nils-herrmann/clean_scirepeval huggingface dataset:
Integrated modeling and reconstruction with sparsity constraints for fDOT

We present a numerical framework for Fluorescence Diffuse Optical Tomography (fDOT) that combines a forward model together with an iterative reconstruction procedure. Using rapid linear solvers, we derived an efficient reconstruction strategy for quadratic regularizers. The method outperforms traditional reconstruction approaches. Starting from quadradic regularization, we then extend the framework to more general Lp constraints. We present reconstruction experiments that confirm the superiority of non-quadratic sparsity promoting regularization.
An Efficient Numerical Method for General $L_{p}$ Regularization in Fluorescence Molecular Tomography

Reconstruction algorithms for fluorescence tomography have to address two crucial issues: 1) the ill-posedness of the reconstruction problem, 2) the large scale of numerical problems arising from imaging of 3-D samples. Our contribution is the design and implementation of a reconstruction algorithm that incorporates general Lp regularization (p ¿ 1). The originality of this work lies in the application of general Lp constraints to fluorescence tomography, combined with an efficient matrix-free strategy that enables the algorithm to deal with large reconstruction problems at reduced memory and computational costs. In the experimental part, we specialize the application of the algorithm to the case of sparsity promoting constraints (L 1). We validate the adequacy of L 1 regularization for the investigation of phenomena that are well described by a sparse model, using data acquired during phantom experiments.
On the optimality of operator-like wavelets for sparse AR(1) processes

Sinusoidal transforms such as the DCT are known to be optimal-that is, asymptotically equivalent to the Karhunen-Loève transform (KLT)-for the representation of Gaussian stationary processes, including the classical AR(1) processes. While the KLT remains applicable for non-Gaussian signals, it loses optimality and, is outperformed by the independent-component analysis (ICA), which aims at producing the most-decoupled representation. In this paper, we consider an extension of the classical AR(1) model that is driven by symmetric-alpha-stable (SαS) noise which is either Gaussian (α = 2) or sparse (0 <; α <; 2). For the sparse (non-Gaussian) regime, we prove that an expansion in a proper wavelet basis (including the Haar transform) is much closer to the optimal orthogonal ICA solution than the classical Fourier-type representations. Our criterion for optimality, which favors independence, is the Kullback-Leibler divergence between the joint pdf of the original signal and the product of the marginals in the transformed domain. We also observe that, for very sparse AR(1) processes (α ≤ 1), the operator-like wavelet transform is indistinguishable from the ICA solution that is determined through numerical optimization.
Multiresolution moment filters

We define multiscale moments that are estimated locally by analyzing an image through a sliding window at multiple scales. When the analysis window satisfies a two-scale relation, we prove that these moments can be computed very efficiently using a multiresolution wavelet-like algorithm. We also show that B-spline windows are best suited for this kind of analysis because, in addition to being refinable, they are positive, symmetric and very nearly isotropic. We present two applications of our method. The first is a feature extraction method for detecting strands of DNA in noisy cryoelectron-micrographs. The second is an extension of the Lucas-Kanade optical flow algorithm (see Lucas, B. and Kanade, T.,  1981) that assumes a local affine model of the motion field. The results obtained in both cases are very promising.
Iterative FBP for improved reconstruction of X-ray differential phase-contrast tomograms

X-ray differential phase-contrast tomography is a recently-developed modality for the imaging of low-contrast biological samples. Its mathematical model is based on the first derivative of the Radon transform and the images, in practice, are reconstructed using a variant of filtered back-projection (FBP). In this paper, we develop an alternative reconstruction algorithm with the aim of reducing the number of required views, while maintaining image quality. To that end, we discretize the forward model based on polynomial B-spline functions. Then, we formulate the reconstruction as a regularized weighted-norm optimization problem with a penalty on the total variation (TV) of the solution. This leads to the derivation of a novel iterative algorithm that involves an alternation of gradient updates (FBP step) and shrinkage-thresholding (within the framework of the fast iterative shrinkage-thresholding algorithm). Experiments with real data suggest that the proposed method significantly improves upon FBP; it can handle a drastic reduction in the number of projections without noticeable degradation of the quality with respect to the standard procedure.
Teaching image-processing programming in Java

Image processing (IP) can be taught very effectively by complementing the basic lectures with computer laboratories where the participants can actively manipulate and process images. This offering can be made even more attractive by allowing the students to develop their own IP code within a reasonable time frame. A designed system to be as "student friendly" as possible is presented. The software is built around ImageJ, a freely available, full-featured, and user-friendly program for image analysis. The students can walk away from the course with an IP system that is operational. Using the ImageAccess interface layer, they can easily program both ImageJ plug-ins and Internet applets. The system that we have described may also appeal to practitioners as it offers simple, full-proof way of developing professional level IP software.
Multiresolution approximation using shifted splines

We consider the construction of least squares pyramids using shifted polynomial spline basis functions. We derive the pre and post-filters as a function of the degree n and the shift parameter /spl Delta/. We show that the underlying projection operator is entirely specified by two transfer functions acting on the even and odd signal samples, respectively. We introduce a measure of shift invariance and show that the most favorable configuration is obtained when the knots of the splines are centered with respect to the grid points (i.e., /spl Delta/=1/2 when n is odd and /spl Delta/=0 when n is even). The worst case corresponds to the standard multiresolution setting where the spline spaces are nested.
A Generalized Sampling Method for Finite-Rate-of-Innovation-Signal Reconstruction

The problem of sampling signals that are not admissible within the classical Shannon framework has received much attention in the recent past. Typically, these signals have a parametric representation with a finite number of degrees of freedom per time unit. It was shown that, by choosing suitable sampling kernels, the parameters can be computed by employing high-resolution spectral estimation techniques. In this letter, we propose a simple acquisition and reconstruction method within the framework of multichannel sampling. In the proposed approach, an infinite stream of nonuniformly-spaced Dirac impulses can be sampled and accurately reconstructed provided that there is at most one Dirac impulse per sampling period. The reconstruction algorithm has a low computational complexity, and the parameters are computed on the fly. The processing delay is minimal just the sampling period. We propose sampling circuits using inexpensive passive devices such as resistors and capacitors. We also show how the approach can be extended to sample piecewise-constant signals with a minimal change in the system configuration. We provide some simulation results to confirm the theoretical findings.
Adaptive Image Resizing Based on Continuous-Domain Stochastic Modeling

We introduce an adaptive continuous-domain modeling approach to texture and natural images. The continuous-domain image is assumed to be a smooth function, and we embed it in a parameterized Sobolev space. We point out a link between Sobolev spaces and stochastic auto-regressive models, and exploit it for optimally choosing Sobolev parameters from available pixel values. To this aim, we use exact continuous-to-discrete mapping of the auto-regressive model that is based on symmetric exponential splines. The mapping is computationally efficient, and we exploit it for maximizing an approximated Gaussian likelihood function. We account for non-Gaussian Lévy-type processes by deriving a more robust estimator that is based on the sample auto-correlation sequence. Both estimators use multiple initialization values for overcoming the local minima structure of the fitting criteria. Experimental image resizing results indicate that the auto-correlation criterion can cope better with non-Gaussian processes and model mismatch. Our work demonstrates the importance of the auto-correlation function in adaptive image interpolation and image modeling tasks, and we believe it is instrumental in other image processing tasks as well.
On the Shiftability of Dual-Tree Complex Wavelet Transforms

The dual-tree complex wavelet transform (DT-\BBCWT) is known to exhibit better shift-invariance than the conventional discrete wavelet transform. We propose an amplitude-phase representation of the DT-IBBC WT which, among other things, offers a direct explanation for the improvement in the shift-invariance. The representation is based on the shifting action of the group of fractional Hilbert transform (fHT) operators, which extends the notion of arbitrary phase-shifts from sinusoids to finite-energy signals (wavelets in particular). In particular, we characterize the shift ability of the DT-\BBCWT in terms of the shifting property of the fHTs. At the heart of the representation are certain fundamental invariances of the fHT group, namely that of translation, dilation, and norm, which play a decisive role in establishing the key properties of the transform. It turns out that these fundamental invariances are exclusive to this group. Next, by introducing a generalization of the Bedrosian theorem for the fHT operator, we derive an explicitly understanding of the shifting action of the fHT for the particular family of wavelets obtained through the modulation of lowpass functions (e.g., the Shannon and Gabor wavelet). This, in effect, links the corresponding dual-tree transform with the framework of windowed-Fourier analysis. Finally, we extend these ideas to the multidimensional setting by introducing a directional extension of the fHT, the fractional directional Hilbert transform. In particular, we derive a signal representation involving the superposition of direction-selective wavelets with appropriate phase-shifts, which helps explain the improved shift-invariance of the transform along certain preferential directions.
Variational Justification of Cycle Spinning for Wavelet-Based Solutions of Inverse Problems

Cycle spinning is a widely used approach for improving the performance of wavelet-based methods that solve linear inverse problems. Extensive numerical experiments have shown that it significantly improves the quality of the recovered signal without increasing the computational cost. In this letter, we provide the first theoretical convergence result for cycle spinning for solving general linear inverse problems. We prove that the sequence of reconstructed signals is guaranteed to converge to the minimizer of some global cost function that incorporates all wavelet shifts.
P-multiresolution Analysis: How to Reduce Ringing and Sparsify the Error

We propose to design the reduction operator of an image pyramid so as to minimize the approximation error in the l(p)-sense (not restricted to the usual p=2), where p can take noninteger values. The underlying image model is specified using shift-invariant basis functions, such as B-splines. The solution is well-defined and determined by an iterative optimization algorithm based on digital filtering. Its convergence is accelerated by the use of first and second order derivatives. For p close to 1, we show that the ringing is reduced and that the histogram of the detail image is sparse as compared with the standard case, where p=2.
Optical Tomographic Image Reconstruction Based on Beam Propagation and Sparse Regularization

Optical tomographic imaging requires an accurate forward model as well as regularization to mitigate missing-data artifacts and to suppress noise. Nonlinear forward models can provide more accurate interpretation of the measured data than their linear counterparts, but they generally result in computationally prohibitive reconstruction algorithms. Although sparsity-driven regularizers significantly improve the quality of reconstructed image, they further increase the computational burden of imaging. In this paper, we present a novel iterative imaging method for optical tomography that combines a nonlinear forward model based on the beam propagation method (BPM) with an edge-preserving three-dimensional (3-D) total variation (TV) regularizer. The central element of our approach is a time-reversal scheme, which allows for an efficient computation of the derivative of the transmitted wave-field with respect to the distribution of the refractive index. This time-reversal scheme together with our stochastic proximal-gradient algorithm makes it possible to optimize under a nonlinear forward model in a computationally tractable way, thus enabling a high-quality imaging of the refractive index throughout the object. We demonstrate the effectiveness of our method through several experiments on simulated and experimentally measured data.
Statistical analysis of functional MRI data in the wavelet domain

The use of the wavelet transform is explored for the detection of differences between brain functional magnetic resonance images (fMRIs) acquired under two different experimental conditions. The method benefits from the fact that a smooth and spatially localized signal can be represented by a small set of localized wavelet coefficients, while the power of white noise is uniformly spread throughout the wavelet space. Hence, a statistical procedure is developed that uses the imposed decomposition orthogonality to locate wavelet-space partitions with large signal-to-noise ratio (SNR), and subsequently restricts the testing for significant wavelet coefficients to these partitions. This results in a higher SNR and a smaller number of statistical tests, yielding a lower detection threshold compared to spatial-domain testing and, thus, a higher detection sensitivity without increasing type I errors. The multiresolution approach of the wavelet method is particularly suited to applications where the signal bandwidth and/or the characteristics of an imaging modality cannot be well specified. The proposed method was applied to compare two different fMRI acquisition modalities, Differences of the respective useful signal bandwidths could be clearly demonstrated; the estimated signal, due to the smoothness of the wavelet representation, yielded more compact regions of neuroactivity than standard spatial-domain testing.
Tip-seeking active contours for bioimage segmentation

In the present paper, we address the problem of segmenting biological objects featuring corners. The main ingredients of our approach are automated feature-detection methods and mechanisms for introducing kinks in parametric spline snakes. We formulate a novel corner potential that enables the accurate segmentation of objects exhibiting sharp tips or acute angles. The optimization of active contours using the proposed keypoint-based energy yields robuster segmentation results and requires fewer parameters than traditional spline-snake approaches for the same task. The performance of our method is illustrated on microscopic images of two families of Rhabditidse roundworms.
3D BBPConvNet to reconstruct parallel MRI

In recent years, compressed sensing techniques have been applied to the reconstruction of parallel magnetic resonance (MR) images. Particularly for 3D MR signal, it is crucial to acquire fewer samples to reduce the distortions caused by long-time acquisitions (e.g., motion, organ dynamics). Motivated by the recent success of ConvNet in 2D image reconstruction, we propose to extend the approach to 3D volume reconstruction and parallel MR imaging. The structure of the proposed network follows FBPConvNet with additional coil compression by SSoS and wavelet transform. A parallelism using two GPUs is also applied to overcome the memory shortage. The proposed method is able to reconstruct a (320 × 320 × 256 × 8) volume in less than 10s with 2 GPUs, while the iterative algorithm ℓ1-ESPIRiT takes over 5 min in CPU.
Centered pyramids

Quadtree-like pyramids have the advantage of re-suiting in a multiresolution representation where each pyramid node has four unambiguous parents. Such a centered topology guarantees a clearly defined up-projection of labels. This concept has been successfully and extensively used in applications of contour detection, object recognition and segmentation. Unfortunately, the quadtree-like type of pyramid has poor approximation powers because of the employed piecewise-constant image model. This paper deals with the construction of improved centered image pyramids in terms of general approximation functions. The advantages of the centered topology such a symmetry, consistent boundary conditions and accurate up-projection of labels are combined with a more faithful image representation at coarser pyramid levels. We start by introducing a general framework for the design of least squares pyramids using the standard filtering and decimation tools. We give the most general explicit formulas for the computation of the filter coefficients by any (well behaving) approximation function in both the continuous (L(2)) and the discrete (l(2)) norm. We then define centered pyramids and provide the filter coefficients for odd spline approximation functions. Finally, we compare the centered pyramid to the ordinary one and highlight some applications.
Isotropic-polyharmonic B-splines and wavelets

We propose the use of polyharmonic B-splines to build non-separable two-dimensional wavelet bases. The central idea is to base our design on isotropic-polyharmonic B-splines, a new type of polyharmonic B-splines that converge to a Gaussian as the order increases. We opt for the quincunx subsampling scheme which allows us to characterize the wavelet spaces with a single wavelet, the isotropic-polyharmonic B-spline wavelet. Interestingly, this wavelet converges to a combination of four Gabor atoms, which are well separated in the frequency domain. We also briefly discuss our Fourier-based implementation and present some experimental results.
Zero-order-free image reconstruction in digital holographic microscopy

We address the problem of zero-order-free image reconstruction in digital holographic microscopy. We show how the goal can be achieved by confining the object-wave modulation to one quadrant of the frequency domain, and by maintaining a reference-wave intensity higher than that of the object. The proposed technique is nonlinear, noniterative, and leads to exact reconstruction in the absence of noise. We also provide experimental results on holograms of yew pollen grains to validate the theoretical results.
Learning Convex Regularizers for Optimal Bayesian Denoising

We propose a data-driven algorithm for the Bayesian estimation of stochastic processes from noisy observations. The primary statistical properties of the sought signal are specified by the penalty function (i.e., negative logarithm of the prior probability density function). Our alternating direction method of multipliers (ADMM) based approach translates the estimation task into successive applications of the proximal mapping of the penalty function. Capitalizing on this direct link, we define the proximal operator as a parametric spline curve and optimize the spline coefficients by minimizing the average reconstruction error for a given training set. The key aspects of our learning method are that the associated penalty function is constrained to be convex and the convergence of the ADMM iterations is proven. As a result of these theoretical guarantees, adaptation of the proposed framework to different levels of measurement noise is extremely simple and does not require any retraining. We apply our method to estimation of both sparse and nonsparse models of Lévy processes for which the minimum mean square error (MMSE) estimators are available. We carry out a single training session for a fixed level of noise and perform comparisons at various signal-to-noise ratio values. Simulations illustrate that the performance of our algorithm are practically identical to the one of the MMSE estimator irrespective of the noise power.
Least-squares image resizing using finite differences

We present an optimal spline-based algorithm for the enlargement or reduction of digital images with arbitrary (noninteger) scaling factors. This projection-based approach can be realized 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. A noteworthy property of the algorithm is that the computational complexity per pixel does not depend on the scaling factor a. For a given choice of basis functions, the results of our method are consistently better than 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. The method can be generalized to include other classes of piecewise polynomial functions, expressed as linear combinations of B-splines and their derivatives.
Reconstruction of Large, Irregularly Sampled Multidimensional Images. A Tensor-Based Approach

Many practical applications require the reconstruction of images from irregularly sampled data. The spline formalism offers an attractive framework for solving this problem; the currently available methods, however, are hard to deploy for large-scale interpolation problems in dimensions greater than two (3-D, 3-D+time) because of an exponential increase of their computational cost (curse of dimensionality). Here, we revisit the standard regularized least-squares formulation of the interpolation problem, and propose to perform the reconstruction in a uniform tensor-product B-spline basis as an alternative to the classical solution involving radial basis functions. Our analysis reveals that the underlying multilinear system of equations admits a tensor decomposition with an extreme sparsity of its one dimensional components. We exploit this property for implementing a parallel, memory-efficient system solver. We show that the computational complexity of the proposed algorithm is essentially linear in the number of measurements and that its dependency on the number of dimensions is significantly less than that of the original sparse matrix-based implementation. The net benefit is a substantial reduction in memory requirement and operation count when compared to standard matrix-based algorithms, so that even 4-D problems with millions of samples become computationally feasible on desktop PCs in reasonable time. After validating the proposed algorithm in 3-D and 4-D, we apply it to a concrete imaging problem: the reconstruction of medical ultrasound images (3-D+time) from a large set of irregularly sampled measurements, acquired by a fast rotating ultrasound transducer.