A Theory for Multiresolution Signal Decomposition: The Wavelet Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Vector quantization and signal compression
Vector quantization and signal compression
Elements of information theory
Elements of information theory
Computational frameworks for the fast Fourier transform
Computational frameworks for the fast Fourier transform
Independent component analysis, a new concept?
Signal Processing - Special issue on higher order statistics
Adaptive blind separation of independent sources: a deflation approach
Signal Processing
High-order contrasts for independent component analysis
Neural Computation
Independent component analysis: algorithms and applications
Neural Networks
Digital Pictures: Representation and Compression
Digital Pictures: Representation and Compression
Characteristic-function-based independent component analysis
Signal Processing - Special section: Security of data hiding technologies
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
IEEE Transactions on Information Theory
Optimal transforms for multispectral and multilayer image coding
IEEE Transactions on Image Processing
A new, fast, and efficient image codec based on set partitioning in hierarchical trees
IEEE Transactions on Circuits and Systems for Video Technology
Covariance Matrix Estimation with Multi-Regularization Parameters based on MDL Principle
Neural Processing Letters
Hi-index | 0.02 |
We present a method for noniterative maximum a posteriori (MAP) tomographic reconstruction which is based on the use of sparse matrix representations. Our approach is to precompute and store the inverse matrix required for MAP reconstruction. This approach has generally not been used in the past because the inverse matrix is typically large and fully populated (i.e., not sparse). In order to overcome this problem, we introduce two new ideas. The first idea is a novel theory for the lossy source coding of matrix transformations which we refer to as matrix source coding. This theory is based on a distortion metric that reflects the distortions produced in the final matrix-vector product, rather than the distortions in the coded matrix itself. The resulting algorithms are shown to require orthonormal transformations of both the measurement data and the matrix rows and columns before quantization and coding. The second idea is a method for efficiently storing and computing the required orthonormal transformations, which we call a sparse-matrix transform (SMT). The SMT is a generalization of the classical FFT in that it uses butterflies to compute an orthonormal transform; but unlike an FFT, the SMT uses the butterflies in an irregular pattern, and is numerically designed to best approximate the desired transforms.We demonstrate the potential of the noniterativeMAPreconstruction with examples from optical tomography. The method requires offline computation to encode the inverse transform. However, once these offline computations are completed, the noniterative MAP algorithm is shown to reduce both storage and computation by well over two orders of magnitude, as compared to a linear iterative reconstruction methods.