nils-herrmann/clean_scirepeval huggingface dataset:
A review of wavelets in biomedical applications

We present an overview of the various uses of the wavelet transform (WT) in medicine and biology. We start by describing the wavelet properties that are the most important for biomedical applications. In particular we provide an interpretation of the the continuous wavelet transform (CWT) as a prewhitening multiscale matched filter. We also briefly indicate the analogy between the WT and some of the the biological processing that occurs in the early components of the auditory and visual system. We then review the uses of the WT for the analysis of 1-D physiological signals obtained by phonocardiography, electrocardiography (ECG), mid electroencephalography (EEG), including evoked response potentials. Next, we provide a survey of wavelet developments in medical imaging. These include biomedical image processing algorithms (e.g., noise reduction, image enhancement, and detection of microcalcifications in mammograms), image reconstruction and acquisition schemes (tomography, and magnetic resonance imaging (MRI)), and multiresolution methods for the registration and statistical analysis of functional images of the brain (positron emission tomography (PET) and functional MRI (fMRI)). In each case, we provide the reader with same general background information and a brief explanation of how the methods work.
MMSE denoising of sparse Lévy processes via message passing

Many recent algorithms for sparse signal recovery can be interpreted as maximum-a-posteriori (MAP) estimators relying on some specific priors. From this Bayesian perspective, state-of-the-art methods based on discrete-gradient regularizers, such as total-variation (TV) minimization, implicitly assume the signals to be sampled instances of Lévy processes with independent Laplace-distributed increments. By extending the concept to more general Lévy processes, we propose an efficient minimum-mean-squared error (MMSE) estimation method based on message-passing algorithms on factor graphs. The resulting algorithm can be used to benchmark the performance of the existing or design new algorithms for the recovery of sparse signals.
Improved Variational Denoising of Flow Fields with Application to Phase-Contrast MRI Data

We propose a new variational framework for the problem of reconstructing flow fields from noisy measurements. The formalism is based on regularizers penalizing the singular values of the Jacobian of the field. Specifically, we rely on the nuclear norm. Our method is invariant with respect to fundamental transformations and can be efficiently solved. We conduct numerical experiments on several phantom data and report improved performance compared to existing vectorial extensions of total variation and curl-divergence regularizations. Finally, we apply our reconstruction method to an experimentally-acquired phase-contrast MRI recording for enhancing the data visualization.
Construction of Hilbert Transform Pairs of Wavelet Bases and Gabor-Like Transforms

We propose a novel method for constructing Hilbert transform (HT) pairs of wavelet bases based on a fundamental approximation-theoretic characterization of scaling functions-the B-spline factorization theorem. In particular, starting from well-localized scaling functions, we construct HT pairs of biorthogonal wavelet bases of L2(R) by relating the corresponding wavelet filters via a discrete form of the continuous HT filter. As a concrete application of this methodology, we identify HT pairs of spline wavelets of a specific flavor, which are then combined to realize a family of complex wavelets that resemble the optimally-localized Gabor function for sufficiently large orders. Analytic wavelets, derived from the complexification of HT wavelet pairs, exhibit a one-sided spectrum. Based on the tensor-product of such analytic wavelets, and, in effect, by appropriately combining four separable biorthogonal wavelet bases of L2(R2), we then discuss a methodology for constructing 2-D directional-selective complex wavelets. In particular, analogous to the HT correspondence between the components of the 1-D counterpart, we relate the real and imaginary components of these complex wavelets using a multidimensional extension of the HT-the directional HT. Next, we construct a family of complex spline wavelets that resemble the directional Gabor functions proposed by Daugman. Finally, we present an efficient fast Fourier transform (FFT)-based filterbank algorithm for implementing the associated complex wavelet transform.
Generalized sampling: a variational approach .II. Applications

For pt.I see ibid., vol.50, no.8, p.1965-76 (2000). The variational reconstruction theory from a companion paper finds a solution consistent with some linear constraints and minimizing a quadratic plausibility criterion. It is suitable for treating vector and multidimensional signals. Here, we apply the theory to a generalized sampling system consisting of a multichannel filterbank followed by a nonuniform sampling. We provide ready-made formulas, which should permit application of the technique directly to problems at hand. We comment on the practical aspects of the method, such as numerical stability and speed. We show the reconstruction formula and apply it to several practical examples, including new variational formulation of derivative sampling, landmark warping, and tomographic reconstruction.
Texture classification and segmentation using wavelet frames

This paper describes a new approach to the characterization of texture properties at multiple scales using the wavelet transform. The analysis uses an overcomplete wavelet decomposition, which yields a description that is translation invariant. It is shown that this representation constitutes a tight frame of l(2) and that it has a fast iterative algorithm. A texture is characterized by a set of channel variances estimated at the output of the corresponding filter bank. Classification experiments with l(2) Brodatz textures indicate that the discrete wavelet frame (DWF) approach is superior to a standard (critically sampled) wavelet transform feature extraction. These results also suggest that this approach should perform better than most traditional single resolution techniques (co-occurrences, local linear transform, and the like). A detailed comparison of the classification performance of various orthogonal and biorthogonal wavelet transforms is also provided. Finally, the DWF feature extraction technique is incorporated into a simple multicomponent texture segmentation algorithm, and some illustrative examples are presented.
Benefits of consistency in image denoising with steerable wavelets

The steerable wavelet transform is a redundant image representation with the remarkable property that its basis functions can be adaptively rotated to a desired orientation. This makes the transform well-suited to the design of wavelet-based algorithms applicable to images with a high amount of directional features. However, arbitrary modification of the wavelet-domain coefficients may violate consistency constraints because a legitimate representation must be redundant. In this paper, by honoring the redundancy of the coefficients, we demonstrate that it is possible to improve the performance of regularized least-squares problems in the steerable wavelet domain. We illustrate that our consistent method significantly improves upon the performance of conventional denoising with steerable wavelets.
Efficient dyadic wavelet transformation of images using interpolation filters

The properties of a special class of overcomplete wavelet transforms specified in terms of an interpolation filter are investigated. The decomposition is obtained by filtering the signal with a sequence of increasingly selective lowpass filters with a dyadic scale progression. The wavelet coefficients are evaluated by simple subtraction of two consecutive lowpass components. The lowpass filter bank is implemented using a standard iterative multiscale algorithm. The impulse responses of the analysis filters are shown to be interpolated versions of each other. This structure is computationally very efficient; it requires a little more than one-fourth as many operations as other comparable wavelet-based algorithms. The corresponding filter bank provides a perfect coverage of the frequency domain, which results in a trivial reconstruction procedure by summation. Extensions to the subsampled case are also presented. The decompositions associated with spline interpolation filters are considered in some detail, and some image processing examples are presented.<<ETX>>
Efficient Shape Priors for Spline-Based Snakes

Parametric active contours are an attractive approach for image segmentation, thanks to their computational efficiency. They are driven by application-dependent energies that reflect the prior knowledge on the object to be segmented. We propose an energy involving shape priors acting in a regularization-like manner. Thereby, the shape of the snake is orthogonally projected onto the space that spans the affine transformations of a given shape prior. The formulation of the curves is continuous, which provides computational benefits when compared with landmark-based (discrete) methods. We show that this approach improves the robustness and quality of spline-based segmentation algorithms, while its computational overhead is negligible. An interactive and ready-to-use implementation of the proposed algorithm is available and was successfully tested on real data in order to segment Drosophila flies and yeast cells in microscopic images.
Binary Compressed Imaging

Compressed sensing can substantially reduce the number of samples required for conventional signal acquisition at the expense of an additional reconstruction procedure. It also provides robust reconstruction when using quantized measurements, including in the one-bit setting. In this paper, our goal is to design a framework for binary compressed sensing that is adapted to images. Accordingly, we propose an acquisition and reconstruction approach that complies with the high dimensionality of image data and that provides reconstructions of satisfactory visual quality. Our forward model describes data acquisition and follows physical principles. It entails a series of random convolutions performed optically followed by sampling and binary thresholding. The binary samples that are obtained can be either measured or ignored according to predefined functions. Based on these measurements, we then express our reconstruction problem as the minimization of a compound convex cost that enforces the consistency of the solution with the available binary data under total-variation regularization. Finally, we derive an efficient reconstruction algorithm relying on convex-optimization principles. We conduct several experiments on standard images and demonstrate the practical interest of our approach.
A Fast Wavelet-Based Reconstruction Method for Magnetic Resonance Imaging

In this work, we exploit the fact that wavelets can represent magnetic resonance images well, with relatively few coefficients. We use this property to improve magnetic resonance imaging (MRI) reconstructions from undersampled data with arbitrary k-space trajectories. Reconstruction is posed as an optimization problem that could be solved with the iterative shrinkage/thresholding algorithm (ISTA) which, unfortunately, converges slowly. To make the approach more practical, we propose a variant that combines recent improvements in convex optimization and that can be tuned to a given specific k-space trajectory. We present a mathematical analysis that explains the performance of the algorithms. Using simulated and in vivo data, we show that our nonlinear method is fast, as it accelerates ISTA by almost two orders of magnitude. We also show that it remains competitive with TV regularization in terms of image quality.
Joint texture and topography estimation for extended depth of field in brightfield microscopy

Brightfield microscopy often suffers from limited depth of field, which prevents thick specimens from being imaged entirely in-focus. By optically sectioning the specimen, the in-focus regions can be acquired over multiple images. Extended depth of field methods aim at combining the information from these images into a single in-focus image of the texture on the specimen's surface. The topography provided by these methods is limited to a map of the selected in-focus image for every pixel and is inherently discretized, which limits its use for quantitative evaluation. In this paper, we propose a joint texture and topography estimation, based on an image formation model for a thick specimen incorporating the point spread function. The problem is stated as a least-squares fitting where the texture and the topography are updated alternately. The method also acts as a deconvolution operation when the in-focus image has some blur left, or when the true in-focus position falls in-between two slices. The feasibility of the method is demonstrated with simulated and experimental results
Multichannel restoration with limited a priori information [electron microscopy of biological macromolecules]

We introduce a method for multichannel restoration of images in which there is severely limited knowledge about the undegraded signal, and possibly the noise. We assume that we know the channel degradations and that there will be a significant noise reduction in a postprocessing stage in which multiple realizations are combined. This post-restoration noise reduction is often performed when working with micrographs of biological macromolecules. The restoration filters are designed to enforce a projection constraint upon the entire system. This projection constraint results in a system that provides an oblique projection of the input signal into the subspace defined by the reconstruction device in a direction orthogonal to a space defined by the channel degradations and the restoration filters. The approach achieves noise reduction without distorting the signal by exploiting the redundancy of the measurements.
Unsupervised texture segmentation using monogenic curvelets and the Potts model

We present a method for the unsupervised segmentation of textured images using Potts functionals, which are a piecewise-constant variant of the Mumford and Shah functionals. We propose a minimization strategy based on the alternating direction method of multipliers and dynamic programming. The strategy allows us to process large feature spaces because the computational cost grows only linearly in the feature dimension. In particular, our algorithm has more favorable computational costs for high-dimensional data than graph cuts. Our feature vectors are based on monogenic curvelets. They incorporate multiple resolutions and directional information. The advantage over classical curvelets is that they yield smoother amplitudes due to the envelope effect of the monogenic signal.
Fractional Laplacian pyramids

We provide an extension of the L2-spline pyramid (Unser et al., 1993) using polyharmonic splines. We analytically prove that the corresponding error pyramid behaves exactly as a multi-scale Laplace operator. We use the multiresolution properties of polyharmonic splines to derive an efficient, non-separable filterbank implementation. Finally, we illustrate the potentials of our pyramid by performing an estimation of the parameters of multivariate fractal processes.
Quantitative Fourier analysis of approximation techniques. I. Interpolators and projectors

We present a general Fourier-based method that provides an accurate prediction of the approximation error as a function of the sampling step T. Our formalism applies to an extended class of convolution-based signal approximation techniques, which includes interpolation, generalized sampling with prefiltering, and the projectors encountered in wavelet theory. We claim that we can predict the L/sup 2/-approximation error by integrating the spectrum of the function to approximate-not necessarily bandlimited-against a frequency kernel E(/spl omega/) that characterizes the approximation operator. This prediction is easier yet more precise than was previously available. Our approach has the remarkable property of providing a global error estimate that is the average of the true approximation error over all possible shifts of the input function. Our error prediction is exact for stationary processes, as well as for bandlimited signals. We apply this method to the comparison of standard interpolation and approximation techniques. Our method has interesting implications for approximation theory. In particular, we use our results to obtain some new asymptotic expansions of the error as T/spl rarr/0, as well as to derive improved upper bounds of the kind found in the Strang-Fix (1971) theory. We finally show how we can design quasi-interpolators that are near optimal in the least-squares sense.
A New Technique for High-Resolution Frequency Domain Optical Coherence Tomography

Frequency domain optical coherence tomography (FDOCT) is a new technique that is well-suited for fast imaging of biological specimens, as well as non-biological objects. The measurements are in the frequency domain, and the objective is to retrieve an artifact-free spatial domain description of the specimen. In this paper, we develop a new technique for model-based retrieval of spatial domain data from the frequency domain data. We use a piecewise-constant model for the refractive index profile that is suitable for multi-layered specimens. We show that the estimation of the layered structure parameters can be mapped into a harmonic retrieval problem, which enables us to use high-resolution spectrum estimation techniques. The new technique that we propose is efficient and requires few measurements. We also analyze the effect of additive measurement noise on the algorithm performance. The experimental results show that the technique gives highly accurate parameter estimates. For example, at 25 dB signal-to-noise ratio, the mean square error in the position estimate is about 0.01 % of the actual value.
Steerable filters for orientation estimation and localization of fluorescent dipoles

Fluorescence localization microscopy (i.e., PALM, STORM) has enabled optical imaging at nanometer-scale resolutions. The localization algorithms used in these techniques rely on fitting a 2-D Gaussian to the in-focus image of individual fluorophores. For fixed fluorophores, however, the observed diffraction pattern depends on the orientation of the underlying molecular dipole and does not necessarily correspond to a section of the system's point spread function. By using a physically realistic image formation model for dipoles to perform the fit, both the position and orientation of the dipole can be estimated with high accuracy, improving upon Gaussian localization. In this paper, we present an algorithm for joint position and orientation estimation based on a 3-D steerable filter, and show that the results are near-optimal with respect to the Cramér-Rao bounds. We show that patterns generated using estimated positions and orientations closely fit experimental measurements.
A complete family of scaling functions: the (/spl alpha/, /spl tau/)-fractional splines

We describe a new family of scaling functions, the (/spl alpha/, /spl tau/)-fractional splines, which generate valid multiresolution analyses. These functions are characterized by two real parameters: /spl alpha/, which controls the width of the scaling functions; and /spl tau/, which specifies their position with respect to the grid (shift parameter). This new family is complete in the sense that it is closed under convolutions and correlations. We give the explicit time and Fourier domain expressions of these fractional splines. We prove that the family is closed under generalized fractional differentiations, and, in particular, under the Hilbert transformation. We also show that the associated wavelets are able to whiten 1/f/sup /spl lambda//-type noise, by an adequate tuning of the spline parameters. A fast (and exact) FFT-based implementation of the fractional spline wavelet transform is already available. We show that fractional integration operators can be expressed as the composition of an analysis and a synthesis iterated filterbank.
Invariances, Laplacian-Like Wavelet Bases, and the Whitening of Fractal Processes

In this contribution, we study the notion of affine invariance (specifically, invariance to the shifting, scaling, and rotation of the coordinate system) as a starting point for the development of mathematical tools and approaches useful in the characterization and analysis of multivariate fractional Brownian motion (fBm) fields. In particular, using a rigorous and powerful distribution theoretic formulation, we extend previous results of Blu and Unser (2006) to the multivariate case, showing that polyharmonic splines and fBm processes can be seen as the (deterministic vs stochastic) solutions to an identical fractional partial differential equation that involves a fractional Laplacian operator. We then show that wavelets derived from polyharmonic splines have a behavior similar to the fractional Laplacian, which also turns out to be the whitening operator for fBm fields. This fact allows us to study the probabilistic properties of the wavelet transform coefficients of fBm-like processes, leading for instance to ways of estimating the Hurst exponent of a multiparameter process from its wavelet transform coefficients. We provide theoretical and experimental verification of these results. To complement the toolbox available for multiresolution processing of stochastic fractals, we also introduce an extended family of multidimensional multiresolution spaces for a large class of (separable and nonseparable) lattices of arbitrary dimensionality.
Blind optimization of algorithm parameters for signal denoising by Monte-Carlo SURE

We consider the problem of optimizing the parameters of an arbitrary denoising algorithm by minimizing Stein's unbiased risk estimate (SURE) which provides a means of assessing the true mean-squared-error (MSE) purely from the measured data assuming that it is corrupted by Gaussian noise. To accomplish this, we propose a novel Monte-Carlo technique based on a black-box approach which enables the user to compute SURE for an arbitrary denoising algorithm with some specific parameter setting. Our method only requires the response of the denoising algorithm to additional input noise and does not ask for any information about the functional form of the corresponding denoising operator. This, therefore, permits SURE-based optimization of a wide variety of denoising algorithms (global-iterative, pointwise, etc). We present experimental results to justify our claims.
Automatic tracking of particles in dynamic fluorescence microscopy

We present a new, robust algorithm for tracking fluorescent particles in dynamic image sequences obtained by brightfield or confocal microscopy. Specifically, we consider the problem of extracting the movement of chromosomal telomeres within the nucleus of a budding yeast cell. Our method has three components. The first is an alignment module that compensates for the movement of the biological structure under investigation. In our application, the images are aligned to the center of gravity of the nucleus which is detected by thresholding and fitted with an ellipse. The second step is a Mexican-hat filtering which we show to be optimally tailored to the detection of a Gaussian-like spot in fractal noise. The final component is a tracking algorithm that uses dynamic programming to extract the optimal (x,y,t) trajectory of a particle. We have implemented the method as a Java Plugin for the public-domain ImageJ software. We have applied it to real data and have obtained results that are as good - if not better as manual tracings. Our new algorithm reduces the analysis time of a 300 image sequence from 10 minutes, when it is done manually, to just a few seconds and offers the benefit of reproducibility.