Stream temperature response to three riparian vegetation scenarios by use of a distributed temperature validated model.

Elevated in-stream temperature has led to a surge in the occurrence of parasitic intrusion proliferative kidney disease and has resulted in fish kills throughout Switzerland's waterways. Data from distributed temperature sensing (DTS) in-stream measurements for three cloud-free days in August 2007 over a 1260 m stretch of the Boiron de Merges River in southwest Switzerland were used to calibrate and validate a physically based one-dimensional stream temperature model. Stream temperature response to three distinct riparian conditions were then modeled: open, in-stream reeds, and forest cover. Simulation predicted a mean peak stream temperature increase of 0.7 °C if current vegetation was removed, an increase of 0.1 °C if dense reeds covered the entire stream reach, and a decrease of 1.2 °C if a mature riparian forest covered the entire reach. Understanding that full vegetation canopy cover is the optimal riparian management option for limiting stream temperature, in-stream reeds, which require no riparian set-aside and grow very quickly, appear to provide substantial thermal control, potentially useful for land-use management.

Spatially adaptive wavelet thresholding with context modeling for image denoising.

The method of wavelet thresholding for removing noise, or denoising, has been researched extensively due to its effectiveness and simplicity. Much of the literature has focused on developing the best uniform threshold or best basis selection. However, not much has been done to make the threshold values adaptive to the spatially changing statistics of images. Such adaptivity can improve the wavelet thresholding performance because it allows additional local information of the image (such as the identification of smooth or edge regions) to be incorporated into the algorithm. This work proposes a spatially adaptive wavelet thresholding method based on context modeling, a common technique used in image compression to adapt the coder to changing image characteristics. Each wavelet coefficient is modeled as a random variable of a generalized Gaussian distribution with an unknown parameter. Context modeling is used to estimate the parameter for each coefficient, which is then used to adapt the thresholding strategy. This spatially adaptive thresholding is extended to the overcomplete wavelet expansion, which yields better results than the orthogonal transform. Experimental results show that spatially adaptive wavelet thresholding yields significantly superior image quality and lower MSE than the best uniform thresholding with the original image assumed known.

Adaptive wavelet thresholding for image denoising and compression.

The first part of this paper proposes an adaptive, data-driven threshold for image denoising via wavelet soft-thresholding. The threshold is derived in a Bayesian framework, and the prior used on the wavelet coefficients is the generalized Gaussian distribution (GGD) widely used in image processing applications. The proposed threshold is simple and closed-form, and it is adaptive to each subband because it depends on data-driven estimates of the parameters. Experimental results show that the proposed method, called BayesShrink, is typically within 5% of the MSE of the best soft-thresholding benchmark with the image assumed known. It also outperforms SureShrink (Donoho and Johnstone 1994, 1995; Donoho 1995) most of the time. The second part of the paper attempts to further validate claims that lossy compression can be used for denoising. The BayesShrink threshold can aid in the parameter selection of a coder designed with the intention of denoising, and thus achieving simultaneous denoising and compression. Specifically, the zero-zone in the quantization step of compression is analogous to the threshold value in the thresholding function. The remaining coder design parameters are chosen based on a criterion derived from Rissanen's minimum description length (MDL) principle. Experiments show that this compression method does indeed remove noise significantly, especially for large noise power. However, it introduces quantization noise and should be used only if bitrate were an additional concern to denoising.

Wavelet thresholding for multiple noisy image copies.

This correspondence addresses the recovery of an image from its multiple noisy copies. The standard method is to compute the weighted average of these copies. Since the wavelet thresholding technique has been shown to effectively denoise a single noisy copy, we consider in this paper combining the two operations of averaging and thresholding. Because thresholding is a nonlinear technique, averaging then thresholding or thresholding then averaging produce different estimators. By modeling the signal wavelet coefficients as Laplacian distributed and the noise as Gaussian, our investigation finds the optimal ordering to depend on the number of available copies and on the signal-to-noise ratio. We then propose thresholds that are nearly optimal under the assumed model for each ordering. With the optimal and near-optimal thresholds, the two methods yield similar performance, and both show considerable improvement over merely averaging.

Set theoretic compression with an application to image coding.

We show that the complete information that is available after an image has been encoded is not just an approximate quantized image version, but a whole set of consistent images that contains the original image by necessity. From this starting point, we develop a set of tools to design a new class of encoders for image compression, based on a set decomposition and recombination of the image features. As an initial validation, we show the results of an experiment where these tools are used to modify the encoding process of block discrete cosine transform (DCT) coding in order to yield less blocking artifacts.

Adaptive scalar quantization without side information.

In this paper, we introduce a novel technique for adaptive scalar quantization. Adaptivity is useful in applications, including image compression, where the statistics of the source are either not known a priori or will change over time. Our algorithm uses previously quantized samples to estimate the distribution of the source, and does not require that side information be sent in order to adapt to changing source statistics. Our quantization scheme is thus backward adaptive. We propose that an adaptive quantizer can be separated into two building blocks, namely, model estimation and quantizer design. The model estimation produces an estimate of the changing source probability density function, which is then used to redesign the quantizer using standard techniques. We introduce nonparametric estimation techniques that only assume smoothness of the input distribution. We discuss the various sources of error in our estimation and argue that, for a wide class of sources with a smooth probability density function (pdf), we provide a good approximation to a "universal" quantizer, with the approximation becoming better as the rate increases. We study the performance of our scheme and show how the loss due to adaptivity is minimal in typical scenarios. In particular, we provide examples and show how our technique can achieve signal-to-noise ratios within 0.05 dB of the optimal Lloyd-Max quantizer for a memoryless source, while achieving over 1.5 dB gain over a fixed quantizer for a bimodal source.

Vector quantization of image subbands: a survey.

Subband and wavelet decompositions are powerful tools in image coding because of their decorrelating effects on image pixels, the concentration of energy in a few coefficients, their multirate/multiresolution framework, and their frequency splitting, which allows for efficient coding matched to the statistics of each frequency band and to the characteristics of the human visual system. Vector quantization (VQ) provides a means of converting the decomposed signal into bits in a manner that takes advantage of remaining inter and intraband correlation as well as of the more flexible partitions of higher dimensional vector spaces. Since 1988, a growing body of research has examined the use of VQ for subband/wavelet transform coefficients. We present a survey of these methods.

Adaptive transforms for image coding using spatially varying wavelet packets.

We introduce a novel, adaptive image representation using spatially varying wavelet packets (WPs), Our adaptive representation uses the fast double-tree algorithm introduced previously (Herley et al., 1993) to optimize an operational rate-distortion (R-D) cost function, as is appropriate for the lossy image compression framework. This involves jointly determining which filter bank tree (WP frequency decomposition) to use, and when to change the filter bank tree (spatial segmentation). For optimality, the spatial and frequency segmentations must be done jointly, not sequentially. Due to computational complexity constraints, we consider quadtree spatial segmentations and binary WP frequency decompositions (corresponding to two-channel filter banks) for application to image coding. We present results verifying the usefulness and versatility of this adaptive representation for image coding using both a first-order entropy rate-measure-based coder as well as a powerful space-frequency quantization-based (SPQ-based) wavelet coder introduced by Xiong et al. (1993).

Image compression using binary space partitioning trees.

For low bit-rate compression applications, segmentation-based coding methods provide, in general, high compression ratios when compared with traditional (e.g., transform and subband) coding approaches. In this paper, we present a new segmentation-based image coding method that divides the desired image using binary space partitioning (BSP). The BSP approach partitions the desired image recursively by arbitrarily oriented lines in a hierarchical manner. This recursive partitioning generates a binary tree, which is referred to as the BSP-tree representation of the desired image. The most critical aspect of the BSP-tree method is the criterion used to select the partitioning lines of the BSP tree representation, In previous works, we developed novel methods for selecting the BSP-tree lines, and showed that the BSP approach provides efficient segmentation of images. In this paper, we describe a hierarchical approach for coding the partitioning lines of the BSP-tree representation. We also show that the image signal within the different regions (resulting from the recursive partitioning) can be represented using low-order polynomials. Furthermore, we employ an optimum pruning algorithm to minimize the bit rate of the BSP tree representation (for a given budget constraint) while minimizing distortion. Simulation results and comparisons with other compression methods are also presented.

Optimal trellis-based buffered compression and fast approximations.

The authors formalize the description of the buffer-constrained adaptive quantization problem. For a given set of admissible quantizers used to code a discrete nonstationary signal sequence in a buffer-constrained environment, they formulate the optimal solution. They also develop slightly suboptimal but much faster approximations. These solutions are valid for any globally minimum distortion criterion, which is additive over the individual elements of the sequence. As a first step, they define the problem as one of constrained, discrete optimization and establish its equivalence to some of the problems studied in the field of integer programming. Forward dynamic programming using the Viterbi algorithm is shown to provide a way of computing the optimal solution. Then, they provide a heuristic algorithm based on Lagrangian optimization using an operational rate-distortion framework that, with computing complexity reduced by an order of magnitude, approaches the optimally achievable performance. The algorithms can serve as a benchmark for assessing the performance of buffer control strategies and are useful for applications such as multimedia workstation displays, video encoding for CD-ROMs, and buffered JPEG coding environments, where processing delay is not a concern but decoding buffer size has to be minimized.

Bit allocation for dependent quantization with applications to multiresolution and MPEG video coders.

We address the problem of efficient bit allocation in a dependent coding environment. While optimal bit allocation for independently coded signal blocks has been studied in the literature, we extend these techniques to the more general temporally and spatially dependent coding scenarios. Of particular interest are the topical MPEG video coder and multiresolution coders. Our approach uses an operational rate-distortion (R-D) framework for arbitrary quantizer sets. We show how a certain monotonicity property of the dependent R-D curves can be exploited in formulating fast ways to obtain optimal and near-optimal solutions. We illustrate the application of this property in specifying intelligent pruning conditions to eliminate suboptimal operating points for the MPEG allocation problem, for which we also point out fast nearly-optimal heuristics. Additionally, we formulate an efficient allocation strategy for multiresolution coders, using the spatial pyramid coder as an example. We then extend this analysis to a spatio-temporal 3-D pyramidal coding scheme. We tackle the compatibility problem of optimizing full-resolution quality while simultaneously catering to subresolution bit rate or quality constraints. We show how to obtain fast solutions that provide nearly optimal (typically within 0.3 dB) full resolution quality while providing much better performance for the subresolution layer (typically 2-3 dB better than the full-resolution optimal solution).

Rate-distortion optimal fast thresholding with complete JPEG/MPEG decoder compatibility.

We show a rate-distortion optimal way to threshold or drop the DCT coefficients of the JPEG and MPEG compression standards. Our optimal algorithm uses a fast dynamic programming recursive structure. The primary advantage of our approach lies in its complete compatibility with standard JPEG and MPEG decoders.

FCO sampling of digital video using perfect reconstruction filter banks.

Three-dimensional nonseparable perfect reconstruction filter banks using three-dimensional nonseparable sampling by two, FCO, are proposed. Filter structures are derived and applied to digital video. Separation into two bands is obtained, and it is shown to perform better from the perceptual point of view than interlaced sequences resulting from the quincunx sampling of a progressively scanned signal in time-vertical dimensions.

Best wavelet packet bases in a rate-distortion sense.

A fast rate-distortion (R-D) optimal scheme for coding adaptive trees whose individual nodes spawn descendents forming a disjoint and complete basis cover for the space spanned by their parent nodes is presented. The scheme guarantees operation on the convex hull of the operational R-D curve and uses a fast dynamic programing pruning algorithm to markedly reduce computational complexity. Applications for this coding technique include R. Coefman et al.'s (Yale Univ., 1990) generalized multiresolution wavelet packet decomposition, iterative subband coders, and quadtree structures. Applications to image processing involving wavelet packets as well as discrete cosine transform (DCT) quadtrees are presented.