Wavelet filter evaluation for image compression

3D photon counting integral imaging by using multi-level decomposition

In this paper, we propose three-dimensional (3D) photon counting integral imaging by using multi-level decomposition such as discrete wavelet transform to improve the visual quality and measurement accuracy under photon-starved conditions. Conventional 3D integral imaging can visualize 3D objects and acquire their depth information. However, the amount of irradiated light on the object causes the degradation of visual quality for 3D images under photon-starved conditions. To visualize 3D objects, photon counting integral imaging has been utilized. It can detect photons from 3D scenes by using a computational photon counting model, which is modelled by the Poisson random process. However, photons occur not only from objects but also in areas where objects do not exist. Moreover, photon fluctuation may occur in the scene through shot noise. Since these noise photons are measurement errors, it may decrease the image quality and accuracy. In contrast, our proposed method uses 2D discrete wavelet transform, which can emphasize the object photons effectively. Finally, our proposed method can enhance the visual quality of 3D images and provide more accurate depth information under photon-starved conditions. To prove the feasibility of our proposed method, we implement the optical experiment and calculate various image quality metrics.

Wi-COVID: A COVID-19 symptom detection and patient monitoring framework using WiFi

The current SARS-CoV-2, better know as COVID-19, has emerged as a serious pandemic with life-threatening clinical manifestations and a high mortality rate. One of the major complications of this disease is the rapid and dangerous pulmonary deterioration that can lead to critical pneumonia conditions, resulting in death. The current healthcare system around the world faces the potential problem of lacking resources to assist a large number of patients at the same time; then, the non-critical patients are mostly referred to perform self-isolation/quarantine at home. This pandemic has placed new demands on the health systems world, asking for novel, rapid and secure ways to monitor patients in order to detect and quickly report patient's symptoms to the healthcare provider, even if they are not in the hospital. While tremendous efforts have been done to develop technologies to detect the virus, create the vaccine, and stop the spread of the disease, it is also important to develop IoT technologies that can help track and monitor diagnosed COVID-19 patients from their homes. In this paper, we explore the possibility of monitoring respiration rates (RR) of COVID-19 patients using a widely-available technology at home – WiFi. Using the at-home WiFi signals, we propose Wi-COVID, a non-invasive and non-wearable technology to monitor the patient and track RR for the healthcare provider. We first introduce the currently available applications that can be done using WiFi signals. Then, we propose the framework scheme for an end-to-end non-invasive monitoring platform of the COVID-19 patients using WiFi. Finally, we present some preliminary results of the proposed framework. We envision the proposed platform as a life-changing technology that leverages WiFi technology as a non-wearable and non-invasive way to monitor COVID-19 patients at home.

Small-Scale Perception in Medical Body Area Networks

Objective: Non-invasive respiration detection methods are of great value to healthcare applications and disease diagnosis with their advantages of minimizing the patient’s physical burden and lessen the requirement of active cooperation of the subject. This method avoids extra preparations, reduces environmental constraints, and strengthens the possibility of real-time respiratory detection. Furthermore, identifying abnormal breathing patterns in real-time is necessary for the diagnosis and monitoring of possible respiratory disorders. Method: A non-invasive method for detecting multiple breathing patterns using C-band sensing technique is presented, which is used for identifying different breathing patterns in addition to extract respiratory rate. We first evaluate the feasibility of this non-contact method in measuring different breathing patterns. Then, we detect several abnormal breathing patterns associated with certain respiratory disorders at real time using C-band sensing technique in indoor environment. Results: Mean square error (MSE) and correlation coefficient (CC) are used to evaluate the correlation between C-band sensing technique and contact respiratory sensor. The results show that all the MSE are less than 0.6 and all CC are more than 0.8, yielding a significant correlation between the two used for detecting each breathing pattern. Clinical Impact: C-band sensing technique is not only used to determine respiratory rates but also to identify breathing patterns, regarding as a preferred noncontact alternative approach to the traditional contact sensing methods. C-band sensing technique also provides a basis for the non-invasive detection of certain respiratory disorders.

Multiresolution vessel detection in magnetic particle imaging using wavelets and a Gaussian mixture model

PURPOSE

Magnetic particle imaging is a tomographic imaging technique that allows one to measure the spatial distribution of superparamagnetic nanoparticles, which are used as tracer. The magnetic particle imaging scanner measures the voltage induced due to the nonlinear magnetization behavior of the nanoparticles. The tracer distribution can be reconstructed from the voltage signal by solving an inverse problem. A possible application is the imaging of vessel structures. In this and many other cases, the tracer is only located inside the structures and a large part of the image is related to background. A detection of the tracer support in early stages of the reconstruction process could improve reconstruction results.

METHODS

In this work, a multiresolution wavelet-based reconstruction combined with a segmentation of the foreground structures is performed. For this, different wavelets are compared with respect to their reconstruction quality. For the detection of the foreground, a segmentation with a Gaussian mixture model is performed, which leads to a threshold-based binary segmentation. This segmentation is done on a coarse level of the reconstruction and then transferred to the next finer level, where it is used as prior knowledge for the reconstruction. This is repeated until the finest resolution is reached.

RESULTS

The approach is evaluated on simulated vessel phantoms and on two real measurements. The results show that this method improves the structural similarity index of the reconstructed images significantly. Among the compared wavelets, the 9/7 wavelets led to the best reconstruction results.

CONCLUSIONS

The early detection of the vessel structures at low resolution helps to improve the image quality. For the wavelet decomposition, the use of 9/7 wavelets is recommended.

Studies on the sparsifying operator in compressive digital holography

In compressive digital holography, we reconstruct sparse object wavefields from undersampled holograms by solving an ℓ₁-minimization problem. Applying wavelet transformations to the object wavefields produces the necessary sparse representations, but prior work clings to transformations with too few vanishing moments. We put several wavelet transformations belonging to different wavelet families to the test by evaluating their sparsifying properties, the number of hologram samples that are required to reconstruct the sparse wavefields perfectly, and the robustness of the reconstructions to additive noise and sparsity defects. In particular, we recommend the CDF 9/7 and 17/11 wavelet transformations, as well as their reverse counter-parts, because they yield sufficiently sparse representations for most accustomed wavefields in combination with robust reconstructions. These and other recommendations are procured from simulations and are validated using biased, noisy holograms.

Prediction of ribosome footprint profile shapes from transcript sequences

MOTIVATION

Ribosome profiling is a useful technique for studying translational dynamics and quantifying protein synthesis. Applications of this technique have shown that ribosomes are not uniformly distributed along mRNA transcripts. Understanding how each transcript-specific distribution arises is important for unraveling the translation mechanism.

RESULTS

Here, we apply kernel smoothing to construct predictive features and build a sparse model to predict the shape of ribosome footprint profiles from transcript sequences alone. Our results on Saccharomyces cerevisiae data show that the marginal ribosome densities can be predicted with high accuracy. The proposed novel method has a wide range of applications, including inferring isoform-specific ribosome footprints, designing transcripts with fast translation speeds and discovering unknown modulation during translation.

AVAILABILITY AND IMPLEMENTATION

A software package called riboShape is freely available at https://sourceforge.net/projects/riboshape

CONTACT

yss@berkeley.edu.

Separation of Doppler radar-based respiratory signatures

Respiration detection using microwave Doppler radar has attracted significant interest primarily due to its unobtrusive form of measurement. With less preparation in comparison with attaching physical sensors on the body or wearing special clothing, Doppler radar for respiration detection and monitoring is particularly useful for long-term monitoring applications such as sleep studies (i.e. sleep apnoea, SIDS). However, motion artefacts and interference from multiple sources limit the widespread use and the scope of potential applications of this technique. Utilising the recent advances in independent component analysis (ICA) and multiple antenna configuration schemes, this work investigates the feasibility of decomposing respiratory signatures into each subject from the Doppler-based measurements. Experimental results demonstrated that FastICA is capable of separating two distinct respiratory signatures from two subjects adjacent to each other even in the presence of apnoea. In each test scenario, the separated respiratory patterns correlate closely to the reference respiration strap readings. The effectiveness of FastICA in dealing with the mixed Doppler radar respiration signals confirms its applicability in healthcare applications, especially in long-term home-based monitoring as it usually involves at least two people in the same environment (i.e. two people sleeping next to each other). Further, the use of FastICA to separate involuntary movements such as the arm swing from the respiratory signatures of a single subject was explored in a multiple antenna environment. The separated respiratory signal indeed demonstrated a high correlation with the measurements made by a respiratory strap used currently in clinical settings.

Design of low-complexity high-performance wavelet filters for image analysis

This paper addresses the construction of a family of wavelets based on halfband polynomials. An algorithm is proposed that ensures maximum zeros at ω = π for a desired length of analysis and synthesis filters. We start with the coefficients of the polynomial (x+1)(n) and then use a generalized matrix formulation method to construct the filter halfband polynomial. The designed wavelets are efficient and give acceptable levels of peak signal-to-noise ratio when used for image compression. Furthermore, these wavelets give satisfactory recognition rates when used for feature extraction. Simulation results show that the designed wavelets are effective and more efficient than the existing standard wavelets.

Digital image processing for visual prosthesis: filtering implications

Investigators around the world are working on retinal neurostimulation as it may restore functional vision to the blind. The image is captured by a camera and after being processed, a series of electrical stimuli are applied to the surviving ganglion cells of the retina. This visual perception is expected to have low resolution. Therefore, there is a need of new algorithms that present the information contained in a visual scene understandable to humans. This study presents a novel multi-resolution algorithm based on wavelet analysis to extract the useful features of an image. Participants in this experiment were able to configure a filter bank to complete a set of everyday tasks. This study shows that wavelet-based algorithms may facilitate improved functional performance in prosthetic vision.

Design of almost symmetric orthogonal wavelet filter bank via direct optimization

It is a well-known fact that (compact-support) dyadic wavelets [based on the two channel filter banks (FBs)] cannot be simultaneously orthogonal and symmetric. Although orthogonal wavelets have the energy preservation property, biorthogonal wavelets are preferred in image processing applications because of their symmetric property. In this paper, a novel method is presented for the design of almost symmetric orthogonal wavelet FB. Orthogonality is structurally imposed by using the unnormalized lattice structure, and this leads to an objective function, which is relatively simple to optimize. The designed filters have good frequency response, flat group delay, almost symmetric filter coefficients, and symmetric wavelet function.

Two-band hybrid FIR-IIR filters for image compression

Two-band analysis-synthesis filters or wavelet filters are used pervasively for compressing natural images. Both FIR and IIR filters have been studied in this context, the former being the most popular. In this paper, we examine the compression performance of these two-band filters in a dyadic wavelet decomposition and attempt to isolate features that contribute most directly to the performance gain. Then, employing the general exact reconstruction condition, hybrid FIR-IIR analysis-synthesis filters are designed to maximize compression performance for natural images. Experimental results are presented that compare performance with the popular biorthogonal filters in terms of peak SNR, subjective quality, and computational complexity.

Wavelet-RX anomaly detection for dual-band forward-looking infrared imagery

This paper describes a new wavelet-based anomaly detection technique for a dual-band forward-looking infrared (FLIR) sensor consisting of a coregistered longwave (LW) with a midwave (MW) sensor. The proposed approach, called the wavelet-RX (Reed-Xiaoli) algorithm, consists of a combination of a two-dimensional (2D) wavelet transform and a well-known multivariate anomaly detector called the RX algorithm. In our wavelet-RX algorithm, a 2D wavelet transform is first applied to decompose the input image into uniform subbands. A subband-image cube is formed by concatenating together a number of significant subbands (high-energy subbands). The RX algorithm is then applied to the subband-image cube obtained from a wavelet decomposition of the LW or MW sensor data. In the case of the dual band, the RX algorithm is applied to a subband-image cube constructed by concatenating together the high-energy subbands of the LW and MW subband-image cubes. Experimental results are presented for the proposed wavelet-RX and the classical constant false alarm rate (CFAR) algorithm for detecting anomalies (targets) in a single broadband FLIR (LW or MW) or in a coregistered dual-band FLIR sensor. The results show that the proposed wavelet-RX algorithm outperforms the classical CFAR detector for both single-band and dual-band FLIR sensors.

Adaptive-compression based congestion control technique for wireless sensor networks

Congestion in a wireless sensor network causes an increase in the amount of data loss and delays in data transmission. In this paper, we propose a new congestion control technique (ACT, Adaptive Compression-based congestion control Technique) based on an adaptive compression scheme for packet reduction in case of congestion. The compression techniques used in the ACT are Discrete Wavelet Transform (DWT), Adaptive Differential Pulse Code Modulation (ADPCM), and Run-Length Coding (RLC). The ACT first transforms the data from the time domain to the frequency domain, reduces the range of data by using ADPCM, and then reduces the number of packets with the help of RLC before transferring the data to the source node. It introduces the DWT for priority-based congestion control because the DWT classifies the data into four groups with different frequencies. The ACT assigns priorities to these data groups in an inverse proportion to the respective frequencies of the data groups and defines the quantization step size of ADPCM in an inverse proportion to the priorities. RLC generates a smaller number of packets for a data group with a low priority. In the relaying node, the ACT reduces the amount of packets by increasing the quantization step size of ADPCM in case of congestion. Moreover, in order to facilitate the back pressure, the queue is controlled adaptively according to the congestion state. We experimentally demonstrate that the ACT increases the network efficiency and guarantees fairness to sensor nodes, as compared with the existing methods. Moreover, it exhibits a very high ratio of the available data in the sink.

VSNR: a wavelet-based visual signal-to-noise ratio for natural images

This paper presents an efficient metric for quantifying the visual fidelity of natural images based on near-threshold and suprathreshold properties of human vision. The proposed metric, the visual signal-to-noise ratio (VSNR), operates via a two-stage approach. In the first stage, contrast thresholds for detection of distortions in the presence of natural images are computed via wavelet-based models of visual masking and visual summation in order to determine whether the distortions in the distorted image are visible. If the distortions are below the threshold of detection, the distorted image is deemed to be of perfect visual fidelity (VSNR = infinity) and no further analysis is required. If the distortions are suprathreshold, a second stage is applied which operates based on the low-level visual property of perceived contrast, and the mid-level visual property of global precedence. These two properties are modeled as Euclidean distances in distortion-contrast space of a multiscale wavelet decomposition, and VSNR is computed based on a simple linear sum of these distances. The proposed VSNR metric is generally competitive with current metrics of visual fidelity; it is efficient both in terms of its low computational complexity and in terms of its low memory requirements; and it operates based on physical luminances and visual angle (rather than on digital pixel values and pixel-based dimensions) to accommodate different viewing conditions.

Hierarchical dynamic range coding of wavelet subbands for fast and efficient image decompression

An image coding algorithm, Progressive Resolution Coding (PROGRES), for a high-speed resolution scalable decoding is proposed. The algorithm is designed based on a prediction of the decaying dynamic ranges of wavelet subbands. Most interestingly, because of the syntactic relationship between two coders, the proposed method costs an amount of bits very similar to that used by uncoded (i.e., not entropy coded) SPIHT. The algorithm bypasses bit-plane coding and complicated list processing of SPIHT in order to obtain a considerable speed improvement, giving up quality scalability, but without compromising coding efficiency. Since each tree of coefficients is separately coded, where the root of the tree corresponds to the coefficient in LL subband, the algorithm is easily extensible to random access decoding. The algorithm is designed and implemented for both 2-D and 3-D wavelet subbands. Experiments show that the decoding speeds of the proposed coding model are four times and nine times faster than uncoded 2-D-SPIHT and 3-D-SPIHT, respectively, with almost the same decoded quality. The higher decoding speed gain in a larger image source validates the suitability of the proposed method to very large scale image encoding and decoding. In the Appendix, we explain the syntactic relationship of the proposed PROGRES method to uncoded SPIHT, and demonstrate that, in the lossless case, the bits sent to the codestream for each algorithm are identical, except that they are sent in different order.

Quantitative and qualitative evaluation of filter characteristics for wavelet packet compression of MR images

We present an analysis of the characteristics of different filters for the compression of magnetic resonance images. Compression rates were 33:1 and 50:1. We compare the performance among different types of wavelets presented in the literature and provide quantitative (percentage of energy retained, peak signal to noise ratio) and qualitative (analysis by a group of seven experts) data to support our conclusions. Different types of coiflets, symlets and biorthogonal wavelets are analyzed, and we conclude that for the images under study (T1 weighed images in three planes), the best results are provided by the biorthogonal spline (Daubechies) wavelet 2,6. Several explanations for these results are mentioned.

Image denoising using the ridgelet bi-frame

We are concerned with the performance evaluation of the ridgelet bi-frame for image denoising application. The ridgelet bi-frame is a new (as far as we know) bi-frame system that can efficiently deal with straight singularities in two dimensions. We show that, for images dominated by straight edges, the ridgelet bi-frame can obtain much better restoration results than wavelet systems. We also investigate the statistical properties of the ridgelet bi-frame coefficients of these images. Results indicate that the marginal distribution of ridgelet bi-frame coefficients has higher kurtosis than that of wavelet coefficients of the same images. We describe a simple method through which statistical denoising algorithms previously developed in the wavelet domain can be conveniently introduced into the ridgelet bi-frame domain. In addition, we use the ridgelet bi-frame to construct another new bi-frame system referred to as the curvelet bi-frame, which can be viewed as a generalized version of the curvelet. Experiment results show that the simple hard-threshold procedure in the curvelet bi-frame domain produces restoration results comparable with those due to the state-of-the-art denoising methods.

A modified SPIHT algorithm for image coding with a joint MSE and classification distortion measure

The set partitioning in hierarchical trees (SPIHT) algorithm is an efficient wavelet-based progressive image-compression technique, designed to minimize the mean-squared error (MSE) between the original and decoded imagery. However, the MSE-based distortion measure is not in general well correlated with image-recognition quality, especially at low bit rates. Specifically, low-amplitude wavelet coefficients that may be important for classification are given low priority by conventional SPIHT. In this paper, we use the kernel matching pursuits (KMP) method to autonomously estimate the importance of each wavelet subband for distinguishing between different textures, with textural segmentation first performed via a hidden Markov tree. Based on subband importance determined via KMP, we scale the wavelet coefficients prior to SPIHT coding, with the goal of minimizing a Lagrangian distortion based jointly on the MSE and classification error. For comparison we consider Bayes tree-structured vector quantization (B-TSVQ), also designed to obtain a tradeoff between MSE and classification error. The performances of the original SPIHT, the modified SPIHT, and B-TSVQ are compared.

JPEG2000 vs. full frame wavelet packet compression for smart card medical records

This paper describes a comparison among different compression methods to be used in the context of electronic health records in the newer version of "smart cards". The JPEG2000 standard is compared to a full-frame wavelet packet compression method at high (33:1 and 50:1) compression rates. Results show that the full-frame method outperforms the JPEG2K standard qualitatively and quantitatively.

Optimization of integer wavelet transforms based on difference correlation structures

In this paper, a novel lifting integer wavelet transform based on difference correlation structure (DCCS-LIWT) is proposed. First, we establish a relationship between the performance of a linear predictor and the difference correlations of an image. The obtained results provide a theoretical foundation for the following construction of the optimal lifting filters. Then, the optimal prediction lifting coefficients in the sense of least-square prediction error are derived. DCCS-LIWT puts heavy emphasis on image inherent dependence. A distinct feature of this method is the use of the variance-normalized autocorrelation function of the difference image to construct a linear predictor and adapt the predictor to varying image sources. The proposed scheme also allows respective calculations of the lifting filters for the horizontal and vertical orientations. Experimental evaluation shows that the proposed method produces better results than the other well-known integer transforms for the lossless image compression.

Wavelet-Based Compression of M-FISH Images

Multiplex fluorescence in situ hybridization (M-FISH) is a recently developed technology that enables multi-color chromosome karyotyping for molecular cytogenetic analysis. Each M-FISH image set consists of a number of aligned images of the same chromosome specimen captured at different optical wavelength. This paper presents embedded M-FISH image coding (EMIC), where the foreground objects/chromosomes and the background objects/images are coded separately. We first apply critically sampled integer wavelet transforms to both the foreground and the background. We then use object-based bit-plane coding to compress each object and generate separate embedded bitstreams that allow continuous lossy-to-lossless compression of the foreground and the background. For efficient arithmetic coding of bit planes, we propose a method of designing an optimal context model that specifically exploits the statistical characteristics of M-FISH images in the wavelet domain. Our experiments show that EMIC achieves nearly twice as much compression as Lempel-Ziv-Welch coding. EMIC also performs much better than JPEG-LS and JPEG-2000 for lossless coding. The lossy performance of EMIC is significantly better than that of coding each M-FISH image with JPEG-2000.

Dynamic contrast-based quantization for lossy wavelet image compression

This paper presents a contrast-based quantization strategy for use in lossy wavelet image compression that attempts to preserve visual quality at any bit rate. Based on the results of recent psychophysical experiments using near-threshold and suprathreshold wavelet subband quantization distortions presented against natural-image backgrounds, subbands are quantized such that the distortions in the reconstructed image exhibit root-mean-squared contrasts selected based on image, subband, and display characteristics and on a measure of total visual distortion so as to preserve the visual system's ability to integrate edge structure across scale space. Within a single, unified framework, the proposed contrast-based strategy yields images which are competitive in visual quality with results from current visually lossless approaches at high bit rates and which demonstrate improved visual quality over current visually lossy approaches at low bit rates. This strategy operates in the context of both nonembedded and embedded quantization, the latter of which yields a highly scalable codestream which attempts to maintain visual quality at all bit rates; a specific application of the proposed algorithm to JPEG-2000 is presented.

Wavelet-based ultra-high compression of multidimensional NMR data sets

The application of a lossy data compression algorithm based on wavelet transform to 2D NMR spectra is presented. We show that this algorithm affords rapid and extreme compression ratios (e.g., 800:1), providing high quality reconstructed 2D spectra. The algorithm was evaluated to ensure that qualitative and quantitative information are retained in the compressed NMR spectra. Whilst the maximum compression ratio that can be achieved depends on the number of signals and on the difference between the most and the least intense peaks (dynamic range), a compression ratio of 80:1 is affordable even for the challenging case of homonuclear 2D experiments of large biomolecules.

Optimization of wavelet decomposition for image compression and feature preservation

A neural-network-based framework has been developed to search for an optimal wavelet kernel that can be used for a specific image processing task. In this paper, a linear convolution neural network was employed to seek a wavelet that minimizes errors and maximizes compression efficiency for an image or a defined image pattern such as microcalcifications in mammograms and bone in computed tomography (CT) head images. We have used this method to evaluate the performance of tap-4 wavelets on mammograms, CTs, magnetic resonance images, and Lena images. We found that the Daubechies wavelet or those wavelets with similar filtering characteristics can produce the highest compression efficiency with the smallest mean-square-error for many image patterns including general image textures as well as microcalcifications in digital mammograms. However, the Haar wavelet produces the best results on sharp edges and low-noise smooth areas. We also found that a special wavelet whose low-pass filter coefficients are 0.32252136, 0.85258927, 1.38458542, and -0.14548269) produces the best preservation outcomes in all tested microcalcification features including the peak signal-to-noise ratio, the contrast and the figure of merit in the wavelet lossy compression scheme. Having analyzed the spectrum of the wavelet filters, we can find the compression outcomes and feature preservation characteristics as a function of wavelets. This newly developed optimization approach can be generalized to other image analysis applications where a wavelet decomposition is employed.

Effects of natural images on the detectability of simple and compound wavelet subband quantization distortions

Quantization of the coefficients within a discrete wavelet transform subband gives rise to distortions in the reconstructed image that are localized in spatial frequency and orientation and are spatially correlated with the image. We investigated the detectability of these distortions: Contrast thresholds were measured for both simple and compound distortions presented in the unmasked paradigm and against two natural-image maskers. Simple and compound distortions were generated through uniform scalar quantization of one or two subbands. Unmasked detection thresholds for simple distortions yielded contrast sensitivity functions similar to those reported for 1-octave Gabor patches. Detection thresholds for simple distortions presented against two natural-image backgrounds revealed that thresholds were elevated across the frequency range of 1.15-18.4 cycles per degree with the greatest elevation for low-frequency distortions. Unmasked thresholds for compound distortions revealed relative sensitivities of 1.1-1.2, suggesting that summation of responses to wavelet distortions is similar to summation of responses to gratings. Masked thresholds for compound distortions revealed relative sensitivities of 1.5-1.7, suggesting greater summation when distortions are masked by natural images.

Mathematical properties of the JPEG2000 wavelet filters

The LeGall 5/3 and Daubechies 9/7 filters have risen to special prominence because they were selected for inclusion in the JPEG2000 standard. We determine their key mathematical features: Riesz bounds, order of approximation, and regularity (Hölder and Sobolev). We give approximation theoretic quantities such as the asymptotic constant for the L2 error and the angle between the analysis and synthesis spaces which characterizes the loss of performance with respect to an orthogonal projection. We also derive new asymptotic error formulae that exhibit bound constants that are proportional to the magnitude of the first nonvanishing moment of the wavelet. The Daubechies 9/7 stands out because it is very close to orthonormal, but this turns out to be slightly detrimental to its asymptotic performance when compared to other wavelets with four vanishing moments.

Efficient sign coding and estimation of zero-quantized coefficients in embedded wavelet image codecs

Wavelet transform coefficients are defined by both a magnitude and a sign. While efficient algorithms exist for coding the transform coefficient magnitudes, current wavelet image coding algorithms are not as efficient at coding the sign of the transform coefficients. It is generally assumed that there is no compression gain to be obtained from entropy coding of the sign. Only recently have some authors begun to investigate this component of wavelet image coding. In this paper, sign coding is examined in detail in the context of an embedded wavelet image coder. In addition to using intraband wavelet coefficients in a sign coding context model, a projection technique is described that allows nonintraband wavelet coefficients to be incorporated into the context model. At the decoder, accumulated sign prediction statistics are also used to derive improved reconstruction estimates for zero-quantized coefficients. These techniques are shown to yield PSNR improvements averaging 0.3 dB, and are applicable to any genre of embedded wavelet image codec.

Four-dimensional wavelet compression of arbitrarily sized echocardiographic data

Wavelet-based methods have become most popular for the compression of two-dimensional medical images and sequences. The standard implementations consider data sizes that are powers of two. There is also a large body of literature treating issues such as the choice of the "optimal" wavelets and the performance comparison of competing algorithms. With the advent of telemedicine, there is a strong incentive to extend these techniques to higher dimensional data such as dynamic three-dimensional (3-D) echocardiography [four-dimensional (4-D) datasets]. One of the practical difficulties is that the size of this data is often not a multiple of a power of two, which can lead to increased computational complexity and impaired compression power. Our contribution in this paper is to present a genuine 4-D extension of the well-known zerotree algorithm for arbitrarily sized data. The key component of our method is a one-dimensional wavelet algorithm that can handle arbitrarily sized input signals. The method uses a pair of symmetric/antisymmetric wavelets (10/6) together with some appropriate midpoint symmetry boundary conditions that reduce border artifacts. The zerotree structure is also adapted so that it can accommodate noneven data splitting. We have applied our method to the compression of real 3-D dynamic sequences from clinical cardiac ultrasound examinations. Our new algorithm compares very favorably with other more ad hoc adaptations (image extension and tiling) of the standard powers-of-two methods, in terms of both compression performance and computational cost. It is vastly superior to slice-by-slice wavelet encoding. This was seen not only in numerical image quality parameters but also in expert ratings, where significant improvement using the new approach could be documented. Our validation experiments show that one can safely compress 4-D data sets at ratios of 128:1 without compromising the diagnostic value of the images. We also display some more extreme compression results at ratios of 2000:1 where some key diagnostically relevant key features are preserved.

Cascaded differential and wavelet compression of chromosome images

This paper proposes a new method for chromosome image compression based on an important characteristic of these images: the regions of interest (ROIs) to cytogeneticists for evaluation and diagnosis are well determined and segmented. Such information is utilized to advantage in our compression algorithm, which combines lossless compression of chromosome ROIs with lossy-to-lossless coding of the remaining image parts. This is accomplished by first performing a differential operation on chromosome ROIs for decorrelation, followed by critically sampled integer wavelet transforms on these regions and the remaining image parts. The well-known set partitioning in hierarchical trees (SPIHT) (Said and Perlman, 1996) algorithm is modified to generate separate embedded bit streams for both chromosome ROIs and the rest of the image that allow continuous lossy-to-lossless compression of both (although lossless compression of the former is commonly used in practice). Experiments on two sets of sample chromosome spread and karyotype images indicate that the proposed approach significantly outperforms current compression techniques used in commercial karyotyping systems and JPEG-2000 compression, which does not provide the desirable support for lossless compression of arbitrary ROIs.

Irreversible compression of medical images

The volume of data from medical imaging is growing at exponential rates, matching or exceeding the decline in the costs of digital data storage. While methods to reversibly compress image data do exist, current methods only achieve modest reductions in storage requirements. Irreversible compression can achieve substantially higher compression ratios without perceptible image degradation. These techniques are routinely applied in teleradiology, and often in Picture Archiving and Communications Systems. The practicing radiologist needs to understand how these compression techniques work and the nature of the degradation that occurs in order to optimize their medical practice. This paper describes the technology and artifacts commonly used in irreversible compression of medical images.

Optimization and implementation of the integer wavelet transform for image coding

This paper deals with the design and implementation of an image transform coding algorithm based on the integer wavelet transform (IWT). First of all, criteria are proposed for the selection of optimal factorizations of the wavelet filter polyphase matrix to be employed within the lifting scheme. The obtained results lead to the IWT implementations with very satisfactory lossless and lossy compression performance. Then, the effects of finite precision representation of the lifting coefficients on the compression performance are analyzed, showing that, in most cases, a very small number of bits can be employed for the mantissa keeping the performance degradation very limited. Stemming from these results, a VLSI architecture is proposed for the IWT implementation, capable of achieving very high frame rates with moderate gate complexity.

Ultrasound and angio image compression by cosine and wavelet transforms

The investigation results for improving lossy compression techniques for ultrasound and angio images are presented. The goal was to determine where the compression process could be improved for the medical application, and to make efforts to improve it. It is proved that the wavelet transform outperforms the discrete cosine transform applied to ultrasound and angio images. A lot of wavelet classes were tried for choosing the best one suited for corresponding image classes, which were characterised by a content complexity criterion. The analysis of international image compression standards was carried out. Special attention was paid to an algorithmical and high level service structure of a new still image compression standard JPEG2000. Its open architecture enables including some wavelet classes which we would like to suggest for medical images. A set of recommendations for acceptable compression ratio for different medical image modalities was developed. It was carried out on the base of compression study performed by the group of angiologists and cardiologists.

Suprathreshold wavelet coefficient quantization in complex stimuli: psychophysical evaluation and analysis

A psychophysical experiment is described that quantifies human sensitivities to suprathreshold distortions caused by wavelet coefficient quantization in natural images, and the resulting analysis is explained. The quantizer step sizes that cause the first three visible degradations relative to the original image are well predicted by exponential functions of subband standard deviation. The resulting root-mean-square (RMS) error in the image is constant for a spatial frequency and is independent of orientation. Contrast sensitivity calculations suggest a higher sensitivity to bands with higher energy, and threshold elevations for the second and third visible degradations are predicted well by the constant-RMS model. A quantization strategy based on the results is proposed for low-bit-rate applications.

Wavelets and imaging informatics: a review of the literature

Modern medicine is a field that has been revolutionized by the emergence of computer and imaging technology. It is increasingly difficult, however, to manage the ever-growing enormous amount of medical imaging information available in digital formats. Numerous techniques have been developed to make the imaging information more easily accessible and to perform analysis automatically. Among these techniques, wavelet transforms have proven prominently useful not only for biomedical imaging but also for signal and image processing in general. Wavelet transforms decompose a signal into frequency bands, the width of which are determined by a dyadic scheme. This particular way of dividing frequency bands matches the statistical properties of most images very well. During the past decade, there has been active research in applying wavelets to various aspects of imaging informatics, including compression, enhancements, analysis, classification, and retrieval. This review represents a survey of the most significant practical and theoretical advances in the field of wavelet-based imaging informatics.

Embedded foveation image coding

The human visual system (HVS) is highly space-variant in sampling, coding, processing, and understanding. The spatial resolution of the HVS is highest around the point of fixation (foveation point) and decreases rapidly with increasing eccentricity. By taking advantage of this fact, it is possible to remove considerable high-frequency information redundancy from the peripheral regions and still reconstruct a perceptually good quality image. Great success has been obtained previously by a class of embedded wavelet image coding algorithms, such as the embedded zerotree wavelet (EZW) and the set partitioning in hierarchical trees (SPIHT) algorithms. Embedded wavelet coding not only provides very good compression performance, but also has the property that the bitstream can be truncated at any point and still be decoded to recreate a reasonably good quality image. In this paper, we propose an embedded foveation image coding (EFIC) algorithm, which orders the encoded bitstream to optimize foveated visual quality at arbitrary bit-rates. A foveation-based image quality metric, namely, foveated wavelet image quality index (FWQI), plays an important role in the EFIC system. We also developed a modified SPIHT algorithm to improve the coding efficiency. Experiments show that EFIC integrates foveation filtering with foveated image coding and demonstrates very good coding performance and scalability in terms of foveated image quality measurement.

Lagrange wavelets for signal processing

This paper deals with the design of interpolating wavelets based on a variety of Lagrange functions, combined with novel signal processing techniques for digital imaging. Halfband Lagrange wavelets, B-spline Lagrange wavelets and Gaussian Lagrange (Lagrange distributed approximating functional (DAF)) wavelets are presented as specific examples of the generalized Lagrange wavelets. Our approach combines the perceptually dependent visual group normalization (VGN) technique and a softer logic masking (SLM) method. These are utilized to rescale the wavelet coefficients, remove perceptual redundancy and obtain good visual performance for digital image processing.

Wavelet operators for nonlinear optical pulse propagation

A method that uses discrete wavelet transforms for the solution of evolution equations that describe optical pulse propagation in nonlinear media is presented. The theory of orthogonal wavelet transforms is outlined and applied to the representation of optical pulses. Wavelet transform representations of propagation operators are presented and applied to the nonlinear Schrödinger equation, yielding results that are indistinguishable from traditional Fourier-based simulations. The compression properties of wavelet representations of optical pulses permit significant improvement in execution speed compared with that of the split-step Fourier method.

Selection of biorthogonal filters for image compression of MR images using wavelet packets

We present an analysis of different filter banks for the compression of magnetic resonance (MR) images of the human brain using wavelet packets based on biorthogonal filters. Initially, peak signal to noise ratio (PSNR) and normalized root mean square (RMS) error criteria are calculated for a series of images compressed with a 33:1 ratio, using filter banks based on biorthogonal wavelet packets. The results lead us to choose a few of these filter banks as optimal for image compression. One of these filters is employed to compress several images at four different compression ratios: 12.5:1, 25:1, 37.5:1 and 50:1. The quality of these images was evaluated by visual analysis by a group of seven experts who graded image quality on a 0-7 scale. Results show that using these filters, we can compress images to a rate of around 30:1 without introducing noticeable differences. Other applications for these filters are currently under study and include the compression/fusion of MR image stacks in order to obtain even better reductions in the amount of data needed to reconstruct complete MRI studies.

Visual communication with retinex coding

Visual communication with retinex coding seeks to suppress the spatial variation of the irradiance (e.g., shadows) across natural scenes and preserve only the spatial detail and the reflectance (or the lightness) of the surface itself. The separation of reflectance from irradiance begins with nonlinear retinex coding that sharply and clearly enhances edges and preserves their contrast, and it ends with a Wiener filter that restores images from this edge and contrast information. An approximate small-signal model of image gathering with retinex coding is found to consist of the familiar difference-of-Gaussian bandpass filter and a locally adaptive automatic-gain control. A linear representation of this model is used to develop expressions within the small-signal constraint for the information rate and the theoretical minimum data rate of the retinex-coded signal and for the maximum-realizable fidelity of the images restored from this signal. Extensive computations and simulations demonstrate that predictions based on these figures of merit correlate closely with perceptual and measured performance. Hence these predictions can serve as a general guide for the design of visual communication channels that produce images with a visual quality that consistently approaches the best possible sharpness, clarity, and reflectance constancy, even for nonuniform irradiances. The suppression of shadows in the restored image is found to be constrained inherently more by the sharpness of their penumbra than by their depth.

Ultrasound grayscale image compression with JPEG and wavelet techniques

The purpose of the study was to evaluate the effects of lossy compression on grayscale ultrasound images to determine how much compression can be applied while still maintaining images that are acceptable for diagnostic purposes. The study considered how the acquisition technique (video frame-grabber versus directly acquired in digital form) influences how much compression can be applied. For directly acquired digital images, the study considered how text (that is burned into the image) affects the compressibility of the image. The lossy compression techniques that were considered include JPEG and a Wavelet algorithm using set partitioning in hierarchical trees (SPIHT).