nils-herrmann/clean_scirepeval huggingface dataset:
The Marr wavelet pyramid

We introduce a new semi-orthogonal complex wavelet basis of L2(R2). The basis functions are associated to the complex gradient-Laplace operator, which plays a central role in image processing. We define analytically a single-generator wavelet that is shifted on the coset positions of the subsampling matrix. Next, we propose the "wavelet Marr pyramid" for an extension of the new basis that achieves near shift-invariance and steerability (using a Gaussian-like smoothing kernel), for a mild redundancy factor only. This new wavelet pyramid decomposition closely mimicks the basic operations of Marx's framework for early vision. The pyramid is implemented by a fast filterbank algorithm using the FFT.
Bayesian Denoising: From MAP to MMSE Using Consistent Cycle Spinning

We introduce a new approach for the implementation of minimum mean-square error (MMSE) denoising for signals with decoupled derivatives. Our method casts the problem as a penalized least-squares regression in the redundant wavelet domain. It exploits the link between the discrete gradient and Haar-wavelet shrinkage with cycle spinning. The redundancy of the representation implies that some wavelet-domain estimates are inconsistent with the underlying signal model. However, by imposing additional constraints, our method finds wavelet-domain solutions that are mutually consistent. We confirm the MMSE performance of our method through statistical estimation of Lévy processes that have sparse derivatives.
Recursive risk estimation for non-linear image deconvolution with a wavelet-domain sparsity constraint

We propose a recursive data-driven risk-estimation method for non-linear iterative deconvolution. Our two main contributions are 1) a solution-domain risk-estimation approach that is applicable to non-linear restoration algorithms for ill- conditioned inverse problems; and 2) a risk estimate for a state-of-the-art iterative procedure, the thresholded Landweber iteration, which enforces a wavelet-domain sparsity constraint. Our method can be used to estimate the SNR improvement at every step of the algorithm; e.g., for stopping the iteration after the highest value is reached. It can also be applied to estimate the optimal threshold level for a given number of iterations.
Autocalibrated signal reconstruction from linear measurements using adaptive GAMP

In this paper, we reconstruct signals from underdetermined linear measurements where the componentwise gains of the measurement system are unknown a priori. The reconstruction is performed through an adaptation of the messagepassing algorithm called adaptive GAMP that enables joint gain calibration and signal estimation. To evaluate our approach, we apply it to the problem of sparse recovery and compare it against an ℓ1-based approach. We numerically show that adaptive GAMP yields excellent results even for a moderate amount of data. It approaches the performance of oracle GAMP where the gains are perfectly known asymptotically.
Linear interpolation of biomedical images using a data-adaptive kernel

In this work, we propose a continuous-domain stochastic model that can be applied to image data. This model is autoregressive, and accounts for Gaussian-type as well as for non-Gaussian-type innovations. In order to estimate the corresponding parameters from the data, we introduce two possible error criteria; namely, Gaussian maximum-likelihood, and least-squares autocorrelation fit. Exploiting the link between autoregressive models and spline approximation, we use our approach to adapt interpolation parameters to a given image. Our numerical results demonstrate that our adaptive approach yields higher SNR values compared to classical polynomial splines for the task of image scaling. They also indicate that our least-squares-based error criterion nearly achieves the oracle performance for parameter estimation, which provides further support to the practical relevance of our model.
A novel non-diffractive reconstruction method for digital holographic microscopy

We present a new method for reconstructing digitally recorded off-axis Fresnel holograms. Currently-used reconstruction methods are based on the simulation and propagation of a reference wave that is diffracted by the hologram. This procedure introduces a twin-image and a zero-order term which are inherent to the diffraction phenomenon. These terms perturb the reconstruction and limit the field of view. Our new approach splits the reconstruction process into two parts. First, we recover the amplitude and the phase in the camera plane from the measured hologram intensity. Our algorithm is based on the hypothesis of a slowly varying object wave which interferes with a more rapidly varying reference wave. In a second step, we propagate this complex wave to refocus it using the Fresnel transform. We therefore avoid the presence of the twin-image and zero-order interference terms. This new approach is flexible and can be adapted easily to complicated experimental setups. We demonstrate its feasibility in the case of digital holographic microscopy and present results for the imaging of living neurons.
Performance Analysis of Reconstruction Techniques for Frequency-Domain Optical-Coherence Tomography

We address the issue of noise robustness of reconstruction techniques for frequency-domain optical-coherence tomography (FDOCT). We consider three reconstruction techniques: Fourier, iterative phase recovery, and cepstral techniques. We characterize the reconstructions in terms of their statistical bias and variance and obtain approximate analytical expressions under the assumption of small noise. We also perform Monte Carlo analyses and show that the experimental results are in agreement with the theoretical predictions. It turns out that the iterative and cepstral techniques yield reconstructions with a smaller bias than the Fourier method. The three techniques, however, have identical variance profiles, and their consistency increases linearly as a function of the signal-to-noise ratio.
An orthogonal family of quincunx wavelets with continuously adjustable order

We present a new family of two-dimensional and three-dimensional orthogonal wavelets which uses quincunx sampling. The orthogonal refinement filters have a simple analytical expression in the Fourier domain as a function of the order /spl lambda/, which may be noninteger. We can also prove that they yield wavelet bases of L/sub 2/(R/sup 2/) for any /spl lambda/>0. The wavelets are fractional in the sense that the approximation error at a given scale a decays like O(a/sup /spl lambda//); they also essentially behave like fractional derivative operators. To make our construction practical, we propose a fast Fourier transform-based implementation that turns out to be surprisingly fast. In fact, our method is almost as efficient as the standard Mallat algorithm for separable wavelets.
Multigrid adaptive image processing

We consider a general weighted least squares approximation problem with a membrane spline regularization term. The key parameters in this formulation are the weighting factors which provide the possibility of a spatial adaptation. We prove that the corresponding space-varying variational problem is well posed, and propose a novel multigrid computational solution. This multiresolution relaxation scheme uses three image pyramids (input data, weights, and current solution) and allows for a very efficient computation with an effective O(N) complexity, where N is the number of pixels. This general multigrid solver can be useful for a variety of image processing tasks. In particular, we propose new multigrid solutions for noise reduction in images (adaptive smoothing spline), interpolation/reconstruction of missing image data, and image segmentation using an adaptive extension of the K-means clustering algorithm.
Full Motion and Flow Field Recovery From Echo Doppler Data

We present a new computational method for reconstructing a vector velocity field from scattered, pulsed-wave ultrasound Doppler data. The main difficulty is that the Doppler measurements are incomplete, for they do only capture the velocity component along the beam direction. We thus propose to combine measurements from different beam directions. However, this is not yet sufficient to make the problem well posed because 1) the angle between the directions is typically small and 2) the data is noisy and nonuniformly sampled. We propose to solve this reconstruction problem in the continuous domain using regularization. The reconstruction is formulated as the minimizer of a cost that is a weighted sum of two terms: 1) the sum of squared difference between the Doppler data and the projected velocities 2) a quadratic regularization functional that imposes some smoothness on the velocity field. We express our solution for this minimization problem in a B-spline basis, obtaining a sparse system of equations that can be solved efficiently. Using synthetic phantom data, we demonstrate the significance of tuning the regularization according to the a priori knowledge about the physical property of the motion. Next, we validate our method using real phantom data for which the ground truth is known. We then present reconstruction results obtained from clinical data that originate from 1) blood flow in carotid bifurcation and 2) cardiac wall motion
Stochastic Models for Sparse and Piecewise-Smooth Signals

We introduce an extended family of continuous-domain stochastic models for sparse, piecewise-smooth signals. These are specified as solutions of stochastic differential equations, or, equivalently, in terms of a suitable innovation model; the latter is analogous conceptually to the classical interpretation of a Gaussian stationary process as filtered white noise. The two specific features of our approach are 1) signal generation is driven by a random stream of Dirac impulses (Poisson noise) instead of Gaussian white noise, and 2) the class of admissible whitening operators is considerably larger than what is allowed in the conventional theory of stationary processes. We provide a complete characterization of these finite-rate-of-innovation signals within Gelfand's framework of generalized stochastic processes. We then focus on the class of scale-invariant whitening operators which correspond to unstable systems. We show that these can be solved by introducing proper boundary conditions, which leads to the specification of random, spline-type signals that are piecewise-smooth. These processes are the Poisson counterpart of fractional Brownian motion; they are nonstationary and have the same 1/ω-type spectral signature. We prove that the generalized Poisson processes have a sparse representation in a wavelet-like basis subject to some mild matching condition. We also present a limit example of sparse process that yields a MAP signal estimator that is equivalent to the popular TV-denoising algorithm.
NON-ITERATIVE EXACT SIGNAL RECOVERY IN FREQUENCY DOMAIN OPTICAL COHERENCE TOMOGRAPHY

We address the problem of exact signal recovery in frequency domain optical coherence tomography (FDOCT) systems. Our technique relies on the fact that, in a spectral interferometry setup, the intensity of the total signal reflected from the object is smaller than that of the reference arm. We develop a novel algorithm to compute the reflected signal amplitude from the interferometric measurements. Our technique is non-iterative, non-linear and it leads to an exact solution in the absence of noise. The reconstructed signal is free from artifacts such as the autocorrelation noise that is normally encountered in the conventional inverse Fourier transform techniques. We present results on synthesized data where we have a benchmark for comparing the performance of the technique. We also report results on experimental FDOCT measurements of the retina of the human eye
Dynamic PET Reconstruction Using Wavelet Regularization With Adapted Basis Functions

Tomographic reconstruction from positron emission tomography (PET) data is an ill-posed problem that requires regularization. An attractive approach is to impose an lscr1-regularization constraint, which favors sparse solutions in the wavelet domain. This can be achieved quite efficiently thanks to the iterative algorithm developed by Daubechies et al., 2004. In this paper, we apply this technique and extend it for the reconstruction of dynamic (spatio-temporal) PET data. Moreover, instead of using classical wavelets in the temporal dimension, we introduce exponential-spline wavelets (E-spline wavelets) that are specially tailored to model time activity curves (TACs) in PET. We show that the exponential-spline wavelets naturally arise from the compartmental description of the dynamics of the tracer distribution. We address the issue of the selection of the ldquooptimalrdquo E-spline parameters (poles and zeros) and we investigate their effect on reconstruction quality. We demonstrate the usefulness of spatio-temporal regularization and the superior performance of E-spline wavelets over conventional Battle-Lemarie wavelets in a series of experiments: the 1-D fitting of TACs, and the tomographic reconstruction of both simulated and clinical data. We find that the E-spline wavelets outperform the conventional wavelets in terms of the reconstructed signal-to-noise ratio (SNR) and the sparsity of the wavelet coefficients. Based on our simulations, we conclude that replacing the conventional wavelets with E-spline wavelets leads to equal reconstruction quality for a 40% reduction of detected coincidences, meaning an improved image quality for the same number of counts or equivalently a reduced exposure to the patient for the same image quality.
Keynote speakers: Sparse modeling and the resolution of inverse problems in biomedical imaging

Michael Unser is professor and director of EPFL's Biomedical Imaging Group, Lausanne, Switzerland. His primary area of investigation is biomedical image processing. He is internationally recognized for his research contributions to sampling theory, wavelets, the use of splines for image processing, stochastic processes, and computational bioimaging. He has published over 250 journal papers on those topics. He is the author with P. Tafti of the book “An introduction to sparse stochastic processes”,
Reconstruction From Multiple Poses in Fluorescence Imaging: Proof of Concept

One disadvantage of all fluorescence imaging modalities is a poor axial resolution. To overcome this issue, we propose a novel approach to reconstruct fluorescence volumes with isotropic high resolution, from images of particle replicates observed at multiple orientations. We design a joint deconvolution-and-multiview reconstruction approach dedicated to three-dimensional fluorescence imaging. We address the computational challenge associated to big data by designing a fast augmented-Lagrangian optimizer. The computational cost of the iterative part of the algorithm does not depend on the number of input particles. We experimentally demonstrate the resolution improvement yielded by our framework and its ability to handle practical constraints like large PSF sizes and large number of particles. The validation is performed on realistic simulated data, which establishes a proof of concept for our framework and defines it as the basis for future extensions.
Bayesian Estimation for Continuous-Time Sparse Stochastic Processes

We consider continuous-time sparse stochastic processes from which we have only a finite number of noisy/noiseless samples. Our goal is to estimate the noiseless samples (denoising) and the signal in-between (interpolation problem). By relying on tools from the theory of splines, we derive the joint a priori distribution of the samples and show how this probability density function can be factorized. The factorization enables us to tractably implement the maximum a posteriori and minimum mean-square error (MMSE) criteria as two statistical approaches for estimating the unknowns. We compare the derived statistical methods with well-known techniques for the recovery of sparse signals, such as the ℓ1 norm and Log (ℓ1-ℓ0 relaxation) regularization methods. The simulation results show that, under certain conditions, the performance of the regularization techniques can be very close to that of the MMSE estimator.
Sparse stochastic processes: A statistical framework for modern signal processing

We introduce an extended family of sparse processes that are specified by a generic (non-Gaussian) innovation model or, equivalently, as solutions of linear stochastic differential equations driven by white Lévy noise. We present the mathematical tools for their characterization. The two leading threads of the exposition are - the statistical property of infinite divisibility, which induces two distinct types of behavior - Gaussian vs. sparse at the exclusion of any other; - the structural link between linear stochastic processes and splines. This allows us to prove that these processes admit a parsimonious representation in some matched wavelet-like basis. We show that these models have predictive power for image compression and that they are applicable to the derivation of statistical algorithms for solving ill-posed inverse problems, including compressed sensing.
Wavelet-Based Detection of Stimulus Responses in Time-Lapse Microscopy

Many experimental paradigms in biology aim at studying the response to coordinated stimuli. In dynamic imaging experiments, the observed data is often not straightforward to interpret and not directly measurable in a quantitative fashion. Consequently, the data is typically preprocessed in an ad hoc fashion and the results subjected to a statistical inference at the level of a population. We propose a new framework for analyzing time-lapse images that exploits some a priori knowledge on the type of temporal response and takes advantage of the spatial correlation of the data. This is achieved by processing the data in the wavelet domain and expressing the time course of each wavelet coefficient by a linear model. We end up with a statistical map in the spatial domain for the contrast of interest (i.e., the stimulus response). The feasibility of the method is demonstrated by an example of intrinsic microscopy imaging of mice's brains during coordinated sensory stimulation
Fast Segmentation From Blurred Data in 3D Fluorescence Microscopy

We develop a fast algorithm for segmenting 3D images from linear measurements based on the Potts model (or piecewise constant Mumford-Shah model). To that end, we first derive suitable space discretizations of the 3D Potts model, which are capable of dealing with 3D images defined on non-cubic grids. Our discretization allows us to utilize a specific splitting approach, which results in decoupled subproblems of moderate size. The crucial point in the 3D setup is that the number of independent subproblems is so large that we can reasonably exploit the parallel processing capabilities of the graphics processing units (GPUs). Our GPU implementation is up to 18 times faster than the sequential CPU version. This allows to process even large volumes in acceptable runtimes. As a further contribution, we extend the algorithm in order to deal with non-negativity constraints. We demonstrate the efficiency of our method for combined image deconvolution and segmentation on simulated data and on real 3D wide field fluorescence microscopy data.
3D steerable wavelets and monogenic analysis for bioimaging

In this paper we introduce a 3D wavelet frame that has the key property of steerability. The proposed wavelet frame relies on the combination of a 3D isotropic wavelet transform with the 3D Riesz operator which brings steerability to the pyramid. The novel transform enjoys self reversibility and exact steering of the basis functions in any 3D direction by linear combination of the primary coefficients. We exploit the link between the Riesz transform and the directional Hilbert transform to define a multiresolution monogenic signal analysis in 3D which achieves multiscale AM/FM signal decomposition. We give an example of application of the 3D monogenic wavelet frame in biological imaging with the enhancement of anisotropic structures in 3D fluorescence microscopy.
Spatio-temporal regularization of flow-fields

We introduce a novel variational framework for the regularized reconstruction of time-resolved volumetric flow fields. Our objective functional takes the physical characteristics of the underlying flow into account in both the spatial and the temporal domains. For an efficient minimization of the objective functional, we apply a proximal-splitting algorithm and perform parallel computations. To demonstrate the utility of our variational method, we first denoise a simulated flow-field in the human aorta and show that our method outperforms spatial-only regularization in terms of signal-to-noise ratio (SNR). We then apply the scheme to a real 3D+time phase-contrast MRI dataset and obtain high-quality visualizations.
A Fast Thresholded Landweber Algorithm for Wavelet-Regularized Multidimensional Deconvolution

We present a fast variational deconvolution algorithm that minimizes a quadratic data term subject to a regularization on the -norm of the wavelet coefficients of the solution. Previously available methods have essentially consisted in alternating between a Landweber iteration and a wavelet-domain soft-thresholding operation. While having the advantage of simplicity, they are known to converge slowly. By expressing the cost functional in a Shannon wavelet basis, we are able to decompose the problem into a series of subband-dependent minimizations. In particular, this allows for larger (subband-dependent) step sizes and threshold levels than the previous method. This improves the convergence properties of the algorithm significantly. We demonstrate a speed-up of one order of magnitude in practical situations. This makes wavelet-regularized deconvolution more widely accessible, even for applications with a strong limitation on computational complexity. We present promising results in 3-D deconvolution microscopy, where the size of typical data sets does not permit more than a few tens of iterations.
Non-Ideal Sampling and Adapted Reconstruction Using the Stochastic Matern Model

The Matern class is a parametric family of autocorrelation functions that is commonly used in geostatistics. We argue that a generalized, anisotropic version of this model is suitable for capturing the correlation structure of a variety of natural images. We specify the optimal space for the MMSE reconstruction of stochastic Matern signals from their uniformly-sampled noisy measurements (generalized sampling problem). We prove that the optimal reconstruction space is generated by the multi-integer shifts of a Matern function which form a Riesz basis. Based on this representation, we propose a practical filter-based reconstruction method that relies on the prior identification of the Matern parameters from the measured data. We present experimental results to justify the use of the Matern model and to demonstrate the performance of our signal-adapted reconstruction technique
3D Poisson microscopy deconvolution with Hessian Schatten-norm regularization

Inverse problems with shot noise arise in many modern biomedical imaging applications. The main challenge is to obtain an estimate of the underlying specimen from measurements corrupted by Poisson noise. In this work, we propose an efficient framework for photon-limited image reconstruction, under a regularization approach that relies on matrix-valued operators. Our regularizers involve the Hessian operator and its eigenvalues. They are second-order regularizers that are well suited to biomedical images. For the solution of the arising minimization problem, we propose an optimization algorithm based on an augmented-Lagrangian formulation and specifically tailored to the Poisson nature of the noise. To assess the quality of the reconstruction, we provide experimental results on 3D image stacks of biological images for microscopy deconvolution.