nils-herrmann/clean_scirepeval huggingface dataset:
Model-Based 2.5-D Deconvolution for Extended Depth of Field in Brightfield Microscopy

Due to the limited depth of field of brightfield microscopes, it is usually impossible to image thick specimens entirely in focus. By optically sectioning the specimen, the in-focus information at the specimen's surface can be acquired over a range of images. Commonly based on a high-pass criterion, extended-depth-of-field methods aim at combining the in-focus information from these images into a single image of the texture on the specimen's surface. The topography provided by such methods is usually limited to a map of selected in-focus pixel positions and is inherently discretized along the axial direction, which limits its use for quantitative evaluation. In this paper, we propose a method that jointly estimates the texture and topography of a specimen from a series of brightfield optical sections; it is based on an image formation model that is described by the convolution of a thick specimen model with the microscope's point spread function. The problem is stated as a least-squares minimization where the texture and topography are updated alternately. This method also acts as a deconvolution when the in-focus PSF has a blurring effect, or when the true in-focus position falls in between two optical sections. Comparisons to state-of-the-art algorithms and experimental results demonstrate the potential of the proposed approach.
A box spline calculus for computed tomography

B-splines are attractive basis functions for the continuous-domain representation of biomedical images and volumes. In this paper, we prove that the extended family of box splines are closed under the Radon transform and derive explicit formulae for their transforms. Our results are general; they cover all known brands of compactly-supported box splines (tensor-product B-splines, separable or not) in any dimensions. In particular, we prove that the 2-D Radon transform of an N-direction box spline is generally a (non-uniform) polynomial spline of degree N -1. The proposed framework allows for a proper discretization of a variety of 2-D and 3-D tomographic reconstruction problems in a box spline basis. It is of relevance for imaging modalities such as X-ray computed tomography and 3-D cryo-electron microscopy.
Fast parametric elastic image registration

We present an algorithm for fast elastic multidimensional intensity-based image registration with a parametric model of the deformation. It is fully automatic in its default mode of operation. In the case of hard real-world problems, it is capable of accepting expert hints in the form of soft landmark constraints. Much fewer landmarks are needed and the results are far superior compared to pure landmark registration. Particular attention has been paid to the factors influencing the speed of this algorithm. The B-spline deformation model is shown to be computationally more efficient than other alternatives. The algorithm has been successfully used for several two-dimensional (2-D) and three-dimensional (3-D) registration tasks in the medical domain, involving MRI, SPECT, CT, and ultrasound image modalities. We also present experiments in a controlled environment, permitting an exact evaluation of the registration accuracy. Test deformations are generated automatically using a random hierarchical fractional wavelet-based generator.
A general sampling theory for nonideal acquisition devices

The authors first describe the general class of approximation spaces generated by translation of a function /spl psi/(x), and provide a full characterization of their basis functions. They then present a general sampling theorem for computing the approximation of signals in these subspaces based on a simple consistency principle. The theory puts no restrictions on the system input which can be an arbitrary finite energy signal; bandlimitedness is not required. In contrast to previous approaches, this formulation allows for an independent specification of the sampling (analysis) and approximation (synthesis) spaces. In particular, when both spaces are identical, the theorem provides a simple procedure for obtaining the least squares approximation of a signal. They discuss the properties of this new sampling procedure and present some examples of applications involving bandlimited, and polynomial spline signal representations. They also define a spectral coherence function that measures the "similarity" between the sampling and approximation spaces, and derive a relative performance bound for the comparison with the least squares solution.
Multiresolution Feature Extraction and Selection for Texture Segmentation

An approach is described for unsupervised segmentation of textured images. Local texture properties are extracted using local linear transforms that have been optimized for maximal texture discrimination. Local statistics (texture energy measures) are estimated at the output of an equivalent filter bank by means of a nonlinear transformation (absolute value) followed by an iterative Gaussian smoothing algorithm. This procedure generates a multiresolution sequence of feature planes with a half-octave scale progression. A feature reduction technique is then applied to the data and is determined by simultaneously diagonalizing scatter matrices evaluated at two different spatial resolutions. This approach provides a good approximation of R.A. Fisher's (1950) multiple linear discriminants and has the advantage of requiring no a priori knowledge. This feature reduction methods appears to be an improvement on the commonly used Karhunen-Loeve transform and allows efficient texture segmentation based on simple thresholding.
Complete parametrization of piecewise polynomial interpolators according to degree, support, regularity, and order

The most essential ingredient of interpolation is its basis function. We have shown in previous papers that this basis need not be necessarily interpolating to achieve good results. On the contrary, several studies have confirmed that non-interpolating bases, such as B-splines and O-moms, perform best. This opens up a much wider choice of basis functions. We give to the designer the tools that will allow him to characterize this enlarged space of functions. In particular, he will be able to specify up-front the four most important parameters for image processing: degree, support, regularity, and order. The theorems presented then allow him to refine his design by dealing with additional coefficients that can be selected freely, without interfering with the main design parameters.
Closed-form alignment of active surface models using splines

We propose a new formulation of the active surface model in 3D. Instead of aligning a shape dictionary through the similarity transform, we consider more flexible affine transformations and introduce an alignment method that is unbiased in the sense that it implicitly constructs a common reference shape. Our formulation is expressed in the continuous domain and we provide an algorithm to exactly implement the framework using spline-based parametric surfaces. We test our model on real 3D MRI data. A comparison with the classical active shape model shows that our method allows us to capture shape variability in a dictionary in a more precise way.
Fast Gabor-like windowed Fourier and continuous wavelet transforms

Fast algorithms for the evaluation of running windowed Fourier and continuous wavelet transforms are presented. The analysis functions approximate complex-modulated Gaussians as closely as desired and may be optimally localized in time and frequency. The Gabor filtering is performed indirectly by convolving a premodulated signal with a Gaussian-like window and demodulating the output. The window functions are either B-splines dilated by an integer factor m or quasi-Gaussians of arbitrary size generated from the n-fold convolution of a symmetrical exponential. Both approaches result in a recursive implementation with a complexity independent of the window size (O(N)).<<ETX>>
Lung Tissue Classification Using Wavelet Frames

We describe a texture classification system that identifies lung tissue patterns from high-resolution computed tomography (HRCT) images of patients affected with interstitial lung diseases (ILD). This pattern recognition task is part of an image-based diagnostic aid system for ILDs. Five lung tissue patterns (healthy, emphysema, ground glass, fibrosis and microdules) selected from a multimedia database are classified using the over/complete discrete wavelet frame decompostion combined with grey-level histogram features. The overall multiclass accuracy reaches 92.5% of correct matches while combining the two types of features, which are found to be complementary.
Exponential-spline wavelet bases

We build a multiresolution analysis based on shift-invariant exponential B-spline spaces. We construct the basis functions for these spaces and for their orthogonal complements. This yields a new family of wavelet-like basis functions of L/sub 2/, with some remarkable properties. The wavelets, which are characterized by a set of poles and zeros, have an explicit analytical form (exponential spline). They are nonstationary is the sense that they are scale-dependent and that they are not necessarily the dilates of one another. They behave like multi-scale versions of some underlying differential operator L; in particular, they are orthogonal to the exponentials that are in the null space of L. The corresponding wavelet transforms are implemented efficiently using an adaptation of Mallat's (1998) filterbank algorithm.
Can localization microscopy benefit from approximation theory?

We introduce a general and computationally efficient approach to 3-D localization microscopy. The main idea is to construct a continuous-domain representation of the PSF by expanding it in a polynomial B-spline basis. This allows us to fit the PSF to the data with sub-pixel accuracy. Since the basis functions are compactly supported, the evaluation of the PSF is computationally efficient. Furthermore, our approach can accommodate for any 3-D PSF design, and it does not require a calibration curve for the axial position. We further introduce a computationally efficient implementation of the least-squares criterion and demonstrate its potential use for fast and accurate reconstruction of super-resolution data.
Image segmentation with background correction using a multiplicative smoothing-spline model

This paper presents an image-segmentation method which compensates multiplicative distortions based on smooth regularity assumptions. In this work, we generalize the original Chan-Vese functional to handle a continuous multiplicative bias. In the derivation of our model, we show that the optimal correction function is necessarily a spline, which we express in terms of discrete coefficients. Following an iterative technique, we propose to find the solution by an alternate optimization of this map and of the segmented domains. In order to maximize the overall efficiency, graph cuts are combined with a specifically designed multigrid algorithm. Our experiments demonstrate the relevance of our approach for biomedical data.
Fast detection and refined scale estimation using complex isotropic wavelets

The dyadic scaling in the discrete wavelet transform can lead to a loss of precision, in comparison to the computationally unrealistic continuous wavelet transform. To overcome this obstacle, we propose a novel method to locally scale wavelets between dyadic scales in an efficient way. We compute complex wavelet coefficients for a tight frame with a dyadic scale progression. Our isotropic complex wavelets are designed such that the deviation from the nominal scale is encoded in the phase of the coefficients. Moreover, the magnitude of the coefficients is used for feature detection. Numerical experiments are presented to justify our method, and we present results for feature extraction from real data.
Realistic Analytical Phantoms for Parallel Magnetic Resonance Imaging

The quantitative validation of reconstruction algorithms requires reliable data. Rasterized simulations are popular but they are tainted by an aliasing component that impacts the assessment of the performance of reconstruction. We introduce analytical simulation tools that are suited to parallel magnetic resonance imaging and allow one to build realistic phantoms. The proposed phantoms are composed of ellipses and regions with piecewise-polynomial boundaries, including spline contours, Bézier contours, and polygons. In addition, they take the channel sensitivity into account, for which we investigate two possible models. Our analytical formulations provide well-defined data in both the spatial and k-space domains. Our main contribution is the closed-form determination of the Fourier transforms that are involved. Experiments validate the proposed implementation. In a typical parallel magnetic resonance imaging reconstruction experiment, we quantify the bias in the overly optimistic results obtained with rasterized simulations-the inverse-crime situation. We provide a package that implements the different simulations and provide tools to guide the design of realistic phantoms.
A family of discrete Fourier transforms with pseudo-cyclic convolution properties

An extended family of Discrete Fourier transforms is introduced. These transforms, which may be implemented by using FFTs, allow the computation of pseudo-cyclic convolutions by multiplication in the transform domain. The choice of a suitable transform (DFT1/4) or the combined use of two complementary transforms allows a fast and efficient computation of aperiodic convolutions of waveforms of duration N by using N-point transforms that require no zero padding. Finally, all members of this family are shown to be equivalent asymptotically to the Karhunen-Loève transform of an arbitrary wide sense stationary process.
Quantitative L/sup 2/ error analysis for interpolation methods and wavelet expansions

Our goal in this paper is to set a theoretical basis for the comparison of re-sampling and interpolation methods. We consider the general problem of the approximation of an arbitrary continuously-defined function f(x)-not necessarily bandlimited-when we vary the sampling step T. We present an accurate L/sup 2/ computation of the induced approximation error as a function of T for a general class of linear approximation operators including interpolation and other kinds of projectors. This new quantitative result provides exact expressions for the asymptotic development of the error as T/spl rarr/0, and also sharp (asymptotically exact) upper bounds.
Accelerated wavelet-regularized deconvolution for 3-D fluorescence microcopy

Modern deconvolution algorithms are often specified as minimization problems involving a non-quadratic regularization functional. When the latter is a wavelet-domain ℓ1-norm that favors sparse solutions, the problem can be solved by a simple iterative shrinkage/thresholding algorithm (ISTA). This approach provides state-of-the-art results in 2-D, but is harder to deploy in 3-D because of its slow convergence. In this paper, we propose an acceleration scheme that turns wavelet-regularized deconvolution into a competitive solution for 3-D fluorescence microscopy. A significant speed-up is achieved though a synergistic combination of subband-adapted thresholds and sequential TwIST updates. We provide a theoretical justification of the procedure together with an experimental evaluation, including the application to real 3-D fluorescence data.
Isotropic resolution in fluorescence imaging by single particle reconstruction

Low axial resolution is a major limitation of fluorescence imaging modalities. We propose a methodology to achieve high isotropic resolution by reconstructing fluorescence volumes from observations of multiple particle replicates with different orientations. The challenge is to conciliate high reconstruction accuracy, requiring a large amount of input 3D data, with computational tractability. We achieve this goal by designing an iterative joint deconvolution and multiview reconstruction algorithm with an efficient augmented-Lagrangian based optimization. The computational cost is limited to only two FFTs per iterations, regardless of the number of input particles. We also adopt the nuclear norm of the Hessian as regularizer to avoid the usual staircase artifacts of the more standard total-variation. Experimental validation on realistic simulated data demonstrate the efficiency and accuracy of our method.
Wavelet-based fMRI statistical analysis and spatial interpretation: a unifying approach

Wavelet-based statistical analysis methods for fMRI are able to detect brain activity without smoothing the data. Typically, the statistical inference is performed in the wavelet domain by testing the t-values of each wavelet coefficient; subsequently, an activity map is reconstructed from the significant coefficients. The limitation of this approach is that there is no direct statistical interpretation of the reconstructed map. In this paper, we propose a new methodology that takes advantage of wavelet processing but keeps the statistical meaning in the spatial domain. We derive a spatial threshold with a proper nonstationary component and determine optimal threshold values by minimizing an approximation error. The sensitivity of our method is comparable to SPM's (Statistical Parametric Mapping).
Fast Computation of Polyharmonic B-Spline Autocorrelation Filters

A fast computational method is given for the Fourier transform of the polyharmonic B-spline autocorrelation sequence in d dimensions. The approximation error is exponentially decaying with the number of terms taken into account. The algorithm improves speed upon a simple truncated-sum approach. Moreover, it is virtually independent of the spline's order. The autocorrelation filter directly serves for various tasks related to polyharmonic splines, such as interpolation, orthonormalization, and wavelet basis design.
Polynomial spline signal approximations: Filter design and asymptotic equivalence with Shannon's sampling theorem

The least-squares polynomial spline approximation of a signal g(t) in L/sub 2/(R) is obtained by projecting g(t) on S/sup n/(R) (the space of polynomial splines of order n). It is shown that this process can be linked to the classical problem of cardinal spline interpolation by first convolving g(t) with a B-spline of order n. More specifically, the coefficients of the B-spline interpolation of order 2n+1 of the sampled filtered sequence are identical to the coefficients of the least-squares approximation of g(t) of order n. It is shown that this approximation can be obtained from a succession of three basic operations: prefiltering, sampling, and postfiltering, which confirms the parallel with the classical sampling/reconstruction procedure for bandlimited signals. The frequency responses of these filters are determined for three equivalent spline representations using alternative sets of shift-invariant basis functions of S/sup n/(R): the standard expansion in terms of B-spline coefficients, a representation in terms of sampled signal values, and a representation using orthogonal basis functions.
Efficient image resizing using finite differences

We present an optimal spline-based algorithm for the enlargement or reduction of digital images with arbitrary scaling factors. This projection-based approach is realizable thanks to a new finite difference method that allows the computation of inner products with analysis functions that are B-splines of any degree n. For a given choice of basis functions, the results of our method are consistently better that those of the standard interpolation procedure; the present scheme achieves a reduction of artifacts such as aliasing and blocking and a significant improvement of the signal-to-noise ratio.
A projected gradient algorithm for image restoration under Hessian matrix-norm regularization

We have recently introduced a class of non-quadratic Hessian-based regularizers as a higher-order extension of the total variation (TV) functional. These regularizers retain some of the most favorable properties of TV while they can effectively deal with the staircase effect that is commonly met in TV-based reconstructions. In this work we propose a novel gradient-based algorithm for the efficient minimization of these functionals under convex constraints. Furthermore, we validate the overall proposed regularization framework for the problem of image deblurring under additive Gaussian noise.
Enlargement or reduction of digital images with minimum loss of information

The purpose of this paper is to derive optimal spline algorithms for the enlargement or reduction of digital images by arbitrary (noninteger) scaling factors. In our formulation, the original and rescaled signals are each represented by an interpolating polynomial spline of degree n with step size one and Delta, respectively. The change of scale is achieved by determining the spline with step size Delta that provides the closest approximation of the original signal in the L(2)-norm. We show that this approximation can be computed in three steps: (i) a digital prefilter that provides the B-spline coefficients of the input signal, (ii) a resampling using an expansion formula with a modified sampling kernel that depends explicitly on Delta, and (iii) a digital postfilter that maps the result back into the signal domain. We provide explicit formulas for n=0, 1, and 3 and propose solutions for the efficient implementation of these algorithms. We consider image processing examples and show that the present method compares favorably with standard interpolation techniques. Finally, we discuss some properties of this approach and its connection with the classical technique of bandlimiting a signal, which provides the asymptotic limit of our algorithm as the order of the spline tends to infinity.
Reconstruction of biomedical images and sparse stochastic modeling

We propose a novel statistical formulation of the image-reconstruction problem from noisy linear measurements. We derive an extended family of MAP estimators based on the theory of continuous-domain sparse stochastic processes. We highlight the crucial roles of the whitening operator and of the Lévy exponent of the innovations which controls the sparsity of the model. While our family of estimators includes the traditional methods of Tikhonov and total-variation (TV) regularization as particular cases, it opens the door to a much broader class of potential functions (associated with infinitely divisible priors) that are inherently sparse and typically nonconvex. We also provide an algorithmic scheme - naturally suggested by our framework - that can handle arbitrary potential functions. Further, we consider the reconstruction of simulated MRI data and illustrate that the designed estimators can bring significant improvement in reconstruction performance.
Reconstruction of Dynamic PET Data Using Spatio-Temporal Wavelet l1 Regularization

Tomographic reconstruction from PET data is an ill-posed problem that requires regularization. Recently, Daubechies et al. proposed an l1 regularization of the wavelet coefficients that can be optimized using iterative thresholding schemes. In this paper, we extend this approach for the reconstruction of dynamic (spatio-temporal) PET data. Instead of using classical wavelets in the temporal dimension, we introduce exponential-spline wavelets that are specially tailored to model time activity curves (TACs) in PET. We show the usefulness of spatio-temporal regularization and the superior performance of E-spline wavelets over conventional Battle-Lemarie wavelets for a 1-D TAC fitting experiment and a tomographic reconstruction experiment.