Michel Barret

Review: On optimal transforms in lossy compression of multicomponent images with JPEG2000

It is well known in transform coding, that the Karhunen-Loeve transform (KLT) is optimal only for Gaussian sources. However, in many applications using JPEG2000 Part 2 codecs, the KLT is generally considered as the optimal linear transform for reducing redundancies between components of multicomponent images. In this paper we present the criterion satisfied by an optimal transform of a JPEG2000 compatible compression scheme, under high resolution quantization hypothesis and without the Gaussianity assumption. We also introduce two variants of the compression scheme and the associated criteria minimized by optimal transforms. Then we give two algorithms, derived of the Independent Component Analysis algorithm ICAinf, that compute the optimal transform, one under the orthogonality constraint and the other without no constraint but invertibility. The computational complexity of the algorithms is evaluated. Finally, comparisons with the KLT are presented on hyperspectral and multispectral satellite images with different measures of distortion, as it is recommended for evaluating the performances of the codec in applications (like classification and target detection). For hyperspectral images, we observe a little but significant gain at medium and high bit-rates of the optimal transforms compared to the KLT. The actual drawback of the optimal transforms is their heavy computational complexity.

ICA based algorithms for computing optimal 1-D linear block transforms in variable high-rate source coding

The Karhunen-Loeve Transform (KLT) is optimal for transform coding of Gaussian sources, however, it is not optimal, in general, for non-Gaussian sources. Furthermore, under the high-resolution quantization hypothesis, nearly everything is known about the performance of a transform coding system with entropy constrained scalar quantization and mean-square distortion. It is then straightforward to find a criterion that, when minimized, gives the optimal linear transform under the abovementioned conditions. However, the optimal transform computation is generally considered as a difficult task and the Gaussian assumption is then used in order to simplify the calculus. In this paper, we present the abovementioned criterion as a contrast of independent component analysis modified by an additional term which is a penalty to non-orthogonality. Then we adapt the icainf algorithm by Pham in order to compute the transform minimizing the criterion either with no constraint or with the orthogonality constraint. Finally, experimental results show that the transforms we introduced can (1) outperform the KLT on synthetic signals, (2) achieve slightly better PSNR for high-rates and better visual quality (preservation of lines and contours) for medium-to-low rates than the KLT and 2-D DCT on grayscale natural images.

Review: On optimal orthogonal transforms at high bit-rates using only second order statistics in multicomponent image coding with JPEG2000

We study a JPEG2000 compatible multicomponent image compression scheme, which consists in applying a discrete wavelet transform (DWT) to each component of the image and a spectral linear transform between components. We consider the case of a spectral transform which adapts to the image and a 2-D DWT with fixed coefficients. In Akam Bita et al. (accepted for publication, [6]) we gave a criterion minimized by optimal spectral transforms. Here, we derive a simplified criterion by treating the transformed coefficients in each subband as having a Gaussian distribution of variance depending on the subband. Its minimization under orthogonality constraint is shown to lead to a joint approximate diagonalization problem, for which a fast algorithm (JADO) is available. Performances in coding of the transform returned by JADO are compared on hyper- and multi-spectral images with the Karhunen-Loeve transform (KLT) and the optimal transform (without Gaussianity assumption) returned by the algorithm OrthOST introduced in Akam Bita et al. (accepted for publication, [6]). For hyper- (resp. multi-) spectral images, we observe that JADO returns a transform which performs appreciably better than (resp. as well as) the KLT at medium to high bit-rates, nearly attaining (resp. slightly below) the performances of the transform returned by OrthOST, with a significantly lower complexity than the algorithm OrthOST.

Adaptive multiresolution decomposition: Application to lossless image compression

In this paper we introduce the use of adaptive filter banks in lossless compression of images with progressive coding in resolution. During the decomposition the filter adapts itself automatically to various regions of the image, preserving the perfect reconstruction property. Effects of parameters used in the decomposition have been studied. Simulation results are given and compared with well-known codecs. The proposed scheme gives, on average, smaller lossless compression bit rate. However, This improvement in performance is achieved at the expense of an increase in computational complexity.

Lossy Hyperspectral Images Coding with Exogenous Quasi Optimal Transforms

It is well known in transform coding that the Karhunen-Loève Transform (KLT) can be suboptimal for non Gaussiansources. However in many applications using JPEG2000Part 2 codecs, the KLT is generally considered as the optimal linear transform for reducing redundancies between components of hyperspectral images. In previous works, optimal spectral transforms (OST) compatible with the JPEG2000 Part 2 standard have been introduced, performing better than the KLT but with an heavier computational cost. In this paper, we show that the OST computed on a learningbasis constituted of Hyperion hyperspectral images issuedfrom one sensor performs very well, and even better thanthe KLT, on other images issued from the same sensor.

Low-Complexity Hyperspectral Image Coding Using Exogenous Orthogonal Optimal Spectral Transform (OrthOST) and Degree-2 Zerotrees

We introduce a low-complexity codec for lossy compression of hyperspectral images. These images have two kinds of redundancies: 1) spatial; and 2) spectral. Our coder is based on a compression scheme consisting in applying a 2-D discrete wavelet transform (DWT) to each component and a linear transform between components to reduce, respectively, spatial and spectral redundancies. The DWT used is the Daubechies 9/7. However, the spectral transform depends on the spectrometer sensor and the kind of images to be encoded. It is calculated once and for all on a set of images (the learning basis) from (only) one sensor, thanks to Akam Bita et al. s OrthOST algorithm that returns an orthogonal spectral transform, whose optimality in high-rate coding has been recently proved under mild conditions. The spectral transform obtained in this way is applied to encode other images from the same sensor. Quantization and entropy coding are then achieved with a well-suited extension to hyperspectral images of the Said and Pearlmans SPIHT algorithm. Comparisons with a JPEG2000 codec using the Karhunen-Loève transform (KLT) to reduce spectral redundancy show good performance for our codec.

Lossy compression of MERIS superspectral images with exogenous quasi optimal coding transforms

Our research focuses on reducing complexity of hyperspectral image codecs based on transform and/or subband coding, so they can be on-board a satellite. It is well-known that the Karhunen-Loève Transform (KLT) can be sub-optimal in transform coding for non Gaussian data. However, it is generally recommended as the best calculable linear coding transform in practice. Now, the concept and the computation of optimal coding transforms (OCT), under low restrictive hypotheses at high bit-rates, were carried out and adapted to a compression scheme compatible with both the JPEG2000 Part2 standard and the CCSDS recommendations for on-board satellite image compression, leading to the concept and computation of Optimal Spectral Transforms (OST). These linear transforms are optimal for reducing spectral redundancies of multi- or hyper-spectral images, when the spatial redundancies are reduced with a fixed 2-D Discrete Wavelet Transform (DWT). The problem of OST is their heavy computational cost. In this paper we present the performances in coding of a quasi optimal spectral transform, called exogenous OrthOST, obtained by learning an orthogonal OST on a sample of superspectral images from the spectrometer MERIS. The performances are presented in terms of bit-rate versus distortion for four various distortions and compared to the ones of the KLT. We observe good performances of the exogenous OrthOST, as it was the case on Hyperion hyper-spectral images in previous works.

Lossy and lossless compression of MERIS hyperspectral images with exogenous quasi-optimal spectral transforms

Our research focuses on reducing complexity of hyperspectral image codecs based on transform and/or subband coding, so they can be on-board a satellite. It is well-known that the Karhunen Loeve transform (KLT) can be sub-optimal for non Gaussian data. However, it is generally recommended as the best calculable coding transform in practice. Now, for a compression scheme compatible with both the JPEG2000 Part2 standard and the CCSDS recommendations for onboard satellite image compression, the concept and computation of optimal spectral transforms (OST), at high bit-rates, were carried out, under low restrictive hypotheses. These linear transforms are optimal for reducing spectral redundancies of multi- or hyper-spectral images, when the spatial redundancies are reduced with a fixed 2-D discrete wavelet transform. The problem of OST is their heavy computational cost. In this paper we present the performances in coding of a quasi-optimal spectral transform, called exogenous OrthOST, obtained by learning an orthogonal OST on a sample of hyperspectral images from the spectrometer MERIS. Moreover, we compute an integer variant of OrthOST for lossless compression. The performances are compared to the ones of the KLT in both lossy and lossless compressions. We observe good performances of the exogenous OrthOST.

ICA-Based Algorithms Applied to Image Coding

Recently, Narozny et al (2005) proposed a new viewpoint in variable high-rate transform coding. They showed that the problem of finding the optimal 1-D linear block transform for a coding system employing entropy-constrained uniform quantization may be viewed as a modified independent component analysis (ICA) problem. By adopting this new view-point, two new ICA-based algorithms, called GCGsup and ICAorth, were then derived for computing respectively the optimal linear transform and the optimal orthogonal transform. In this paper, we show that the transforms returned by GCGsup and ICAorth can achieve better visual image quality (better preservation of lines and contours) than the KLT and 2-D discrete cosine transform (DCT) when applied to the compression of well-known grayscale images.

On hybrid filter bank A/D converters with arbitrary over-sampling rate

Hybrid filter banks (HFB) analog/digital (A/D) systems permit wide-band, high frequency conversion. This paper presents a method for designing output digital filters of the HFB, when analog input filters are easy-to-implement (typically second order) and consequently can work at high rate. The constraint of quantization noise amplification due to the digital output filters is taken into account by using the Lagrange multiplier method. In order to improve quality of the output signal in spite of this constraint, degrees of freedom are added by using a K-channels HFB associated with an oversampling factor M less than K and by imposing a condition stronger than that of Nyquist on the input signal.