Tomographic reconstruction from positron emission tomography (PET) data is an ill-posed problem that requires regularization. An attractive approach is to impose an l(1) -regularization constraint, which favors sparse solutions in the wavelet domain. This can be achieved quite efficiently thanks to the iterative algorithm developed by Daubechies et al., 2004. In this paper, we apply this technique and extend it for the reconstruction of dynamic (spatio-temporal) PET data. Moreover, instead of using classical wavelets in the temporal dimension, we introduce exponential-spline wavelets (E-spline wavelets) that are specially tailored to model time activity curves (TACs) in PET. We show that the exponential-spline wavelets naturally arise from the compartmental description of the dynamics of the tracer distribution. We address the issue of the selection of the "optimal" E-spline parameters (poles and zeros) and we investigate their effect on reconstruction quality. We demonstrate the usefulness of spatio-temporal regularization and the superior performance of E-spline wavelets over conventional Battle-LemariE wavelets in a series of experiments: the 1-D fitting of TACs, and the tomographic reconstruction of both simulated and clinical data. We find that the E-spline wavelets outperform the conventional wavelets in terms of the reconstructed signal-to-noise ratio (SNR) and the sparsity of the wavelet coefficients. Based on our simulations, we conclude that replacing the conventional wavelets with E-spline wavelets leads to equal reconstruction quality for a 40% reduction of detected coincidences, meaning an improved image quality for the same number of counts or equivalently a reduced exposure to the patient for the same image quality.

Image-scrambling schemes are designed to render the image content unintelligible. Wyner has proposed an elegant one-dimensional (1-D) scrambling scheme without bandwidth expansion, making use of the discrete prolate spheroidal sequences (DPSS). The DPSS are optimal regarding their energy concentration in a given frequency subband. In this paper, we propose the two-dimensional (2-D) extension and application of this algorithm. We discuss new possibilities introduced by the 2-D approach. We also include experimental results.

This paper proposes a new family of bivariate, nonseparable splines, called hex-splines, especially designed for hexagonal lattices. The starting point of the construction is the indicator function of the Voronoi cell, which is used to define in a natural way the first-order hex-spline. Higher order hex-splines are obtained by successive convolutions. A mathematical analysis of this new bivariate spline family is presented. In particular, we derive a closed form for a hex-spline of arbitrary order. We also discuss important properties, such as their Fourier transform and the fact they form a Riesz basis. We also highlight the approximation order. For conventional rectangular lattices, hex-splines revert to classical separable tensor-product B-splines. Finally, some prototypical applications and experimental results demonstrate the usefulness of hex-splines for handling hexagonally sampled data.

A new fuzzy filter is presented for the noise reduction of images corrupted with additive noise. The filter consists of two stages. The first stage computes a fuzzy derivative for eight different directions. The second stage uses these fuzzy derivatives to perform fuzzy smoothing by weighting the contributions of neighboring pixel values. Both stages are based on fuzzy rules which make use of membership functions. The filter can be applied iteratively to effectively reduce heavy noise. In particular, the shape of the membership functions is adapted according to the remaining noise level after each iteration, making use of the distribution of the homogeneity in the image. A statistical model for the noise distribution can be incorporated to relate the homogeneity to the adaptation scheme of the membership functions. Experimental results are obtained to show the feasibility of the proposed approach. These results are also compared to other filters by numerical measures and visual inspection.

In this paper, we propose a robust wavelet domain method for noise filtering in medical images. The proposed method adapts itself to various types of image noise as well as to the preference of the medical expert; a single parameter can be used to balance the preservation of (expert-dependent) relevant details against the degree of noise reduction. The algorithm exploits generally valid knowledge about the correlation of significant image features across the resolution scales to perform a preliminary coefficient classification. This preliminary coefficient classification is used to empirically estimate the statistical distributions of the coefficients that represent useful image features on the one hand and mainly noise on the other. The adaptation to the spatial context in the image is achieved by using a wavelet domain indicator of the local spatial activity. The proposed method is of low complexity, both in its implementation and execution time. The results demonstrate its usefulness for noise suppression in medical ultrasound and magnetic resonance imaging. In these applications, the proposed method clearly outperforms single-resolution spatially adaptive algorithms, in terms of quantitative performance measures as well as in terms of visual quality of the images.

Resampling techniques are commonly required in digital image processing systems. Many times the classical interpolation functions are used, i.e., nearest-neighbour interpolation and bilinear interpolation, which are prone to the introduction of undesirable artifacts due to aliasing such as moire patterns. This paper presents a novel approach which minimizes the loss of information, in a least-squares sense, while resampling between orthogonal and hexagonal lattices. Making use of an extension of 2D splines to hexagonal lattices, the proper reconstruction function is derived. Experimental results for a printing application demonstrate the feasibility of the proposed method and are compared against the classical techniques.

We describe the validation process of a functional metadata document encapsulated in an MPEG-21 digital item. The validation starts with an MPEG-21 digital item containing the functional metadata and ends with a valid functional metadata document or with a list of error codes. Since the W3C schema language does not suffice to validate all relationships within a functional metadata document, a set of extra rules is defined. These rules are implemented through the use of transformations on functional metadata documents. These transformations are implemented using XSLT.

In the digital prepress workflow, images are represented in the CMYK colour space. Lossy image compression alleviates the need for high storage and bandwidth capacities, resulting from the high spatial and tonal resolution. After the image has been printed on paper, the introduced visual quality loss should not be noticeable to a human observer. Since visual image quality depends on the compression algorithm both quantitatively and qualitatively, and since no visual image quality models incorporating the end‐to‐end image reproduction process are satisfactory, an experimental comparison is the only viable way to quantify subjective image quality. This paper presents the results from an intensive psychovisual study based on a two‐alternative forced‐choice approach involving 164 people, with expert and non‐expert observers distinguished. The primary goal is to evaluate two previously published adaptations of JPEG to CMYK images, and to determine a visually lossless compression ratio threshold for typical printing applications. The improvements are based on tonal decorrelation and overlapping block transforms. Results on three typical prepress test images indicate that the proposed adaptations are useful and that for the investigated printing configuration, compression ratios up to 20 can be used safely.

The optimal one-dimensional (1-D) window, an index-limited sequence with maximum energy concentration in a finite frequency interval, is related to a particular discrete prolate spheroidal sequence. This letter presents the N-dimensional (N-D) extension, i.e., the N-D window with limited support and maximum energy concentration in a general nonseparable N-D passband. These windows can be applied to multidimensional filter design and the design of optimal convolution functions. We show the three-dimensional (3-D) optimal window based on a rhombic dodecahedron as a passband region.

This paper presents a new wavelet-based image denoising method, which extends a "geometrical" Bayesian framework. The new method combines three criteria for distinguishing supposedly useful coefficients from noise: coefficient magnitudes, their evolution across scales and spatial clustering of large coefficients near image edges. These three criteria are combined in a Bayesian framework. The spatial clustering properties are expressed in a prior model. The statistical properties concerning coefficient magnitudes and their evolution across scales are expressed in a joint conditional model. The three main novelties with respect to related approaches are (1) the interscale-ratios of wavelet coefficients are statistically characterized and different local criteria for distinguishing useful coefficients from noise are evaluated, (2) a joint conditional model is introduced, and (3) a novel anisotropic Markov random field prior model is proposed. The results demonstrate an improved denoising performance over related earlier techniques.

In this paper we give an overview of classical and fuzzy-classical filters for image noise reduction. Together with our overview (2001) of fuzzy filters, this paper can be seen as a preparation to our comparative study of classical and fuzzy filters for image noise reduction.

In this paper we give an overview of existing fuzzy filters for image noise reduction. The paper is a sequel to our overview of classical and fuzzy-classical filters (2001), and can be seen as a preparation to our comparative study of classical and fuzzy filters for image noise reduction. We discuss the ideas behind and the construction of the following fuzzy filters: the "fuzzy inference ruled by else-action" filters, the "fuzzy control based" filters, and the GOA filter. Our goal is to give a consistent overview of these fuzzy filters, and to clearly show the mutual differences between them.

In this paper we present the results of a comparative study of classical and fuzzy filters for image noise reduction. The discussed fuzzy filters are classified, and their performance is compared with classical filters and evaluated by numerical and visual experiments.

This paper describes a novel global-to-local method for the adaptive enhancement and unsupervised segmentation of brain tissues in MRI (magnetic resonance imaging) images. Three brain tissues are of interest: CSF (cerebrospinal fluid), GM (gray matter), WM (white matter). Firstly, we de-noise the image using wavelet thresholding, and segment the image with minimum error thresholding. Both the thresholdings are global-wise. Subsequently, we combine locally adaptive weighted median and weighted average filters with FCM (fuzzy C-means) clustering to achieve a local-wise segmentation. The performance of the proposed method is quantitatively validated by four indices with respect to a MRI brain phantom.

In quantitative coronary angiography (QCA), quantification parameters of the coronary arteries are determined using two dimensional (2D) projections of the three dimensional (3D) vessel structures. Unfortunately, the results of this quantification depend on the viewing angles corresponding with the used projections. To deal with this viewpoint dependency, multiple computer systems have been developed to determine the optimal angiographic viewing angles, the angles corresponding with the viewpoints perpendicular to the vessel segments of interest, which are the best possible viewpoints to perform QCA. We developed a system that determines the optimal viewpoints and QCA parameters without creating a reconstruction. Hence the proposed system is very simple and fast. The variation and deviation on results obtained using images of static phantoms are much smaller the inaccuracies due to the movements of the arteries.

We propose an efficient and fast wavelet based technique for speckle removal from SAR images. It relies on realistic distributions of the wavelet coefficients which represent mainly speckle noise on the one hand and those that represent the useful signal corrupted by speckle on the other. We propose analytic models for these distributions, and compute their parameters automatically from a given SAR image. The resulting algorithm strongly suppresses speckle, while preserving image details and sharpness.

20 to 50 percent of neonates with very low birth weight (VLBW:<1500 g) suffer from white matter damage (leukomalacia). Nowadays the diagnosis of WMD is still solely dependent on the visual interpretation by an expert. A need for a (semi-) computerized way of segmenting the affected regions, in order to make quantitative measurements as an aid to the subjective diagnosis, is felt. Applying active contours for this purpose, is a classical approach. The performance of active contours for this purpose, however, is heavily deteriorated by the presence of speckle noise. In this paper a new filter, taking into account local statistics in the image, is proposed; it removes a significant amount of speckle noise in the healthy parts, while it makes the areas affected by WMD more uniform, thus severely improving the performance of the active contour. The results show that applying an active contour after the proposed technique yields a segmentation much closer to that of an expert.

Summary form only given. An evaluation is made of different approaches to removing interframe redundancies. The test images we used are the MRI and CT images available from the Visual Human Project. Firstly, we found that linear predictive techniques are not able to provide any compression improvement. Even an optimal linear predictor (least-squares optimization), which holds pixels from the current and the previous frames, does not outperform the very simple 2D lossless JPEG predictor number 7. However nonlinear techniques, such as context-modeling do yield better results. In a simple experiment, lossless JPEG was estimated to code intraframe prediction errors using an interframe context. The context for coding the current pixel is formed by the magnitude of the prediction error of the corresponding pixel in the previous frame. Note that this prediction error comes from the intraframe prediction step in the previous frame. Using this interframe context-modeling approach, a reduction of the bit rate of up to 1 bit per pixel is obtainable. It is obvious that the context serves as an edge-detector, albeit a very simple and straightforward one. A new technique is proposed based on the 2D lossless image compressor JPEG-LS. The existing context-modeling scheme is extended to also catch the interframe redundancies. The interframe context is very similar to the abovementioned one, however the sign of the prediction error in the previous frame is also used.

The visual interpretation of ultrasound brain images is a proven method to detect the white matter damage at an early stage. A problem, common to all medical ultrasound images, is the presence of speckle noise, which not only complicates the visual interpretation of images, but also quantitative measurements. This paper proposes a new filter that removes a significant amount of speckle noise from ultrasound images, while preserving details very well. The filter is based on a new cleaning technique that operates on the detail images of a wavelet decomposition. The paper illustrates that the proposed technique has some advantages over other popular techniques, i.e., the ones proposed by Lee (1980), Frost (1982), Malfait and Roose (1997), and Sattar et al. (1997).

We propose a new wavelet-based method for image denoising that applies the Bayesian framework, using prior knowledge about the spatial clustering of the wavelet coefficients. Local spatial interactions of the wavelet coefficients are modeled by adopting a Markov random field model. An iterative updating technique known as iterated conditional modes (ICM) is applied to estimate the binary masks containing the positions of those wavelet coefficients that represent the useful signal in each subband. For each wavelet coefficient a shrinkage factor is determined, depending on its magnitude and on the local spatial neighbourhood in the estimated mask. We derive analytically a closed form expression for this shrinkage factor.

The interlaced video scan format suffers from major flaws such as visual artifacts and unsuitability for devices such as LCD displays, video printers, computers which require or prefer the progressive scan format. De-interlacing algorithms convert a video signal from the interlaced scan format to the progressive scan format. Next to simple spatial interpolation, two categories of de-interlacing techniques are available: motion adaptive and motion compensating methods. The latter have more potential to produce better results but are also more complex since they require accurate subpixel motion estimation. This paper presents a motion compensating de-interlacing technique based on the Irani and Peleg (1991) superresolution algorithm. Appropriate weighting terms are introduced to take into account the interlaced scanning format. Two operational modes are derived: a single iteration mode for real time video de-interlacing, and a multiple iteration mode for enhanced still image generation.

CMYK color images are used extensively in prepress applications. When compressing those color images one has to deal with four different color channels. Usually compression algorithms only take into account the spatial redundancy that is present in the image data. This approach does not yield an optimal data reduction since there also exists a high correlation between the different colors in natural images. This paper shows that a significant gain in data reduction can be achieved by exploiting this color redundancy. Some popular transform coders, including DCT‐based JPEG and the SPIHT wavelet coder, were used for reducing the spatial redundancy. The performance of the algorithms was evaluated using a quality criterion based on human perception like the mean CIEL*a*b*ΔE error.

We propose a novel imaging system useful in dermatology, more precisely, for the follow-up of patients with an increased risk of skin cancer. The system consists of a Pentium PC equipped with an RGB frame grabber, a three-chip charge coupled devices (CCD) camera controlled by the serial port and equipped with a zoom lens and a halogen annular light source. Calibration of the imaging system provides a way to transform the acquired images, which are defined in an unknown color space, to a standard, well-defined color space called sRGB. sRGB has a known relation to the CIE1 XYZ and CIE L*a*b* colorimetric spaces. These CIE color spaces are based on the human vision, and they allow the computation of a color difference metric called CIE deltaE*ab, which is proportional to the color difference, as seen by a human observer. Several types of polynomial RGB to sRGB transforms will be tried, including some optimized in perceptually uniform color spaces. The use of a standard and well-defined color space also allows meaningful exchange of images, e.g., in teledermatology. The calibration procedure is based on 24 patches with known color properties, and it takes about 5 minutes to perform. It results in a number of settings called a profile that remains valid for tens of hours of operation. Such a profile is checked before acquiring images using just one color patch, and is adjusted on the fly to compensate for short-term drift in the response of the imaging system. Precision or reproducibility of subsequent color measurements is very good with (deltaE*ab) = 0.3 and deltaE*ab < 1.2. Accuracy compared with spectrophotometric measurements is fair with (deltaE*ab) = 6.2 and deltaE*ab < 13.3.

A minimum-norm least-squares image-reconstruction method for the reconstruction of magnetic resonance images from non-Cartesian sampled data is proposed. The method is based on a general formalism for continuous-to-discrete mapping and pseudoinverse calculation. It does not involve any regridding or interpolation of the data and therefore the methodology differs fundamentally from existing regridding-based methods. Moreover, the method uses a continuous representation of objects in the image domain instead of a discretized representation. Simulations and experiments show the possibilities of the method in both radial and spiral imaging. Simulations revealed that minimum-norm least-squares image reconstruction can result in a drastic decrease of artifacts compared with regridding-based reconstruction. Besides, both in vivo and phantom experiments showed that minimum-norm least-squares image reconstruction leads to contrast improvement and increased signal-to-noise ratio compared with image reconstruction based on regridding. As an appendix, an analytical calculation of the raw data corresponding to the well-known Shepp and Logan software head phantom is presented.

Deinterlacing algorithms are used to convert an interlaced video sequence to the progressive scan format. Interlaced video exposes artifacts like line flicker and line crawling and is unsuitable for progressive media. Picture quality can be improved significantly when a proper deinterfacing algorithm is applied. The paper presents a motion adaptive technique based on a fuzzy motion detector. Preliminary experiments show results using this approach.

Summary form only given. In the pre-press industry color images have both a high spatial and a high color resolution. Such images require a considerable amount of storage space and impose long transmission times. Data compression is desired to reduce these storage and transmission problems. Because of the high quality requirements in the pre-press industry only lossless compression is acceptable. Most existing lossless compression schemes operate on gray-scale images. In this case the color components of color images must be compressed independently. However, higher compression ratios can be achieved by exploiting inter-color redundancies. We present a new technique for exploiting inter-component redundancies. The technique is based on a modified Karhunen-Loeve transform (KLT) scheme in combination with a novel quantization scheme that guarantees losslessness. The KLT decorrelates the color components. It is recomputed on a block by block basis and is therefore spatially adaptive. Spatial redundancies are removed using predictive techniques (lossless JPEG predictor no. 7 and the CALIC-predictor). The data which remains after the (spatial and color) decorrelation should be entropy-coded, but in the current implementation of our scheme only the entropy of the remaining data is computed. Note that in each block some block-dependent information must be sent, such as entropy-coder initialization information and KLT-descriptors (i.e., the rotation angles of the orthogonal KLT-matrix).

Applications such as printing on demand and personalized printing have arisen where lossless halftone image compression can be useful for increasing transmission speed and lowering storage costs. We present an improvement on the context modeling scheme by adapting the context template to the periodic structure of the halftone image. This is a non-trivial problem for which we propose a fast close-to-optimal context template selection scheme based on the calculation and sorting of the autocorrelation function on a part of the image. For evaluating our scheme, we have also investigated the compression performance of a suboptimal approach based on an incremental exhaustive search; this approach can be used in practice for decompression but not for compression because of timing requirements. We have experimented with classical halftones of different resolutions and sizes and screened under different angles.

This paper addresses the efficient high-compression coding of palettized color images. The most common methods for the lossy compression of color images rely on independent block oriented transform coding of the three or four color components. These techniques do not make use of the high redundancy of the color components and introduce some very undesirable errors at high compression, in particular block distortion. We present an efficient and original technique to code color images with a small number of colors. This is an important class of images in multimedia applications. The technique codes the according luminance image using an existing segmented image coding method for monochrome images. The color information is independently represented in a bit map. The method does not rely on the commonly used color separation and shows a far better subjective image quality than JPEG at high compression.

We present two new quantitative methods to determine motion intervals in projection reconstruction (PR) magnetic resonance (MR) imaging. Both methods do not use any a priori information concerning the motion and can be implemented easily. In the first section of this paper, the theoretical concept that formed the basis for the development of these methods, is described. It is shown that the phase difference between the complex means of two consecutive 1D PR signals equals zero when no motion occurs. When motion does occur, it becomes large. Similar conclusions can be drawn when the root mean square deviation between two consecutive projections is considered: it remains very small as long as no motion occurs, while it has a large value when rotational motion or translational motion with high-frequency components occur. These conclusions are used to determine the motion intervals in PR data. The motion-detection methods prove to be able to detect motion intervals with an accuracy of one repetition time.

A new method to make an automatic initial estimation of the position of the middle of the left ventricular (LV) myocardial wall (LV myocardial midwall) in emission tomograms is presented. This method eliminates the manual interaction still required by other, more accurate LV delineation algorithms, and which consists of indicating the LV long axis and/or the LV extremities. A well-known algorithm from the world of neural networks, Kohonen's self-organizing maps, was adapted to use general shapes and to behave well for data with large background noise. >