Fast wavelet transforms based on the extended lapped transform

A new family of wavelet transforms (WTs) based on the extended lapped transform (ELT) is introduced. A new optimisation criterion for the ELT butterfly angles is presented, leading to ELT-based WTs with virtually the same performance but a much lower computational complexity than the standard maximally-regular WTs.<>     

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.     

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).     

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     

Symmetric delay factorization: generalized framework forparaunitary filter banks

The symmetric delay factorization (SDF) was introduced to synthesize linear-phase paraunitary filter banks (LPPUFBs) with uniform order (i.e., filter length equal to NM for arbitrary N) and real-valued coefficients. The SDF presents the advantage of decomposing the polyphase transfer matrix (PTM) into only orthogonal matrices, even at the boundary of finite-duration signals, simplifying significantly the design of time-bounded filter banks (TBFBs) or of time-varying filter banks (TVFBs). However, the symmetric delay factorization applies only to LPPUFBs. On the other hand, lattice structures, as well as finite-size lattice structures, are proposed for classes of nonlinear-phase paraunitary filter banks, as the modulated lapped transform (MLT) and the extended tapped transform (ELT). This paper describes a new minimal and complete symmetric delay factorization valid for a larger class of paraunitary filter banks, encompassing paraunitary cosine modulated filter banks, with nonlinear phase basis functions, as well as for a set of LPPUFBs including the linear-phase lapped orthogonal transforms (LOTs) and the generalized tapped orthogonal transforms (GenLOTs). The derivations for filter banks with even and odd numbers of channels are formulated in a unified form. This approach opens new perspectives in the design of time-varying filter banks used for image and video compression, especially in the framework of region or object-based coding     

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.     

Time-varying lapped transforms and wavelet packets

The perfect reconstruction conditions for a time-varying lapped transform (paraunitary filter bank) are developed through the factorization of the transform matrix into sparse factors. A general formulation is presented allowing one to switch between two paraunitary filter banks. However, the extended lapped transform (ELT) is often used as an example. Furthermore, an adaptive wavelet packet is developed employing a time varying, tree association of ELTs. In all cases perfect reconstruction is inherently assured     

Biorthogonal and nonuniform lapped transforms for transform codingwith reduced blocking and ringing artifacts

New lapped transforms are introduced. The lapped biorthononal transform (LBT) and hierarchical lapped biorthogonal transform (HLBT) are appropriate for image coding, and the modulated HLBT biorthogonal transform (MMLBT) and nonuniform modulated lapped biorthogonal transform (NMLBT) are appropriate for audio coding. The HLBT has a significantly lower computational complexity than the lapped orthogonal transform (LOT), essentially no blocking artifacts, and fewer ringing artifacts than the commonly used discrete cosine transform (DCT). The LBT and HLBT have transform coding gains that are typically between 0.5 and 1.2 dB higher than that of the DCT. Image coding examples using JPEG and embedded zerotree coders demonstrate the better performance of the LET and HLBT. The NMLBT has fewer ringing artifacts and better reproduction of transient sounds than the MLT, as shown in audio coding examples. Fast algorithms for both the HLBT and the NMLBT are presented     

Variable-length lapped transforms with a combination of multiple synthesis filter banks for image coding.

A class of lapped transforms for image coding, which are characterized by variable-length synthesis filters, is introduced. In this class, the synthesis filter bank (FB) is first defined with an arbitrary combination of finite impulse response synthesis filters of perfect reconstruction FBs. An analysis FB is then obtained using direct matrix inversion or iterative implementation of Neumann series expansion. Moreover, to improve compression, we introduce a unitary transform that follows the analysis FB. This class enables a greater freedom of design than previously presented variable-length lapped transforms. We illustrate several design examples and present experimental results for image coding, which indicate that the proposed transforms are promising and comparable with conventional subband transforms including wavelets.     

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     

Group testing for image compression using alternative transforms

This paper extends the group testing for wavelets (IEEE Trans. Image Process. 11 (2002) 901) algorithm to code coefficients from the wavelet packet transform, the discrete cosine transform, and various lapped transforms. Group testing offers a noticeable improvement over zerotree coding techniques on these transforms; is inherently flexible; and can be adapted to different transforms with relative ease. The new algorithms are competitive with many recent state-of-the-art image coders that use the same transforms.     

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.     

话音的频域编码

本文阐述了语言信号的子带及变换编码原理,为了消除分块效应,介绍了一种作为语言编码新方法的搭接式变换和与此有关的快速算法及滤波器设计。最后,对于为实现最佳比特分配所需的提取副信息的一种方法作了简要的说明。     

Narrow-band interference excision in spread spectrum systems usinglapped transforms

In order to mitigate narrow-band interference in spread spectrum communications systems, novel communications receivers incorporating transform domain filtering techniques are designed. In this paper, lapped transforms are used to transform the received data signal to the transform domain wherein adaptive excision is performed. Transform domain detection algorithms, which yield bit decisions based on the remaining signal energy, are analyzed and, together with excision, are employed on a block-by-block basis to suppress single-tone and narrow-band Gaussian interference. System performance is analytically quantified in terms of the overall system bit-error rate (BER). Subsequent results are presented for a variety of channel conditions and compared to those obtained using excision algorithms based on orthonormal block transforms (Medley 1995). These results demonstrate the improved performance and increased robustness with respect to jammer frequency and bandwidth of lapped transform domain excision techniques relative to similar algorithms based on nonweighted block transforms     

On lapped orthogonal transforms [signal coding applications]

The energy compaction performance of several lapped orthogonal transforms (LOTs) are presented. It is shown that the LOT outperforms the conventional block transforms for all the cases considered. The performance of the poorly performing block transforms for high correlation sources increased dramatically in their LOT versions. It is found that the energy compaction performance of the LOT versions of the different block transforms considered is about the same. Therefore, the choice of LOT is based on the efficiency of the transform algorithm. The LOT is an alternative to the block transforms for signal coding applications. Also, the blocking effect is reduced with the increase in the computational complexity of the transform algorithm     

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     

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.     

LINC: a common theory of transform and subband coding

A common theory of lapped orthogonal transforms (LOTs) and critically sampled filter banks, called L into N coding (LINC), is presented. The theory includes a unified analysis of both coding methods and identity relations between the transform, inverse transform, analysis filter bank, and synthesis filter bank. A design procedure for LINC analysis/synthesis systems, which satisfy the conditions for perfect reconstruction, is developed. The common LINC theory is used to define an ideal LINC system which is used, together with the power spectral density of the input signal, to calculate theoretical bounds for the coding gain. A generalized overlapping block transform (OBT) with time domain aliasing cancellation (TDAC) is used to approximate the ideal LINC. A generalization of the OBT includes multiple block overlap and additional windowing. A recursive design procedure for windows of arbitrary lengths is presented. The coding gain of the generalized OBT is higher than that of the Karhunen-Loeve transform (KLT) and close to the theoretical bounds for LINC. In the case of image coding, the generalized OBT reduces the blocking effects when compared with the DCT     

Encoding of images based on a lapped orthogonal transform

Traditional block transform image coding systems generate artifacts near block boundaries which degrade low bit rate coded images. To reduce these artifacts, a class of unitary transformations, called lapped orthogonal transforms (LOT), is investigated. The basis function on which the signal is projected are overlapped for adjacent blocks. An example of an LOT optimized in terms of energy compaction is numerically derived, using an augmented Lagrangian optimization algorithm. Using this LOT, intraframe coding experiments for 256×240 pixel images were performed at bit rates between 0.1 and 0.35 bits/pixel. The LOT improved the coded image subjective quality over other transforms. The LOT was also used in interframe full-motion video coding experiments for head and shoulder sequences at 28 and 56 kb/s. Significant improvement resulted at low data rates and if no motion compensation were used. However, the improvement was no longer significant at 56 kb/s with full motion compensation     

Arbitrary resizing of images in DCT domain using lapped transforms

An arbitrary L/M-fold image resizing method using lapped transforms is presented. The resizing operation is carried out in the lapped transform domain, by converting the images in the discrete cosine transform (DCT) domain into those in the lapped transform domain and vice versa. The proposed method provides visually fine images, while reducing the blocking effect to a very low level for images compressed at low bit rates.