Search 250 million research papers

Lapped Orthogonal Transform

Nirdosh Bhatnagar · 2020

Cited by 1

Integer lapped biorthogonal transform

Zhong Guang-jun, Cheng Li-zhi, Huowang Chen · 2002

A type of lapped biorthogonal transform that can map integers to integers is considered. Based on the computational structure of the proposed lapped transform, an efficient multiplierless algorithm for the lapped biorthogonal transform (LBT), called integer lapped biorthogonal transform (IntLBT), is proposed. The proposed IntLBT is implemented by a series of dyadic lifting steps, and provides fast, efficient computation of the transform coefficients as well as the ability to map integers to integers. Application of the novel IntLBT in lossy image coding gains very competitive results comparing to the performance of the much more complex Cohen-Daubechies-Feauveau (CDF) 9/7-tap biorthogonal wavelet with irrational coefficients.

Cited by 0

The generalized lapped biorthogonal transform

Trac D. Tran, Ricardo L. de Queiroz, Truong Q. Nguyen · 2002

A lattice structure based on the singular value decomposition (SVD) is introduced. The lattice can be proven to use a minimal number of delay elements and to completely span a large class of M-channel linear phase perfect reconstruction filter banks (LPPRFB): all analysis and synthesis filters have the same FIR length of L=KM, sharing the same center of symmetry. The lattice also structurally enforces both linear phase and perfect reconstruction properties, is capable of providing fast and efficient implementation, and avoids the costly matrix inversion problem in the optimization process. From a block transform perspective, the new lattice represents a family of generalized lapped biorthogonal transforms (GLBT) with arbitrary integer overlapping factor K. The relaxation of the orthogonal constraint allows the GLBT to have significantly different analysis and synthesis basis functions which can then be tailored appropriately to fit a particular application. Several design examples are presented along with a high-performance GLBT-based progressive image coder to demonstrate the superiority of the new lapped transforms.

Cited by 25

Extended lapped transform in image coding

Ricardo L. de Queiroz, K.R. Rao · IEEE Transactions on Image Processing · 1995

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).

Cited by 8

An Orientation-Selective Orthogonal Lapped Transform

Dietmar Kunz · IEEE Transactions on Image Processing · 2008

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.

Cited by 11

Biorthogonal frequency-varying modulated lapped transform

Yixin Gao, Guizhong Liu · 2009

In this paper we introduce a biorthogonal frequency-varying modulated lapped transform (BFV-MLT) with flexible tiling behavior of time-frequency plane and attenuation of ringing artifacts. Biorthogonality allows accessorial freedom in designing the analysis and synthesis filter-banks and FVMLT provides nonuniform decomposition of signals with ideal time or frequency resolutions. By constructing a new approach to FV-MLT, we incorporate biorthogonality into FV-MLT easily and achieve flexible representations of signals plus freedom in filter-bank design. We also prove that perfect reconstruction holds in BFV-MLT which confirms its application in compression schemes.

Cited by 1

The two-dimensional lapped Hadamard transform

Shogo Muramatsu, Akihisa Yamada, Hironori Kiya · 1998

In this paper, a 2-D binary-valued (BV) lapped transform (LT) is proposed. The proposed LT has basis images which take only BV elements and satisfies the axial-symmetric (AS) property. In 1D, there is no 2-point LT with the symmetric basis vectors. Hence, in 2D, there is no 2/spl times/2-point separable ASLT. By taking non-separable BV basis images, this paper shows that a 2/spl times/2-point ASLT can be obtained. For its similarity to the Hadamard transform (HT), this paper refer to it as the lapped Hadamard transform (LHT). The efficient implementation is also given.

Cited by 3

Denoising in the lapped transform domain

Seungjoon Yang, Thanh-Trung Nguyen · 2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03). · 2004

In this paper, we extend the results of the denoising in the wavelet domain to the lapped transform (LT) domain. The LT coefficients are rearranged into the octave based representation, and their statistics are modeled by the same methods as the wavelet coefficients. Since the part of the LT that follows the discrete cosine transform (DCT) is orthogonal, the problem of removing the quantization noise introduced in the DCT based codecs can be solved in the LT domain. The maximum a posteriori (MAP) estimator is obtained, which provides a novel approach to the image compression artifact reduction problem. The proposed method removes the additive noise and the quantization noise effectively with the significant improvement of image quality.

Cited by 5

Transform/subband coding of speech with the lapped orthogonal transform

H.S. Malvar, Rodrigo Pereira da Costa Duarte · 2003

Efficient transform/subband signal coders can be designed using the lapped orthogonal transform (LOT). With the LOT, blocking effects in the reconstructed signal are absent, as demonstrated previously in image coding contexts. What limited the application of the LOT to a broader class of signals, including speech, was the lack of a fast LOT algorithm for large block sizes. The authors define a new version of the LOT that is fast-computable for any block size. A speech processing example demonstrates the efficiency of the LOT in reducing blocking effects.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Cited by 3

Directional Lapped Orthogonal Transform: Theory and Design

Shogo Muramatsu, Dandan Han, Tomoya Kobayashi et al. · IEEE Transactions on Image Processing · 2012

This paper proposes a directional design method of 2-D nonseparable linear-phase paraunitary filter banks. The proposed method is based on a lattice structure consisting of the 2-D separable DCT block and nonseparable support extension processes. Because of the nonseparability, the bases are allowed to be directional with the critically fixed subsampling, overlapping, orthogonal, symmetric, real-valued, and compact support properties. First, a novel vanishing moment (VM) condition is introduced as a suitable directional constraint, where the moment is referred to as the trend VM. The condition forces wavelet filters, i.e., high-pass and bandpass filters, to annihilate trend-surface components. Second, some theoretical properties of TVMs are discussed for general 2-D paraunitary systems, and then, the properties are applied to the lattice parameters. In order to verify the significance, several design examples are shown, the trend-surface annihilation properties are numerically confirmed, and the denoising capability is evaluated for images through shrinkage. It is shown that our proposed transforms yield perceptually preferable results.

Cited by 34

Image coding with a lapped orthogonal transform.

CUHK Digital Repository (Chinese University of Hong Kong) · 1993

Cited by 0

Optimized extended lapped transform and novel FPGA implementation

Kai Wan, Yiqun Zhu · 2013

The Modulated Filter-Banks (MFB) has been adopted in communication standards because of its improved windowing function against Fast Fourier Transform (FFT) based Orthogonal Frequency Division Multiplexing (OFDM). It has shown better resiliency to Inter-Symbol Interference (ISI), Inter-Carrier Interference (ICI), Narrow Band Interference (NBI), and Frequency Selective Fading. The recently adopted MFB in industrial standards is called Perfect Reconstructed Cosine Modulated Filter-Banks (PR-CMFB). There are three types of structure for its implementation, Extended Lapped Transform (ELT), Lattice structure, and Polyphase structure. The ELT defeats the Polyphase and Lattice structures because it is suitable for Very Large Scale Integrated-Circuit (VLSI) implementation. However, there is no difference in computational complexity between them. This paper optimizes the ELT structure to bring out its potential in the VLSI implementation. The proposed ELT reduces the required number of multipliers by half. The implementation on Field Programmable Gate Array (FPGA) is done to approve that. The simulation results show the proposed ELT has doubled throughput and one thirds of logic elements (LEs) are reserved when comparing to the conventional ELT.

Cited by 0

Fast Algorithm for the Modulated Complex Lapped Transform

Rico Malvar · 2005

We present a complete derivation for a new algorithm for fast computation of the modulated complex lapped transform (MCLT), which we have previously presented. In particular, we present explicit formulas and flowgraphs not only for the direct transform, but also for the inverse transform. For a length-M MCLT, the direct transform algorithm is based on computing a length-2M fast Fourier transform (FFT) plus M butterfly-like stages, without data shuffling. That reduces the number of operations and memory accesses needed to compute the MCLT when compared to previous algorithms. Compared to the original DCT-IV-based algorithm, a software implementation of the new algorithm running in a personal computer leads to 25% faster execution.

Cited by 17

Implementation of modulated lapped transform using programmable logic

Caishi Jing, Heng‐Ming Tai · 2003

This paper presents a hardware implementation of the modulated lapped transform (MLT) which is commonly used in audio and video compression applications. The MLT is formulated into the form that takes advantage of the embedded FFT in the programmable logic devices.

Cited by 2

An acoustic echo canceller using lapped orthogonal transform

Che‐Ho Wei, Chung-Pei Tsai · 2002

In the teleconference system or the hands-free telephone, the speech broadcasted from the loudspeaker can be transformed back to the talker as a far-end talker-echo. The far-end talker-echo can be eliminated by an acoustic echo canceller. An acoustic echo canceller based on the lapped orthogonal transform (LOT) using discrete Walsh-Hadamard transform (DWHT) as the building block for the fast algorithm is presented. The new structure can provide better ERLE and tracking capability than the structure using the LOT presented by Malver (1992). The computation complexity of the new structure is much lower than the orthogonal transform LMS structure.

Cited by 0

Despeckling SAR images in the lapped transform domain

Deepika Hazarika, Manabendra Bhuyan · 2013

In this paper, a novel lapped transform (LT) based approach to SAR image despeckling is introduced. It is shown that LT coefficients of the log transformed, noise free SAR images, obey Generalized Gaussian distribution. The proposed method uses a Bayesian minimum mean square error (MMSE) estimator which is based on modeling the global distribution of the rearranged LT coefficients in a subband using Generalized Gaussian distribution. Finally the proposed algorithm is implemented in cycle spinning mode to compensate for the lack of translation invariance property of LT. Experiments are carried out using synthetically speckled natural and SAR images. The proposed Bayesian based technique in LT based framework, when compared with several existing despeckling techniques, yields very good despeckling results while preserving the important details and textural information of the scene.

Cited by 6

Lapped Orthogonal Transform Coding by Amplitude and Group Partitioning

Xiangyu Zou And, Xiangyu Zou, William A. Pearlman · 1999

Transform coding has been the focus of the research for image compression. In previous research, the Amplitude and Group Partitioning (AGP) coding scheme is proved to be a low complexity algorithm with high performance 1,2 , clearly one of the state-of-art transform coding techniques. However, the previous AGP is used along with the Discrete Cosine Transform (DCT) and the discrete wavelet transform. In this paper, a different transform, the Lapped Orthogonal Transform (LOT), replaces the DCT in conjunction with the AGP. This is the first time LOT and AGP have been combined in a coding method. The definition and design of the LOT are discussed. An objective metric to measure the performance of transform, coding gain, is calculated for both the DCT and the LOT. The LOT has slightly higher coding gain than the DCT. The principles of the LOT based AGP image codec (LOT-AGP) are presented and a complete codec, encoder and decoder, is implemented in software. The performance of the LOT-AGP ...

Cited by 0

Lapped Transform via Time-Domain Pre- and Post-Processing

Trac D. Tran · 2001

| This paper demonstrates that a large family of lapped transforms with symmetric basis functions can be constructed by adding simple timedomain pre- and post-processing modules onto existing block DCT based infrastructures. A subset of the resulting solutions is closed-form, fast computable, modular, near optimal in the energy compaction sense, and leads to an elegant boundary handling of nite-length data. Numerous design examples with arbitrary number of channels and arbitrary number of borrowed samples are presented along with the practical application in image coding. I.

Cited by 0

Secure Robust Digital Watermarking Using the Lapped Orthogonal Transform

Pereira, Shelby, O'Ruanaidh, Joséph John, Pun, Thierry · Archive ouverte UNIGE (University of Geneva) · 1999

Digital watermarks have been proposed as a method for discouraging illicit copying and distribution of copyright material. One approach to Transform Domain image watermarking is to divide the image into separate blocks and compute the transform of each block. The watermark is inserted in the transform domain and the inverse transform is then computed. Such an approach is particularly effective against JPEG compression where 8 x 8 blocks are used in conjunction with the DCT. Using small blocks allows the watermark to be embedded adaptively as a function of the luminance and texture. However for small block sizes blocking artifacts are observed when the strength of the watermark is increased. In order to circumvent this problem, we propose a new approach based on Lapped Orthogonal Transforms (LOT) in which the watermark is inserted adaptively into the LOT domain. Robustness of the watermark to operations such as lossy compression is achieved by using a spread spectrum signal which is added in the LOT domain. The keys used to embed the spread spectrum signal are generated, certified, authenticated and securely distributed using a public key infrastructure containing an electronic copyright office and a certification authority. In addition to the above we propose using an invisible template to reverse the effects of rotation, rescaling and cropping on a watermarked image. This separate invisible template is based on the properties of the Fourier Transform. Finally, we objectively evaluate the performance of the proposed algorithm in order to demonstrate the robustness of the proposed technique with respect to a number of common image processing operations including JPEG compression, rotation, scaling and cropping.

Cited by 3Open access

Lapped transform via time-domain pre- and post-filtering

Trac D. Tran, Jie Liang, Chengjie Tu · IEEE Transactions on Signal Processing · 2003

This paper presents a general framework of constructing a large family of lapped transforms with symmetric basis functions by adding simple time-domain pre- and post-processing modules onto existing block discrete cosine transform (DCT)-based infrastructures. A subset of the resulting solutions is closed-form, fast computable, modular, near optimal in the energy compaction sense and leads to an elegant boundary handling of finite-length data. Starting from these solutions, a general framework for block-based signal decomposition with a high degree of flexibility and adaptivity is developed. Several simplified models are also introduced to approximate the optimal solutions. These models are based on cascades of plane rotation operators and lifting steps, respectively. Despite tremendous savings in computational complexity, the optimized results of these simplified models are virtually identical to that of the complete solution. The multiplierless versions of these pre- and post-filters when combined with an appropriate multiplierless block transform, such as the binDCT, which is described in an earlier paper by Liang and Tran (see IEEE Trans. Signal Processing, vol.49, p.3032-44, Dec. 2001), generate a family of very large scale integration (VLSI)-friendly fast lapped transforms with reversible integer-to-integer mapping. Numerous design examples with arbitrary number of channels and arbitrary number of borrowed samples are presented.

Cited by 159