Blur identification is a crucial first step in many image restoration techniques. An approach for identifying image blur using vector quantizer encoder distortion is proposed. The blur in an image is identified by choosing from a finite set of candidate blur functions. The method requires a set of training images produced by each of the blur candidates. Each of these sets is used to train a vector quantizer codebook. Given an image degraded by unknown blur, it is first encoded with each of these codebooks. The blur in the image is then estimated by choosing from among the candidates, the one corresponding to the codebook that provides the lowest encoder distortion. Simulations are performed at various bit rates and with different levels of noise. Results show that the method performs well even at a signal-to-noise ratio (SNR) as low as 10 dB.

This correspondence presents an improved version of an algorithm designed to perform image restoration via nonlinear interpolative vector quantization (NLIVQ). The improvement results from using lapped blocks during the decoding process. The algorithm is trained on original and diffraction-limited image pairs. The discrete cosine transform is again used in the codebook design process to control complexity. Simulation results are presented which demonstrate improvements over the nonlapped algorithm in both observed image quality and peak signal-to-noise ratio. In addition, the nonlinearity of the algorithm is shown to produce super-resolution in the restored images.

Synthetic aperture radar (SAR) is a remote-sensing technology that uses the motion of the radar transmitter to synthesize an antenna aperture much larger than the actual antenna aperture to yield high-spatial resolution radar images. In this paper, trellis-coded quantization (TCQ) techniques are shown to provide a high-performance, low bit-error sensitivity solution to the problem of downlink data rate reduction for SAR systems. Trellis-coded vector quantization (TCVQ) and universal TCQ coding systems are discussed, implemented, and compared with other data compression schemes [block adaptive quantization (BAQ) and VQ] that can be used to compress SAR phase history data.

A new form of trellis coded quantization based on uniform quantization thresholds and "on-the-fly" quantizer training is presented. The universal trellis coded quantization (UTCQ) technique requires neither stored codebooks nor a computationally intense codebook design algorithm. Its performance is comparable with that of fully optimized entropy-constrained trellis coded quantization (ECTCQ) for most encoding rates. The codebook and trellis geometry of UTCQ are symmetric with respect to the trellis superset. This allows sources with a symmetric probability density to be encoded with a single variable-rate code. Rate allocation and quantizer modeling procedures are given for UTCQ which allow access to continuous quantization rates. An image coding application based on adaptive wavelet coefficient subblock classification, arithmetic coding, and UTCQ is presented. The excellent performance of this coder demonstrates the efficacy of UTCQ. We also present a simple scheme to improve the perceptual performance of UTCQ for certain imagery at low bit rates. This scheme has the added advantage of being applied during image decoding, without the need to reencode the original image.

We present a wavelet based non-linear interpolative vector quantization scheme for joint compression and restoration of images; two tasks which are traditionally regarded as having conflicting goals. Vector quantizer codebook training is done using a training set consisting of pairs of the original image and its diffraction-limited counterpart. The designed VQ is then used to compress and simultaneously restore diffraction-limited images. Results from simulations indicate that the image produced at the output of the decoder is quantitatively and visually superior to the diffraction-limited image at the input to the encoder. We also compare the performance of several wavelet filters in our algorithm.

Algorithms for image recovery with super-resolution from sequences of short-exposure images are presented. Both deconvolution from wavefront sensing (DWFS) and blind deconvolution are explored. A multiframe algorithm is presented for DWFS which is based on maximum a posteriori (MAP) formulation. A multiframe blind deconvolution algorithm is presented based on a maximum likelihood formulation with strict constraints incorporated using nonlinear reparameterizations. Quantitative simulation of imaging through atmospheric turbulence and wavefront sensing are used to demonstrate the super-resolution performance of the algorithms.

This paper presents a novel technique for image restoration based on nonlinear interpolative vector quantization (NLIVQ). The algorithm performs nonlinear restoration of diffraction-limited images concurrently with quantization. It is trained on image pairs consisting of an original image and its diffraction-limited counterpart. The discrete cosine transform is used in the codebook design process to control complexity. Simulation results are presented that demonstrate improvements in visual quality and peak signal-to-noise ratio of the restored images.

Large telescopes have reached a limit of practical realization, restricted by the high costs of manufacturing large and precise optics. To overcome these limitations, images can be collected from a strip aperture which rotates to synthesize a circular one. Variations of a Poisson maximum a priori (PMAP) algorithm are applied to the collection of frames to reconstruct and super-resolve the image set producing an estimate of the original object. We provide a brief discussion of the algorithms along with examples of their performance in a simulated imaging environment, with two different algorithm formulations.

Many systems in widespread use concentrate on the imaging of binary objects, e.g., the archival storage of text documents on microfilm or the facsimile transmission of text. Due to the imperfect nature of such systems, the binary image is unavoidably corrupted by blur and noise to form a grey-scale image. We present a technique to reverse this degradation which maps the binary object reconstruction problem into a Viterbi state-trellis. We assign states of the trellis to possible outcomes of the reconstruction estimate and search the trellis in the usual optimal fashion. Our method yields superior estimates of the original binary object over a wide range of signal-to-noise ratios (SNR) when compared with conventional Wiener filter (WF) estimates. For moderate blur and SNR levels, the estimates produced approach the maximum likelihood (ML) bound on estimation performance.

Synthetic aperture radar (SAR) is a remote-sensing technology which uses the motion of the radar transmitter to synthesize an antenna aperture much larger than the actual antenna aperture to yield high spatial resolution radar images. Trellis coded quantization (TCQ) techniques are shown to provide a high performance, low bit-error sensitivity solution to the problem of downlink data rate reduction for SAR systems. Trellis coded vector quantization (TCVQ) and universal trellis coded quantization (UTCQ) coding systems are implemented and compared with other data compression schemes (block adaptive quantization (BAQ or BFPQ) and vector quantization (VQ)) that can be used to compress SAR phase history data.

A training-sequence-based entropy-constrained predictive trellis coded quantization (ECPTCQ) scheme is presented for encoding autoregressive sources. For encoding a first-order Gauss-Markov source, the mean squared error (MSE) performance of an eight-state ECPTCQ system exceeds that of entropy-constrained differential pulse code modulation (ECDPCM) by up to 1.0 dB. In addition, a hyperspectral image compression system is developed, which utilizes ECPTCQ. A hyperspectral image sequence compressed at 0.125 b/pixel/band retains an average peak signal-to-noise ratio (PSNR) of greater than 43 dB over the spectral bands.

Two multiframe formulations of Hunt's Poisson maximum a posteriori (MAP) image restoration algorithm (Hunt and Sementilli, 1992; and Hunt 1995) are presented as a means to restore an astronomical object from multiple short-exposure images. This work anticipates accurate wavefront sensor estimates of the optical transfer function of the atmosphere and telescope combination. Theoretical discussion of the algorithms is presented with simulation results. These results indicate that the multiframe algorithms produce significantly better restorations than single frame algorithms. Additionally, our studies demonstrate that the multiframe algorithms presented accomplish super-resolution.

Improving the resolving power of diffraction-limited imaging devices has most often been accomplished with costly increases in the size of the imaging aperture. To minimize cost and construction difficulty yet still improve image resolution we use a dilute aperture imaging system followed by post-processing with the Poisson maximum a-posteriori (PMAP) algorithm to achieve image reconstruction and super-resolution. We give a description of the algorithm as well as show an example of its performance on images taken with a dilute aperture optical system.

An algorithm based on nonlinear interpolative vector quantization (NLIVQ) is presented which accomplishes image restoration concurrently with image compression. The algorithm is applied to the problem of deblurring noise-free diffraction-limited images by training with a large set of blurred and original image pairs. Simulation results demonstrate a quantitative improvement in images processed by the algorithm, as measured by image peak signal-to-noise ratio (PSNR), as well as a significant improvement in perceived image quality. A theoretical formulation of the algorithm is presented along with a discussion of implementation, training and simulation results.

A model-based iterative Poisson maximum aposteriori (MAP) algorithm is extended to include a rigid projection on convex sets (POCS) step. Such an extension yields a significantly faster convergence to a perceptually and measurably better estimate of a class of objects. Both the MAP and POCS approaches have been shown to be highly successful at incorporating prior knowledge into nonlinear restoration schemes. This work shows a method for improving the restoration capabilities of an iterative MAP deconvolution technique by using spatial constraints in a POCS enhancement which shrinks the space of feasible solutions and suggests directions for future refinements.

Two systems are presented for compression of hyperspectral imagery which utilize trellis coded quantization (TCQ). Specifically, the first system uses TCQ to encode transform coefficients resulting from the application of an 8/spl times/8/spl times/8 discrete cosine transform (DCT). The second systems uses DPCM to spectrally decorrelate the data, while a 2D DCT coding scheme is used for spatial decorrelation. Side information and rate allocation strategies are discussed. Entropy-constrained code-books are designed using a modified version of the generalized Lloyd algorithm. These entropy constrained systems achieve compression ratios of greater than 70:1 with average PSNRs of the coded hyperspectral sequences exceeding 40.0 dB.>

A predictive image coder having minimal decoder complexity is presented. The image coder utilizes recursive interpolative DPCM in conjunction with adaptive classification, entropy-constrained trellis coded quantization, and optimal rate allocation to obtain signal-to-noise ratios (SNRs) in the range of those provided by the most advanced transform coders.

We took a multi-resolution approach to the signature verification problem. The top-level representation of signatures was the global geometric features. A multi-resolution representation of signatures was obtained using the wavelet transformation. We built VQ and network classifiers to demonstrate the advantages of the multi-resolution approach. High verification rates were achieved based on a limited database.

A training-sequence-based entropy-constrained predictive trellis coded quantization (ECPTCQ) scheme is presented for encoding autoregressive sources. For encoding a first-order Gauss-Markov source, the MSE performance of an 8-state ECPTCQ system exceeds that of entropy-constrained DPCM by up to 1.0 dB. In addition, a hyperspectral image compression system is developed which utilizes ECPTCQ. A hyperspectral image sequence compressed at 0.15 bits/pixel/band retains peak signal-to-noise ratios greater than 42 dB over most spectral bands.>

A predictive image coder having minimal decoder complexity is presented. The image coder utilizes recursive interpolative DPCM in conjunction with adaptive classification, entropy-constrained trellis coded quantization, and optimal rate allocation to obtain signal-to-noise ratios in the range of the most advanced transform coders.>

The adoption of new imaging modalities offers new challenges for the modelling of image formation and image restoration. Millimeter wave imaging, a totally passive method for imaging at microwave frequencies, requires statistical models that are different from normal visible optical assumptions. We examine some of the relevant issues and derive a non-linear Bayes estimate of the object, given a passive millimeter wave image.>

Multiresolution methods have played a prominent role in image processing since the early eighties. Concurrently, multigrid methods have gained wide acceptance in numerical methods. These two concepts are similar in certain aspects. In this paper, we discuss these similarities in the context of image deconvolution problems. A unified space decomposition formulation linking multiresolution and multigrid methods is presented. In addition, certain earlier deconvolution schemes based on background-detail methods, Grenander's method of sieves etc. are interpreted as variations based on this common formulation.>

Voiced-unvoiced-silence classification of speech was done using a multilayer feedforward network. The network performance was evaluated and compared to that of a maximum-likelihood classifier. Results indicated that the network performance was not significantly affected by the size of the training set and a classification rate as high as 96% was obtained.>

A new nonrecurrent associative memory model is proposed. This model is composed of a nonlinear transformation in the spectral domain followed by the association. The Moore-Penrose pseudoinverse is employed to obtain the least squares optimal solution. Computer simulations are done to evaluate the performance of the model. The simulations use one-dimensional speech signals and two-dimensional head/shoulder images. Comparison of the proposed model with the classical optimal linear associative memory and an optimal nonlinear associative memory is presented.

A new version of the discrete cosine transform (DCT) is introduced. The performance of this new version of the DCT for digital filtering and transform coding is compared to the old version of DCT [1] with various criteria; i.e., variance distribution, residual correlation, Wiener filtering, and maximum-reducible-bits.

An improved numerical solution method for maximum a posteriori image restoration is presented. Results of the use of this method are shown to be superior to previous MAP restorations and equal or better than some common linear restorations. A natural convergence criterion is defined and shown to be a good indicator of restoration quality. The effects of the parameters of the MAP restorations are discussed.

Previous work on sectional methods in image processing is extended to the processing of degradations produced by space variant point spread functions.

A new method for relating subjective and objective image data measures is proposed in power-law stimulus-response models, which have been successfully employed in other problems in experimental psychology but not in image quality models. The results of a viewing experiment to explore this model are presented.

Prior techniques in digital image restoration have assumed linear relations between the original blurred image intensity, the silver density recorded on film, and the film-grain noise. In this paper a model is used which explicitly includes nonlinear relations between intensity and film density, by use of the D-log E curve. Using Gaussian models for the image and noise statistics, a maximum a posteriori (Bayes) estimate of the restored image is derived. The MAP estimate is nonlinear, and computer implementation of the estimator equations is achieved by a fast algorithm based on direct maximization of the posterior density function. An example of the restoration method implemented on a digital image is shown.

Signal deconvolution is a problem commonly found in digital signal processing. If the recorded data is a nonlinear transformation of the degraded data, then linear techniques for deconvolution are not applicable. Herein we review the nonlinear Bayesian estimate for deconvolution and show that it may be implemented in a sectioned form for processing on-going data streams.

An analysis of the effects of finite aperture sizes in the scan and display of images is presented. The scanning aperture results in degrading the sample spectrum; the display results in a failure of the Shannon–Whittaker reconstruction theorem. Both effects can be partially corrected for, so as to give an image that is less degraded by scan and display. An example of correction of an actual image is presented as a demonstration.

Constrained least squares estimation is a technique for solution of integral equations of the first kind. The problem of image restoration requires the solution of an integral equation of the first kind. However, application of constrained least squares estimation to image restoration requires the solution of extremely large linear systems of equations. In this paper we demonstrate that, for convolution-type models of image restoration, special properties of the linear system of equations can be used to reduce the computational requirements. The necessary computations can be carried out by the fast Fourier transform, and the constrained least squares estimate can be constructed in the discrete frequency domain. A practical procedure for constrained least squares estimation is presented, and two examples are shown as output from a program for the CDC 7600 computer which performs the constrained least squares restoration of digital images.

This note considers the problem of minimizing the computation time required for digital filtering of pictures by the technique of sectioning. Direct enumeration on a computer was used to tabulate the optimum section size, and tables of the optimum section sizes are presented. The tables are compared with previously tabulated optimum sections for one-dimensional filtering; the optimal two-dimensional section sizes have linear dimensions twice as great as the optimal one-dimensional sections. To explain this discrepancy, analytical models are developed for the optimum one-and two-dimensional sections. The analytical models verify the tabulated data on optimum section size, and demonstrate why optimal two-dimensional sections are greater in size than corresponding one-dimensional sections.

It is possible to view the discrete Fourier transform as the result of approximating the Fourier integral by a trapezoidal rule integration formula. In this correspondence the effects of using higher ordered Newton–Cotes integration formulas are examined. It is shown that in computing the spectrum of a bandlimited process, the trapezoidal rule is preferred when judged by the criterion of choosing the integration formula which leads to the coarsest sampling of the data.