We present a lossless compressor for multispectral images that combines two classical tools: wavelets and neural
networks. Due to their huge dimensions, images are split into small blocks and the wavelet transform that maps
integers to integers is applied to each block -and each band- to decorrelate it. In order to increase even more the
compression rates achieved by the wavelet transform, coefficients in the two finest scales are predicted by means
of neural networks, which use causal information (ie, coefficients already coded) to get nonlinear estimates. In
this work, we add coefficients from other spectral bands to compute the prediction, besides those coefficients
belonging to the same band, which lie in a causal neighbourhood. The differences are then coded with a context
based arithmetic coder. Several options regarding initialization, training and architecture of the neural networks
are analyzed. Comparison results with other lossless compressors (with respect to the coding time and the
bitrates achieved) are given.
Inspired by previous work on the modelling of wavelet coefficients, and on the observed differences between distributions of wavelet coefficients belonging to different landscapes, we present a lossless compressor of multi-spectral images based on the prediction of wavelet coefficients, conditioned to the landscape. This compressor operates blockwise. The wavelet transform is applied to each block, and detail coefficients from the two finest scales are predicted by means of a linear combination of other coefficients, which may belong to the same band as the predicted coefficient, or to a previously coded band. The weights for the lineal combination are estimated on-line: for each detail subband, the compressor is trained on all the detail coefficients belonging to the same class. In addition, a different band ordering is considered for each block. Differences in prediction are coded with a conditional entropy coder. Preliminary results reveal that we obtain more accurate predictions.
We present a lossless compressor for multispectral Landsat images that exploits interband and intraband correlations. The compressor operates on blocks of 256 x 256 pixels, and performs two kinds of predictions.
For bands 1, 2, 3, 4, 5, 6.2 and 7, the compressor performs an integer-to-integer wavelet transform, which is applied to each block separately. The wavelet coefficients that have not yet been encoded are predicted by means of a linear combination of already coded coefficients that belong to the same orientation and spatial location in the same band, and coefficients of the same location from other spectral bands. A fast block classification is performed
in order to use the best weights for each landscape. The prediction errors or differences are finally coded with an entropy - based coder.
For band 6.1, we do not use wavelet transforms, instead, a median edge detector is applied to predict a pixel, with the information of the neighbouring pixels and the equalized pixel from band 6.2. This technique exploits better the great similarity between histograms of bands 6.1 and 6.2. The prediction differences are finally coded with a context-based entropy coder.
The two kinds of predictions used reduce both spatial and spectral correlations, increasing the compression rates. Our compressor has shown to be superior to the lossless compressors Winzip, LOCO-I, PNG and JPEG2000.
The performance of a balanced, nonseparable orthogonal multiwavelet for edge detection is analized. We present two alternative methods to meet this objective: in the first one the normed fine detail coefficients of the multiwavelet transform are thresholded, in the other, we adapt the modulus maxima algorithm to nonseparable multiwavelets. Results are highly satisfactory.
We present a coder that yields good quality images at very high compression rates. It performs embedded coding and can carry out both lossy and lossless compression, properties which are suitable for progressive transmission. It is based on an integer to integer wavelet transform, and uses augmented zerotrees with a hybrid technique that incorporates bitplane coding as well.
We analyze the properties of orthogonality, short support, polynomial approximation order and balancing in the context of nonseparable bidimensional multi wavelets with quincunx decimation, and obtain conditions on the filter coefficients of the multi scaling function. These conditions are exploited to find examples of multi wavelets. The definition of balanced multi wavelets is extended to the bidimensional case for any dilation matrix. Relations between balancing and polynomial approximation order are investigated, and new are given. We find that for the dilation matrices chosen there can be no order are investigated, and new results are given. We find that for the dilation matrices chosen there can be no order 2 balanced multi wavelets of accuracy 2. The procedure for calculating the multi wavelet transform is outlined, and we given results of applying some of the wavelet found for image compression.
Multiwavelets in one dimension have given good results for image compression. On the other hand, nonseparable bidimensional wavelets have certain advantages over the tensor product of 1D wavelets. In this work we give examples of multiwavelets that are bidimensional and nonseparable. They correspond to the dilation matrices D1 equals [1 1;1 -1], a reflection followed by an expansion of (root)2, or to D2 equals [1 1;1 1], a rotation followed by an expansion of (root)2, and possess suitable properties for image compression: short support and 2 or 3 vanishing moments. Multiwavelets are derived from multiscaling functions. Conditions on the matrix coefficients of the dilation equation are exploited to build examples of orthogonal, nonseparable, compactly supported, bidimensional multiscaling functions of accuracy 2 and 3. They are continuous and the joint spectral radius is estimated. To the author's knowledge no examples of bidimensional multiscaling functions with these characteristics had been found previously. Coefficients for the corresponding multiwavelets are given. Multiscaling functions and multiwavelets are plotted with a cascade algorithm.
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