factorization, and the second enforces certain relationships between the lattice coefficients to obtain variable length filters. Various necessary conditions for the existence of meaningful solutions are derived and discussed in both cases. Finally, several design and image coding examples are presented to confirm the validity of the theory     

Extended lapped transforms: properties, applications, and fastalgorithms

The family of lapped orthogonal transforms is extended to include basis functions of arbitrary length. Within this new family, the extended lapped transform (ELT) is introduced, as a generalization of the previously reported modulated lapped transform (MLT). Design techniques and fast algorithms for the ELT are presented, as well as examples that demonstrate the good performance of the ELT in signal coding applications. Therefore, the ELT is a promising substitute for traditional block transforms in transform coding systems, and also a good substitute for less efficient filter banks in subband coding systems     

Algorithm-based low-power transform coding architectures: themultirate approach

In most low-power VLSI designs, the supply voltage is usually reduced to lower the total power consumption. However, the device speed will be degraded as the supply voltage goes down. In this paper, we propose new algorithmic-level techniques to compensate the increased delays based on the multirate approach. We apply the technique of polyphase decomposition to design low-power transform coding architectures, in which the transform coefficients are computed through decimated low-speed input sequences. Since the operating frequency is M-times slower than the original design while the system throughput rate is still maintained, the speed penalty can be compensated at the architectural level. We start with the design of low-power multirate discrete cosine transform (DCT)/inverse discrete cosine transform (IDCT) VLSI architectures. Then the multirate low-power design is extended to the modulated lapped transform (MLT), extended lapped transform (ELT), and a unified low-power transform coding architecture. Finally, we perform finite-precision analysis for the multirate DCT architectures. The analytical results can help us to choose the optimal wordlength for each DCT channel under required signal-to-noise ratio (SNR) constraint, which can further reduce the power consumption at the circuit level. The proposed multirate architectures can also be applied to very high-speed block discrete transforms in which only low-speed operators are required     

A unified approach to lapped orthogonal transforms

The general conditions of exact reconstruction and a recursive design procedure for lapped orthogonal transform (LOT) with arbitrary length of overlapping are presented. It is shown that LOT can be realized with any standard block transform, discrete cosine transform (DCT), for example, and an additional processing. This processing must also satisfy the same conditions for exact reconfigurations and it may be pretransform processing in the time domain or post-transform processing in the transform domain. In a few examples it is shown that the LOT has a higher coding gain and smaller blocking effects then DCT. With the proposed LOT design procedure, two optimizations, the coding gain maximization and the blocking effect minimization, are presented and compared.     

Synthesis filterbank with low hardware complexity for subband imagecoding

Different algorithms are evaluated and optimizations are performed to obtain a filterbank for subband coding of images especially suited for very large scale integration (VLSI) implementation. Based on a filterbank consisting of two finite impulse response (FIR) filters combined with an 8-point discrete cosine transform (DCT), we investigate how the quantization of filter coefficients and twiddle factors in different algorithms affects the quality of the filterbank. It is found that a DCT based on a Stasinksi (1989) algorithm with twiddle factors of only 5 b together with FIR filter coefficients of 10 b gives a filterbank with high coding gain, no blocking artifacts, and limited ringing. The VLSI complexity is comparable to that of DCT transforms.     

An orientation-selective orthogonal lapped transform

A novel critically sampled orientation-selective orthogonal lapped transform called the lapped Hartley transform (LHT) is derived. In a first step, overlapping basis functions are generated by modulating basis functions of a 2-D block Hartley transform by a cosine wave. To achieve invertibility and orthogonality, an iterative filter is applied as prefilter in the analysis and as postfilter in the synthesis operation, respectively. Alternatively, filtering can be restricted to analysis or synthesis, ending up with a biorthogonal transform (LHT-PR, LHT-PO). A statistical analysis based on a 4000-image data base shows that the LHT and LHT-PO have better redundancy removal properties than other block or lapped transforms. Finally, image compression and noise removal examples are given, showing the advantages of the LHT especially in images containing oriented textures.     

Generalized block-lifting factorization of M-channel biorthogonal filter banks for lossy-to-lossless image coding

Generalized block-lifting factorization of M-channel (M > 2) biorthogonal filter banks (BOFBs) for lossy-to-lossless image coding is presented in this paper. Since the proposed block-lifting structure is more general than the conventional lifting factorizations and does NOT require many restrictions such as paraunitary, number of channels, and McMillan degree in each building block unlike the conventional lifting factorizations, its coding gain is higher than that of the previous methods. Several proposed BOFBs are designed and applied to image coding. Comparing the results with conventional lossy-to-lossless image coding structures, including the 5/3- and 9/7-tap discrete wavelet transforms in JPEG 2000 and a 4 × 8 hierarchical lapped biorthogonal transform in JPEG XR, the proposed BOFBs achieve better result in both objective measure and perceptual visual quality for the images with a lot of high-frequency components.     

Directional Lapped Transforms for Image Coding

In this paper, we present the design of directional lapped transforms for image coding. A lapped transform, which can be implemented by a prefilter followed by a discrete cosine transform (DCT), can be factorized into elementary operators. The corresponding directional lapped transform is generated by applying each elementary operator along a given direction. The proposed directional lapped transforms are not only nonredundant and perfectly reconstructed, but they can also provide a basis along an arbitrary direction. These properties, along with the advantages of lapped transforms, make the proposed transforms appealing for image coding. A block-based directional transform scheme is also presented and integrated into HD Phtoto, one of the state-of-the-art image coding systems, to verify the effectiveness of the proposed transforms.     

一种符合ITU-T指标要求的嵌入式立体声语音频编码方法

 基于国际电信联盟标准化组织(ITU-T)编码标准G.729.1,本文提出了一种嵌入式变速率立体声语音与音频编码方法.本算法利用G.729.1和改进的调制叠接变换(Modulated Lapped Transform,MLT)编码技术对输入信号的中值与边带信息进行分层编码,形成具有嵌入式结构的码流.编码器可处理宽带和超宽带的立体声信号,宽带立体声信号编码的最大码率为48kb/s,超宽带立体声信号编码的最大速率为64kb/s.实现结果表明,本编码器的编码质量均达到了ITU-T对G.EV-VBR立体声编码的指标要求.     

Lapped unimodular transform and its factorization

Two types of lapped transforms have been studied in detail in the literature, namely, the lapped orthogonal transform (LOT) and its extension, the biorthogonal lapped transform (BOLT). In this paper, we will study the lapped unimodular transform (LUT). All three transforms are first-order matrices with finite impulse response (FIR) inverses. We will show that like LOT and BOLT, all LUTs can be factorized into degree-one unimodular matrices. The factorization is both minimal and complete. We will also show that all first-order systems with FIR inverses can be minimally factorized as a cascade of degree-one LOT, BOLT, and LUT building blocks. Two examples will be given to demonstrate that despite having a very small system delay, the LUTs have a satisfactory performance in comparison with LOT and BOLT.     

The GenLOT: generalized linear-phase lapped orthogonal transform

The general factorization of a linear-phase paraunitary filter bank (LPPUFB) is revisited. From this new perspective, a class of lapped orthogonal transforms with extended overlap (generalized linear-phase lapped orthogonal transforms (GenLOTs)) is developed as a subclass of the general class of LPPUFB. In this formulation, the discrete cosine transform (DCT) is the order-1 GenLOT, the lapped orthogonal transform is the order-2 GenLOT, and so on, for any filter length that is an integer multiple of the block size. The GenLOTs are based on the DCT and have fast implementation algorithms. The implementation of GenLOTs is explained, including the method to process finite-length signals. The degrees of freedom in the design of GenLOTs are described, and design examples are presented along with image compression tests     

Design of orthogonal and biorthogonal lapped transforms satisfyingperception related constraints

We propose a new efficient method for the design of orthogonal and biorthogonal lapped transforms for image coding applications. It is shown how perception related constraints such as decay and smoothness of the filters' impulse responses can be incorporated in the optimization procedure. A decomposition of lapped transforms (orthogonal and biorthogonal) with 50% overlap leads to an efficient recursive optimization procedure, which is robust with respect to initial solutions. The importance of this decomposition lies in the fact that it allows to decouple the design of the even-symmetric and the odd-symmetric filters and hence drastically reduces the number of variables to be optimized. It furthermore reveals all the variables predetermined by perception related and coding-efficiency related constraints imposed on the filters. We present design and coding examples demonstrating the perceptual performance and the rate distortion performance of the resulting transforms.     

Modulated Lapped Transform Domain Acoustic Echo Canceller with Double Talk Detector

A complete acoustic echo cancellation system with double talk detection capability is presented in this paper. The proposed system includes a new acoustic echo canceller (AEC) based on the modulated lapped transform (MLT) domain adaptive structure and a robust two-stage double talk detector (DTD) to cope with MLT domain AEC. The proposed AEC achieves better signal decorrelation via orthogonal MLT of size 2N× N rather than N× N square orthogonal transform such as DCT, DFT, etc. Both the input signal and the desired response are modulated lapped transformed in order to reduce the adaptation error between them so that the signal adaptation is purely operated in MLT domain. As a complementary of this, a two-stage DTD is developed to stabilize the operation of the AEC. The proposed DTD has robust algorithm structure and it allows faster switching according to the talker state change.Several simulation results with a synthetic and real speech are presented to demonstrate the performance of the proposed AEC and DTD. The proposed MLT based AEC proven to be very useful for the echo cancellation applications requiring high convergence speed and good echo attenuation. It can achieves faster convergence rate by more than twice over those of traditional DCT based AEC with an additional advantage of 10–15 dB ERLE improvement. On the other hand, a proposed two-stage DTD is shown to react quickly to both the onset and the end of the double-talk with reasonable high accuracy.