Low-complexity compression of multispectral images based on classified transform coding

Compression of remote-sensing images can be necessary in various stages of the image life, and especially on-board a satellite before transmission to the ground station. Although on-board CPU power is quite limited, it is now possible to implement sophisticated real-time compression techniques, provided that complexity constraints are taken into account at design time. In this paper we consider the class-based multispectral image coder originally proposed in [Gelli and Poggi, Compression of multispectral images by spectral classification and transform coding, IEEE Trans. Image Process. (April 1999) 476–489 [5]] and modify it to allow its use in real time with limited hardware resources. Experiments carried out on several multispectral images show that the resulting unsupervised coder has a fully acceptable complexity, and a rate–distortion performance which is superior to that of the original supervised coder, and comparable to that of the best coders known in the literature.     

Sensor fusion of multispectral imagery

A new algorithm is presented for the sensor fusion of imagery obtained at different bandwidths. The algorithm performs image fusion using a method based on principal components. The effectiveness of the algorithm has been demonstrated by applying it to fuse intensified CCD and infrared images     

Suboptimality of the Karhunen-Loeve transform for transform coding

We examine the performance of the Karhunen-Loeve transform (KLT) for transform coding applications. The KLT has long been viewed as the best available block transform for a system that orthogonally transforms a vector source, scalar quantizes the components of the transformed vector using optimal bit allocation, and then inverse transforms the vector. This paper treats fixed-rate and variable-rate transform codes of non-Gaussian sources. The fixed-rate approach uses an optimal fixed-rate scalar quantizer to describe the transform coefficients; the variable-rate approach uses a uniform scalar quantizer followed by an optimal entropy code, and each quantized component is encoded separately. Earlier work shows that for the variable-rate case there exist sources on which the KLT is not unique and the optimal quantization and coding stage matched to a "worst" KLT yields performance as much as 1.5 dB worse than the optimal quantization and coding stage matched to a "best" KLT. In this paper, we strengthen that result to show that in both the fixed-rate and the variable-rate coding frameworks there exist sources for which the performance penalty for using a "worst" KLT can be made arbitrarily large. Further, we demonstrate in both frameworks that there exist sources for which even a best KLT gives suboptimal performance. Finally, we show that even for vector sources where the KLT yields independent coefficients, the KLT can be suboptimal for fixed-rate coding.     

K-L变换编码与DCT变换编码及其比较

讨论了DCT变换和K－L变换的基本过程，通过便证系统地就两者之间的若干问题进行了比较与分析。     

Optimally adaptive transform coding

The optimal linear block transform for coding images is well known to be the Karhunen-Loeve transformation (KLT). However, the assumption of stationarity in the optimality condition is far from valid for images. Images are composed of regions whose local statistics may vary widely across an image. While the use of adaptation can result in improved performance, there has been little investigation into the optimality of the criterion upon which the adaptation is based. In this paper we propose a new transform coding method in which the adaptation is optimal. The system is modular, consisting of a number of modules corresponding to different classes of the input data. Each module consists of a linear transformation, whose bases are calculated during an initial training period. The appropriate class for a given input vector is determined by the subspace classifier. The performance of the resulting adaptive system is shown to be superior to that of the optimal nonadaptive linear transformation. This method can also be used as a segmentor. The segmentation it performs is independent of variations in illumination. In addition, the resulting class representations are analogous to the arrangement of the directionally sensitive columns in the visual cortex.     

Hadamard transform image coding

The introduction of the fast Fourier transform algorithm has led to the development of the Fourier transform image coding technique whereby the two-dimensional Fourier transform of an image is transmitted over a channel rather than the image itself. This devlopement has further led to a related image coding technique in which an image is transformed by a Hadamard matrix operator. The Hadamard matrix is a square array of plus and minus ones whose rows and columns are orthogonal to one another. A high-speed computational algorithm, similar to the fast Fourier transform algorithm, which performs the Hadamard transformation has been developed. Since only real number additions and subtractions are required with the Hadamard transform, an order of magnitude speed advantage is possible compared to the complex number Fourier transform. Transmitting the Hadamard transform of an image rather than the spatial representation of the image provides a potential toleration to channel errors and the possibility of reduced bandwidth transmission.     

Optimal transforms for multispectral and multilayer image coding

Multispectral images are composed of a series of images at differing optical wavelengths. Since these images can be quite large, they invite efficient source coding schemes for reducing storage and transmission requirements. Because multispectral images include a third (spectral) dimension with nonstationary behavior, these multilayer data sets require specialized coding techniques. The authors develop both a theory and specific methods for performing optimal transform coding of multispectral images. The theory is based on the assumption that a multispectral image may be modeled as a set of jointly stationary Gaussian random processes. Therefore, the methods may be applied to any multilayer data set which meets this assumption. Although the authors do not assume the autocorrelation has a separable form, they show that the optimal transform for coding has a partially separable structure. In particular, they prove that a coding scheme consisting of a frequency transform within each layer followed by a separate KL transform across the layers at each spatial frequency is asymptotically optimal as the block size becomes large. Two simplifications of this method are also shown to be asymptotically optimal if the data can be assumed to satisfy additional constraints. The proposed coding techniques are then implemented using subband filtering methods, and the various algorithms are tested on multispectral images to determine their relative performance characteristics.     

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     

Compression of multispectral images by spectral classification andtransform coding

This paper presents a new technique for the compression of multispectral images, which relies on the segmentation of the image into regions of approximately homogeneous land cover. The rationale behind this approach is that, within regions of the same land cover, the pixels have stationary statistics and are characterized by mostly linear dependency, contrary to what usually happens for unsegmented images. Therefore, by applying conventional transform coding techniques to homogeneous groups of pixels, the proposed algorithm is able to effectively exploit the statistical redundancy of the image, thereby improving the rate distortion performance. The proposed coding strategy consists of three main steps. First, each pixel is classified by vector quantizing its spectral response vector, so that both a reliable classification and a minimum distortion encoding of each vector are obtained. Then, the classification map is entropy encoded and sent as side information, Finally, the residual vectors are grouped according to their classes and undergo Karhunen-Loeve transforming in the spectral domain and discrete cosine transforming in the spatial domain. Numerical experiments on a six-band thematic mapper image show that the proposed technique outperforms the conventional transform coding technique by 1 to 2 dB at all rates of interest.     

Minimum mean-squared error transform coding and subband coding

Knowledge of the power spectrum of a stationary random sequence can be used for quantizing the signal efficiently and with minimum mean-squared error. A multichannel filter is used to transform the random sequence into an intermediate set of variables that are quantized using independent scalar quantizers, and then inverse-filtered, producing a quantized version of the original sequence. Equal word-length and optimal word-length quantization at high bit rates is considered. An analytical solution for the filter that minimizes the mean-squared quantization error is obtained in terms of its singular value decomposition. The performance is characterized by a set of invariants termed second-order modes, which are derived from the eigenvalue decomposition of the matrix-valued power spectrum. A more general rank-reduced model is used for decreasing distortion by introducing bias. The results are specialized to the case when the vector-valued time series is obtained from a scalar random sequence, which gives rise to a filter bank model for quantization. The asymptotic performance of such a subband coder is derived and shown to coincide with the asymptotic bound for transform coding. Quantization employing a single scalar pre- and postfilter, traditional transform coding using a square linear transformation, and subband coding in filter banks, arise as special cases of the structure analyzed here     

Practical applications of coding

Coding applications have grown rapidly in the past several years with cost-effective performance demonstrated on several channels. Convolutional coding with soft-decision Viterbi decoding has emerged as a standard technique and is particularly well adapted to the commnnication satellite channel. Decoder implementations are discussed and examples are cited. Robustness of code performance is emphasized and instances of actual coding gain surpassing theoretical or basic coding gain are given. Some promising future directions are noted.     

Estimation of subpixel vegetation density of natural regions usingsatellite multispectral imagery

A procedure is presented for estimating the subpixel fractional canopy density of natural or undisturbed semivegetated regions on a pixel-by-pixel basis using one satellite multispectral image and a physical modeling approach. The method involves applying a model of the bulk, nondimensional plant geometry combined with a simple model of canopy reflectance and transmittance to the red and near-infrared reflectance space of the atmospherically corrected satellite image. Shadow effects are parameterized assuming Poisson-distributed and geometrically similar plant canopies. The method is applied to the estimation of fractional cover and leaf area index, using Landsat thematic mapper imagery, of two physiologically different plant communities. The first is the Landes Forest, a coniferous region in south central France, during the June 1986 HAPEX-Mobilhy Experiment. The second is the semiarid Walnut Gulch basin of southeast Arizona that contains predominantly shrubs and grasses, during the June 1990 MONSOON Experiment. The procedure offers a physically based alternative to empirical vegetation indices for estimating regionally variable canopy densities of natural, homogeneous systems with little or no ground truth     

Image coding using wavelet transform

A scheme for image compression that takes into account psychovisual features both in the space and frequency domains is proposed. This method involves two steps. First, a wavelet transform used in order to obtain a set of biorthogonal subclasses of images: the original image is decomposed at different scales using a pyramidal algorithm architecture. The decomposition is along the vertical and horizontal directions and maintains constant the number of pixels required to describe the image. Second, according to Shannon's rate distortion theory, the wavelet coefficients are vector quantized using a multiresolution codebook. To encode the wavelet coefficients, a noise shaping bit allocation procedure which assumes that details at high resolution are less visible to the human eye is proposed. In order to allow the receiver to recognize a picture as quickly as possible at minimum cost, a progressive transmission scheme is presented. It is shown that the wavelet transform is particularly well adapted to progressive transmission.     

Adaptive transform tree coding of images

A tree code, asymptotically optimal for stationary Gaussian sources and squared error distortion, is applied suboptimally to encode the discrete cosine transform (DCT) of image subblocks. The variance spectrum of each block DCT is estimated and specified uniquely by a set of one-dimensional autoregressive parameters. The average pel rate for each block is allowed to vary to meet the specification of the same average distortion per block. Since the variance spectrum and rate are different for every block. so is the code tree. Comparative coding simulations with a 256×256 and 512×512 image show that DCT tree coding with postcoding is clearly superior to DCT quantization and that a variable block rate assignment gains about 3 dB over a fixed block rate assignment     

VQ-adaptive block transform coding of images

Two new design techniques for adaptive orthogonal block transforms based on vector quantization (VQ) codebooks are presented. Both techniques start from reference vectors that are adapted to the characteristics of the signal to be coded, while using different methods to create orthogonal bases. The resulting transforms represent a signal coding tool that stands between a pure VQ scheme on one extreme and signal-independent, fixed block transformation-like discrete cosine transform (DCT) on the other. The proposed technique has superior compaction performance as compared to DCT both in the rendition of details of the image and in the peak signal-to-noise ratio (PSNR) figures.     

Hyperspectral resolution enhancement using high-resolution multispectral imagery with arbitrary response functions

A maximum a posteriori (MAP) estimation method for improving the spatial resolution of a hyperspectral image using a higher resolution auxiliary image is extended to address several practical remote sensing situations. These include cases where: 1) the spectral response of the auxiliary image is unknown and does not match that of the hyperspectral image; 2) the auxiliary image is multispectral; and 3) the spatial point spread function for the hyperspectral sensor is arbitrary and extends beyond the span of the detector elements. The research presented follows a previously reported MAP approach that makes use of a stochastic mixing model (SMM) of the underlying spectral scene content to achieve resolution enhancement beyond the intensity component of the hyperspectral image. The mathematical formulation of a generalized form of the MAP/SMM estimate is described, and the enhancement algorithm is demonstrated using various image datasets.     

Digital image coding using legendre transform

Image coding can be implemented through DPCM, transform, hybrid, or segmentation coding techniques. Some transform coding techniques, such as cosine and Hadamard, have been exhaustively analyzed and evaluated, while others, such as Legendre, have not. This paper introduces the use of Legendre transform in image coding. The transform matrix for different block sizes is calculated, the fast algorithm is derived, and the performance is evaluated through both mean square error and subjective quality. The results obtained have indicated that the system performance is comparable with that of optimum KLT and cosine transforms; moreover, it is simpler in implementation.     

Vector-scalar classification for transform image coding

This paper introduces vector-scalar classification (VSC) for discrete cosine transform (DCT) coding of images. Two main characteristics of VSC differentiate it from previously proposed classification methods. First, pattern classification is effectively performed in the energy domain of the DCT subvectors using vector quantization. Second, the subvectors, instead of the DCT vectors, are mapped into a prescribed number of classes according to a pattern-to-class link established by scalar quantization. Simulation results demonstrate that the DCT coding systems based on VSC are superior to the other proposed DCT coding systems and are competitive compared to the best subband and wavelet coding systems reported in the literature.     

Vector-lifting schemes for lossless coding and progressive archival of multispectral images

In this paper, a nonlinear subband decomposition scheme with perfect reconstruction is proposed for lossless and progressive coding of multispectral images. The merit of this new scheme is to exploit efficiently the spatial and the spectral redundancies contained in the multispectral images related to a scene of interest. Besides, the proposed method is suitable for telebrowsing applications. Experiments carried out on real scenes allow to assess its performances. The simulation results demonstrate that our approach leads to improved compression performances compared with currently used lossless coders.