Jerome M. Shapiro

An embedded wavelet hierarchical image coder

A simple, yet remarkably effective, image compression algorithm that has the property that the bits in the bit stream are generated in order of importance, yielding fully hierarchical image compression suitable for embedded coding or progressive transmission, is described. Given an image bit stream, the decoder can cease decoding at the same image that would have been encoded at the bit rate corresponding to the truncated bit stream. The compression algorithm is based on three key concepts: (1) wavelet transform or hierarchical subband decomposition, (2) prediction of the absence of significant information across scales by exploiting the self-similarity inherent in images, and (3) hierarchical entropy-coded quantization.<<ETX>>

Multispectral KLT-wavelet data compression for Landsat thematic mapper images

The authors report a methodology that enhances the compression of Landsat thematic mapper (TM) multispectral imagery, while reducing the image information loss. The method first removes interband correlation of the image data by use of the Karhunen-Loeve transform (KLT) to produce the image principal components. Each principal component is spatially decorrelated using a discrete wavelet transform. The resulting coefficients are then quantized and losslessly encoded. Image compressions of typically 80:1 demonstrate that the method should be quite suitable for rapid browsing applications where small amounts of image loss are tolerable.<<ETX>>

A fast technique for identifying zerotrees in the EZW algorithm

The embedded zerotree wavelet (EZW) algorithm has become a popular benchmark for image compression algorithms. The current paper presents a fast technique for identifying zerotrees for all dominant passes in the encoder prior to encoding. The key is initializing a data structure called a zerotree map with the largest power of two smaller than a given coefficient, and then completing the zerotree map by bitwise-ORing the values of potential parents with those of their children. This simple operation can be performed in parallel with the wavelet transform operation and thus is efficient for both hardware and software implementations.

Optimal bit allocation in the presence of quantizer feedback

The authors consider the problem of optimal bit allocation in various forms of predictive coding, where the predictor itself has errors resulting from previous quantization. The solution to this problem has potential application to many forms of image and video coding where predictive coding is used. In predictive coding, the input to the quantizer can be decomposed into the innovation, i.e., the part of the quantizer input signal due to the quantization of the predictor. The natural question that arises is whether it is better to allocate more bits to the predictor, since quantization errors persist longer, or to allocate more bits to coding the total residual. This problem is analyzed for predictive video coding through the use of a simple parametric distortion-rate model for the propagation of quantization errors. This model provides a framework in which the optimal bit allocation problem can be solved in the presence of quantizer feedback. An exact MMSE (minimum mean-square error) solution is obtained that involves solving one nonlinear monotonic equation for one Lagrange multiplier, after which the bit allocation has a closed-form analytic solution. Since the MMSE solution does not produce equal distortion in all frames, the optimal MINMAX (minimize the maximum) bit allocation that minimizes the frame distortion subject to equal distortions per frame is also introduced.<<ETX>>

Adaptive McClellan transformations for quincunx filter banks

A technique is developed for the design of 2-D nonseparable two-channel filter banks for a quincunx sampling lattice, where the isopotentials of the frequency response can be optimized and adapted to the input signals statistics. By employing known odd-length symmetric linear phase filter banks as the l-D prototype filters for 2-D filters parameterized by the McClellan transformation, conditions are derived such that the resulting 2-D two-channel filter bank retains the perfect-reconstruction or aliasing-free properties of the 1-D prototype two-channel filter bank. A particular two-parameter transformation function is developed that has sufficient flexibility to adapt its orientation in any direction and whose optimization involves a simple constrained least-squares problem in which the feasible set lies within a circle. The results have practical applications in many areas of image and video processing where multirate filter banks are used. >

Adaptive multidimensional perfect reconstruction filter banks using McClellan transformations

A technique for the design of 2D nonseparable perfect reconstruction filter banks is developed where the isopotentials of the frequency response can be optimized and adapted to local signal statistics. By employing existing odd-length symmetric perfect reconstruction filterbanks as the 1D normal filters for a 2D filter parameterized by the McClellan transformation, conditions under which the resulting 2D filter bank retains the perfect reconstruction property are derived. A two-parameter transformation function is developed whose optimization involves a simple constrained least-squares problem in which the feasible set lies on a circle. The results have practical applications in many areas of image and video processing where multirate filterbanks are used.<<ETX>>

Multispectral Image Compression By Wavelet / Karhunen-loeve Transformation

andsat Thematic Mapper (TM) multispectral imagery, while reducing image information loss. The method first removes interband correldtion of the image data by use of the Karhnnen-Loeve transform to prc luce the image principal components over the seven Landsat bands. The prin- cipal components are then compressed using wavelet and lossless en- coding techniques. Image compressions of typically of