In this paper we report a new set of rotation invariant features for texture classification. The proposed feature set is based on principles of image approximation using multiresolution (MR) frame decompositions. Features are obtained from sequential approximation error curves (SAECs) obtained from the reconstruction error of texture approximations. These approximations are formed by the sequential addition of frame coefficients in decreasing magnitude order. Feature selection consist of taking points along the SAEC. It is found that SAECs are oblivious to rotation, allowing the generation of rotationally blind feature sets. Hence, the computational complexity of classification systems is reduced by eliminating the need for feature post-processing (e.g., DFT-encoding) to achieve rotation invariance (RI). We test the rotationally-blind feature sets for texture classification using different MR frame decompositions and data sets. We show that the proposed SAEC-based feature set achieve classification rates competitive with other schemes using a smaller feature set.

In this paper, minimization of the maximum absolute error (MAE) is achieved under a JPEG 2000 framework when a compression ratio is specified. The process is founded on our recent JPEG 2000-based algorithm for minimizing bit rate for a desired MAE using a residual coding approach [Lucero, A., et al., 2006; Lucero, A., et al., 2005; Yee, Y., et al., 2007] that uses the EBCOT coder separately. This type of algorithm uses the lossy and lossless capabilities of JPEG 2000 to achieve a desired MAE or a desired total bit rate. The technique to achieve the lowest MAE possible for a specified average bit rate is developed here for application to 3-D scientific data sets. Lossy compression is applied to the original data, while lossless compression is employed on the quantized residuals (the difference between the original and the lossy decompressed data). The lowest MAE is achieved by optimizing the allocation of the desired total bit rate between the two contributing rates corresponding to the lossy and the lossless compression steps. The methodology for achieving minimum MAE and results for 3-D meteorological data are presented here.

Computer modeling programs that generate three-dimensional (3-D) data on fine grids are capable of generating very large amounts of information. These data sets, as well as 3-D sensor/measured data sets, are prime candidates for the application of data compression algorithms. A very flexible and powerful compression algorithm for imagery data is the newly released JPEG 2000 standard. JPEG 2000 also has the capability to compress volumetric data, as described in Part 2 of the standard, by treating the 3-D data as separate slices. As a decoder standard, JPEG 2000 does not describe any specific method to allocate bits among the separate slices. This paper proposes two new bit allocation algorithms for accomplishing this task. The first procedure is rate distortion optimal (for mean squared error), and is conceptually similar to postcompression rate distortion optimization used for coding codeblocks within JPEG 2000. The disadvantage of this approach is its high computational complexity. The second bit allocation algorithm, here called the mixed model (MM) approach, mathematically models each slice's rate distortion curve using two distinct regions to get more accurate modeling at low bit rates. These two bit allocation algorithms are applied to a 3-D Meteorological data set. Test results show that the MM approach gives distortion results that are nearly identical to the optimal approach, while significantly reducing computational complexity.

We evaluate a compression scheme that exploits inter-slice redundancy in medical imaging that is compatible with the JPEG 2000 core coding system extensions (part 2). The scheme consists of applying a decorrelating transform in the cross-slice vertical direction subsequently compressing each slice with a core part 1 JPEG 2000 coder. The rates for each slice are chosen according to a heuristic log-based allocation algorithm. Two transforms were considered, the KLT and the DWT 9/spl times/7. A gain of up to 4-4 dB in RMSE was achieved using the DWT 9/spl times/7 over a baseline JPEG 2000 system that uses no decorrelating transform.

The problem of optimal bit rate allocation for 3-D JPEG2000 compression is dicussed. In this paper we consider data where the 2-D slices are compressed using JPEG2000, and the third dimension is decorrelated using the Karhunen-Loeve Transform. Here two new methods are proposed. The first approach is called the Rate Distortion Optimal (RDO) method and is based on Post-Compression Rate-Distortion (PCRD) optimization concept. The second approach is here called the Mixed Model (MM) approach and consists of extending the traditional high-resolution model with a region that is accurate for low bit rates. The proposed bit allocation methods are tested by applying them to Meteorological (Met) data. The specific data set used was generated by the Battlescale Forecast Model (BFM). The test results shows that these approach significantly reduces the computational complexity.

This paper presents the latest results of an ongoing project to assess the impact of lossy compression applied to three-dimensional meteorological data. The main innovative outcomes presented are based on different bit allocation techniques used to compress Karhunen-Loeve transformed data. The transform is applied in the z-direction (between slices) as suggested in the JPEG2000 Part 2 standard. New results using these bit allocation techniques are presented on two data sets. The performance results are presented in terms of SNR, root-mean squared error (RMSE), and the maximum absolute error (MAE) for the entire cube of data.

This paper focuses on the parameters selection that optimizes JPEG 2000 compression for meteorological data. In particular, a procedure for bit rate allocation for different slices of data is proposed. The selection is based on the variances of individual slices and a mixed model approximation of MSE. The solution of the constrained minimization problem for MSE is obtained using Lagrange multipliers. This procedure allows the incorporation of other constraints in this problem such as noninteger bit rates, limited range of possible bit rates, etc. Experimental results are given for all six variables. The reduction of MSE also led to the reduction of maximum absolute error in most cases.

In this paper, a study on 3D GRIB (GRIdded Binary) meteorological data is presented. The study consists of statistical analysis and lossy compression experiments on the data. In order to achieve compression ratios in the range of 10 to 100, lossy JPEG2000 compression was used on horizontal slices of the data. When compressing the data, an evaluation was performed to determine benefits of pre-processing the data by applying a set of different transforms in the z-direction. The transforms used in the z-direction included the Karhunen-Loeve transform (KLT) and the 9/7 wavelet filters. Results obtained in the data analysis and compression are presented.

This paper deals with the recovery of an image when some partially redundant subband data has been irreversibly corrupted. The approach presented assumes an overcomplete subband decomposition and uses a local optimal recovery estimator that works as a block processing scheme. The method takes advantage of the inherent correlation and redundancy among the remaining uncorrupted subband data. We view this approach as an alternative or as a complementary method to be used with forward error correcting codes requiring only error detection capability. We test the performance using row/column separable processing on images.

In this paper a wavelet based algorithm, its architecture and VLSI implementation for a hierarchical image coding technique is presented. The algorithm is based on a biorthogonal expansion involving a pair of mother wavelets, which are 2D discrete pyramid-shaped versions of the piecewise linear B-spline. The implementation is block oriented and includes a post-processing zerotree coding scheme to obtain further compression. The wavelet transform is computed using a previously designed array of replicated cells. The complementary architecture for the zerotree coding scheme is introduced in this paper.

A new adaptive autoregressive spectral estimator which incorporates prior frequency location information in frequency estimation from noisy data is developed. This method is formulated to exploit some of the same structural features of the problems as the principal component modified covariance (PCMC) technique. When the given samples are corrupted by noise and the extra information is available, the minimum norm least squares solution given by the PCMC is not chosen; instead, a frequency weight function is defined from prior information and then used to find the minimum weighted norm least squares solution for the autoregressive parameters. Adaptive modification of the frequency weight further enhances the performance of the estimator. Examples are included to illustrate the improvement achieved with the use of prior information.>

The authors consider the problem of multichannel sampling for the case in which the input signal bandwidth is smaller than the maximum possible that allows exact recovery (from sub-Nyquist samples taken uniformly from each channel). They focus on this reduced bandwidth case for two channels. They show that, for this case, the conditions which the prefilters must satisfy are less restrictive in some parts of the frequency axis, compared to the full bandwidth case. For a given set of valid prefilters, there is a family of possible postfilters which allows exact recovery of the input, rather than one choice, as in the standard case. It is shown that, if the samples are corrupted by additive white random noise sequence values, the extra flexibility of the postfilters can be used to select an optimal choice that minimizes the reconstruction noise power. An example is provided in which a standard ill-posed reconstruction system can be replaced with one that leads to a well-posed reconstruction when the input is of reduced bandwidth.>

A nonseparable pyramid method based on a wavelet expansion is developed for image coding. It achieves high compression rates and at the same time allows a very efficient algorithmic implementation. In particular it uses only two additions and a shift (division by 2) for each image pixel during coding or decoding. Because the operations needed are mostly independent of each other and have a high degree of regularity, it is also possible to design very-large-scale integration (VLSI) hardware to perform this operation using an array of simple basic cells. For a typical 513*513 image one can achieve a peak signal-to-noise ratio of 30 dB with an entropy of 0.133 b/pixel. Transmitted coefficient values can be encoded with pulse code modulation to allow for simpler hardware while still requiring only 0.385 b/pixel, giving a very simple overall coding system.>

The generalized multichannel sampling theorem of A. Papoulis (1977) assumes a bandlimited signal simultaneously processed by a bank of m linear time-invariant (LTI) prefilters; the filter outputs are then sampled and the original signal recovered from these samples by means of m LTI postfilters. Consideration is given to the stability (well-posedness) of the signal reconstruction with respect to additive noise perturbations of the sample values. It is shown that the reconstruction is stable if and only if the postfilter transfer functions are square integrable, thus proving a converse to the ill-posedness result K.F. Cheung and R.J. Marks (1985) while giving an alternative proof of their theorem.>

An algorithm is presented for extrapolation and spectral estimation of discrete-time signals from a set of samples. First, we assume the given samples are those of a length N sequence that is a member of a signal class consisting of the collection of outputs of a known filter with limited-energy inputs. Then we estimate by finding the signal that goes through the samples and which gives the best estimate of an arbitrary time or frequency sample using a minmax criterion. This estimate is linear and optimal over all the signals in the class and over all possible data. Next we obtain a series of signal estimates, each of which assumes the signal belongs to a different class. We make these classes depend on the data recursively by re-defining them using the previous signal estimate. Convergence of the algorithm is discussed and an example is provided to illustrate the technique.

A technique for spectral estimation given a finite number of measurements of a two-dimensional band-limited signal of time t and space x is used on signals which are transient propagating waves, The theory of optimal estimation for deterministic signals is presented in two-dimensions for signals which are assumed to be contained in a wedge-shaped region of the two-dimensional frequency plane. We also consider samples which contain errors. An example with exact signal samples shows a spectral estimate with all the basic features of our test signal. After adding noise to this signal, we encounter more difficulties in recovering the original spectrum.