Integer sinusoidal transforms for image processing

The sine and cosine transforms, which are popular transforms for image coding, are members of a sinusoidal transform family. Each member of the family is the optimal KLT of a Markov process. This paper derives the conditions under which the order-8 sinusoidal transforms can be approximated by orthogonal integer transforms which can be implemented using integer arithmetic. Some integer transforms are derived as examples. The results show that for the popular even sine-1, even sine-2 and the cosine transforms, there is an infinite number of integer transforms and some have their transform component magnitudes less than eight. In LSI implementation, if low implementation cost and fast computation speed are paramount, then an integer transform of small component magnitudes can be chosen. If better performance is desired, integer transforms whose elements have larger magnitudes can be used. The availability of many integer transforms provides a design engineer the freedom to trade-off performance against simple implementation and speed.     

Intra-Predictive Transforms for Block-Based Image Coding

This paper presents the theory and the design of intra-predictive transforms, which unify the inter-block prediction and block-based transforms in block-based image coding. Motivated by interpreting inter-block prediction as a transform with a larger size, we derive the concept of intra-predictive transforms. Conventional predictions and transforms can be viewed as special cases of intra-predictive transforms. Intra-predictive transforms are able to exploit both inter and intra-block correlations. We derive the tight upper bound of the coding gain of intra-predictive transforms for stationary Gaussian sources. It turns out that the coding gain can be greater than that of conventional transforms. The optimal intra-predictive transform that achieves the upper bound is also derived. We also design a practical intra-predictive transform using frequency-domain prediction that can achieve better performance in image coding while exhibiting low computational complexity. Experimental results confirm the effectiveness of the proposed intra-predictive transforms in block-based image coding systems and show the improvements over the current design.     

An effective wavelet matrix transform approach for efficientsolutions of electromagnetic integral equations

An effective numerical method based on wavelet matrix transforms for efficient solution of electromagnetic (EM) integral equations is proposed. Using the wavelet matrix transform produces highly sparse moment matrices which can be solved efficiently. A fast construction method for various orthonormal or nonorthonormal wavelet basis matrices is also given. It has been found that using nonsimilarity wavelet matrix transforms such as nonsimilarity nonorthonormal cardinal spline wavelet (NSNCSW) transform, one can obtain a much higher compression rate and much better accuracy of the approximate solutions than using similarity wavelet transforms such as Daubechies' (1992) orthonormal wavelet (DOW) transform. Numerical examples are given to show the validity and effectiveness of the method     

Design of prefilters for discrete multiwavelet transforms

The pyramid algorithm for computing single wavelet transform coefficients is well known. The pyramid algorithm can be implemented by using tree-structured multirate filter banks. The authors propose a general algorithm to compute multiwavelet transform coefficients by adding proper premultirate filter banks before the vector filter banks that generate multiwavelets. The proposed algorithm can be thought of as a discrete vector-valued wavelet transform for certain discrete-time vector-valued signals. The proposed algorithm can be also thought of as a discrete multiwavelet transform for discrete-time signals. The authors then present some numerical experiments to illustrate the performance of the algorithm, which indicates that the energy compaction for discrete multiwavelet transforms may be better than the one for conventional discrete wavelet transforms     

基于多尺度变换的直觉模糊推理图像融合算法

提出了基于多尺度变换的直觉模糊推理医学图像融合方法,针对4种多尺度变换对图像融合的影响进行了分析。文中融合算法是利用4种多尺度变换对待融合图像进行分解,并对得到的低频分量和高频分量采用直觉模糊推理融合规则进行处理,最后将融合后的低频分量和高频分量经逆变换得到融合图像。实验结果表明本文算法优于传统的模糊推理图像融合算法,并且在变换域中,Contourlet变换下的融合结果要优于其它3种变换。     

Image and video processing using discrete fractional transforms

The mathematical transforms such as Fourier transform, wavelet transform and fractional Fourier transform have long been influential mathematical tools in information processing. These transforms process signal from time to frequency domain or in joint time–frequency domain. In this paper, with the aim to review a concise and self-reliant course, the discrete fractional transforms have been comprehensively and systematically treated from the signal processing point of view. Beginning from the definitions of fractional transforms, discrete fractional Fourier transforms, discrete fractional Cosine transforms and discrete fractional Hartley transforms, the paper discusses their applications in image and video compression and encryption. The significant features of discrete fractional transforms benefit from their extra degree of freedom that is provided by fractional orders. Comparison of performance states that discrete fractional Fourier transform is superior in compression, while discrete fractional cosine transform is better in encryption of image and video. Mean square error and peak signal-to-noise ratio with optimum fractional order are considered quality check parameters in image and video.     

Transform-based image enhancement algorithms with performancemeasure

This paper presents a new class of the "frequency domain"-based signal/image enhancement algorithms including magnitude reduction, log-magnitude reduction, iterative magnitude and a log-reduction zonal magnitude technique. These algorithms are described and applied for detection and visualization of objects within an image. The new technique is based on the so-called sequency ordered orthogonal transforms, which include the well-known Fourier, Hartley, cosine, and Hadamard transforms, as well as new enhancement parametric operators. A wide range of image characteristics can be obtained from a single transform, by varying the parameters of the operators. We also introduce a quantifying method to measure signal/image enhancement called EME. This helps choose the best parameters and transform for each enhancement. A number of experimental results are presented to illustrate the performance of the proposed algorithms.     

SAR amplitude probability density function estimation based on a generalized Gaussian model.

In the context of remotely sensed data analysis, an important problem is the development of accurate models for the statistics of the pixel intensities. Focusing on synthetic aperture radar (SAR) data, this modeling process turns out to be a crucial task, for instance, for classification or for denoising purposes. In this paper, an innovative parametric estimation methodology for SAR amplitude data is proposed that adopts a generalized Gaussian (GG) model for the complex SAR backscattered signal. A closed-form expression for the corresponding amplitude probability density function (PDF) is derived and a specific parameter estimation algorithm is developed in order to deal with the proposed model. Specifically, the recently proposed "method-of-log-cumulants" (MoLC) is applied, which stems from the adoption of the Mellin transform (instead of the usual Fourier transform) in the computation of characteristic functions and from the corresponding generalization of the concepts of moment and cumulant. For the developed GG-based amplitude model, the resulting MoLC estimates turn out to be numerically feasible and are also analytically proved to be consistent. The proposed parametric approach was validated by using several real ERS-1, XSAR, E-SAR, and NASA/JPL airborne SAR images, and the experimental results prove that the method models the amplitude PDF better than several previously proposed parametric models for backscattering phenomena.     

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     

提升多小波变换及其在图像编码中的应用

多小波是一种新的小波．他在理论上所表现出来的优势以及他在应用领域所具有的潜力．使其受到高度重视。在短短的几年时间内，他在图像处理方面的应用已取得了一定的成效。提升方法不仅是现存小波变换的一种快速算法．而且是构造新的小波变换的一种工具。根据提升方法和多小波变换的特点，介绍了一种实现多小波变换的提升方法．并把这种提升多小波变换应用于图像处理，结果表明有很好的效果。     

Performance Evaluation for Transform Coding Using a Nonseparable Covariance Model

Intraframe transform coding of pictures for the case of a nonseparable covariance model is considered. Performances of the Walsh-Hadamard, discrete cosine and Karhunen-Loeve transforms are compared based on the compaction of signal energy in the transform components, and, the degree of decorrelation of the data. The results demonstrate that the performances of the discrete cosine and Karhunen-Loéve transforms compare closely, as is the case with a separable covariance model. The corresponding performance of the Walsh-Hadamard transform is inferior.     

Scattering-Based Tomography for HRR and SAR Prediction

This paper introduces a method for predicting HRR radar signatures and SAR images by creating a parametric three-dimensional scattering model from existing measured or model-based HRR signatures and/or SAR images. The method identifies potential three-dimensional persistent scatterers and estimates their scattering patterns. The results are parametric HRR signature and SAR image reconstruction functions of range, azimuth, and elevation.The modeling is accomplished through a scattering-based tomography technique. This technique localizes potential scatterers by using a filtered back-projection algorithm for the inverse radon transform. Once found, potential scatterers may then have their two-dimensional (azimuth and elevation) scattering patterns parameterized through the use of a truncated spherical harmonic series.Results using the reconstructions from HRR data are presented. A M109 model is reconstructed based on HRR signatures. The model allows us to predict what the vehicle would look like from any arbitrary orientation using SAR. Finally an M548 vehicle is modeled using 26 measured HRR signatures. The model is shown to be better than the synthetic model data. Additionally we show that the new model results can be combined with the synthetic data to provide a better target model for signature matching.     

Properties and relations for fast linearly independent arithmetic transforms

New fast linearly independent arithmetic (LIA) transforms are introduced here which can be used to represent any functions of binary variables. The transforms are grouped into classes where consistent formulas relating forward and inverse transform matrices are obtained. All the presented transforms have the same computational cost, which is lower than the computational cost of the well-known fixed polarity arithmetic transforms. General classifications and fast forward and inverse transform definitions for all the fast LIA transforms are given. Various properties and mutual relations that exist for the different transforms and their corresponding spectra are also shown. The presented relations and properties reduce the computational cost of finding the best LIA polynomial expansion based on the new transforms.     

Theoretical foundations of transform coding

Discusses various aspects of transform coding, including: source coding, constrained source coding, the standard theoretical model for transform coding, entropy codes, Huffman codes, quantizers, uniform quantization, bit allocation, optimal transforms, transforms visualization, partition cell shapes, autoregressive sources, transform optimization, synthesis transform optimization, orthogonality and independence, and departures form the standard model     

Linear Companding Transform for the Reduction of Peak-to-Average Power Ratio of OFDM Signals

A major drawback of orthogonal frequency-division multiplexing (OFDM) signals is their high peak-to-average power ratio (PAPR), which causes serious degradation in performance when a nonlinear power amplifier (PA) is used. Companding transform (CT) is a well-known method to reduce PAPR without restrictions on system parameters such as number of subcarriers, frame format and constellation type. Recently, a linear nonsymmetrical companding transform (LNST) that has better performance than logarithmic-based transforms such as $mu$-law companding was proposed. In this paper, a new linear companding transform (LCT) with more design flexibility than LNST is proposed. Computer simulations show that the proposed transform has a better PAPR reduction and bit error rate (BER) performance than LNST with better power spectral density (PSD).      

New fast discrete sine transform with offset

A new fast even discrete sine transform with offset (FEDSTo) has been developed and implemented for use in picture processing. This FEDSTo is faster than FDCTs for many block sizes and produces pictures that are subjectively much better than those of other available fast discrete transforms when only one-dimensional blocks are used and low sequency coefficients are retained for transmission.     

An efficient six-parameter perspective motion model for VVC

Tilt and pan camera movements are common in computer games or social media videos. These types of videos contain numerous perspective transforms while today’s video codecs rely on translational and affine motion models for motion compensation. The general perspective motion model with 8 parameters (8PMM) has unreasonably high processing time. In this paper, the eight-parameter perspective transform is simplified into a six-parameter transform to keep the time complexity within an acceptable range while modeling the most relevant transforms. Also, two motion prediction modes, Advanced Perspective Motion Vector Prediction (APMVP) and Perspective Model Merge (PMM), are proposed. The implementation results show an average of 7.0% BD-rate reduction over H.266/VVC Test Model with a maximum of 20% encoding time overhead. The results also show a 71% processing time reduction in comparison to 8PMM while experiencing an average of 5.6% increase in BD-Rate. Much better visual quality is measured through VMAF quality meter.     

基于仿射变换模型的图像跟踪系统的实现

文中设计研制了一种新型的基于仿射变换模型的实时图像跟踪系统。本跟踪系统已经通过实践检验,能够稳定的、准确的、快速的跟踪目标。并且系统有很大的升级潜力,除了能够满足仿射变换跟踪的要求之外,还能适用于其他的一些算法,构成鲁棒性更强的图像跟踪系统。实践证明该跟踪系统性能优于经典的相关跟踪系统。     

Color image segmentation using adaptive color quantization and multiresolution texture characterization

This paper presents a new hybrid color image segmentation approach, which attempts two different transforms for texture representation and extraction. The 2-D discrete wavelet transform that can express the variance in frequency and direction of textures, and the contourlet transform that represents boundaries even more accurately are applied in our algorithm. The whole segmentation algorithm contains three stages. First, an adaptive color quantization scheme is utilized to obtain a coarse image representation. Then, the tiny regions are combined based on color information. Third, the proposed energy transform function is used as a criterion for image segmentation. The motivation of the proposed method is to obtain the complete and significant objects in the image. Ultimately, according to our experiments on the Berkeley segmentation database, our techniques have more reasonable and robust results than other two widely adopted image segmentation algorithms, and our method with contourlet transform has better performance than wavelet transform.     

On the rate-distortion performance and computational efficiency ofthe Karhunen-Loeve transform for lossy data compression

We examine the rate-distortion performance and computational complexity of linear transforms for lossy data compression. The goal is to better understand the performance/complexity tradeoffs associated with using the Karhunen-Loeve transform (KLT) and its fast approximations. Since the optimal transform for transform coding is unknown in general, we investigate the performance penalties associated with using the KLT by examining cases where the KLT fails, developing a new transform that corrects the KLT's failures in those examples, and then empirically testing the performance difference between this new transform and the KLT. Experiments demonstrate that while the worst KLT can yield transform coding performance at least 3 dB worse than that of alternative block transforms, the performance penalty associated with using the KLT on real data sets seems to be significantly smaller, giving at most 0.5 dB difference in our experiments. The KLT and its fast variations studied here range in complexity requirements from O(n (2)) to O(n log n) in coding vectors of dimension n. We empirically investigate the rate-distortion performance tradeoffs associated with traversing this range of options. For example, an algorithm with complexity O(n(3/2)) and memory O(n) gives 0.4 dB performance loss relative to the full KLT in our image compression experiments.