nils-herrmann/clean_scirepeval huggingface dataset:
Photo Realistic Image Completion via Dense Correspondence

In this paper, we propose an image completion algorithm based on dense correspondence between the input image and an exemplar image retrieved from the Internet. Contrary to traditional methods which register two images according to sparse correspondence, in this paper, we propose a hierarchical PatchMatch method that progressively estimates a dense correspondence, which is able to capture small deformations between images. The estimated dense correspondence has usually large occlusion areas that correspond to the regions to be completed. A nearest neighbor field (NNF) interpolation algorithm interpolates a smooth and accurate NNF over the occluded region. Given the calculated NNF, the correct image content from the exemplar image is transferred to the input image. Finally, as there could be a color difference between the completed content and the input image, a color correction algorithm is applied to remove the visual artifacts. Numerical results show that our proposed image completion method can achieve photo realistic image completion results.
Sparse Sampling of Signal Innovations

Sparse sampling of continuous-time sparse signals is addressed. In particular, it is shown that sampling at the rate of innovation is possible, in some sense applying Occam's razor to the sampling of sparse signals. The noisy case is analyzed and solved, proposing methods reaching the optimal performance given by the Cramer-Rao bounds. Finally, a number of applications have been discussed where sparsity can be taken advantage of. The comprehensive coverage given in this article should lead to further research in sparse sampling, as well as new applications. One main application to use the theory presented in this article is ultra-wide band (UWB) communications.
Low-Rate Reduced Complexity Image Compression using Directionlets

The standard separable two-dimensional (2-D) wavelet transform (WT) has recently achieved a great success in image processing because it provides a sparse representation of smooth images. However, it fails to capture efficiently one-dimensional (1-D) discontinuities, like edges and contours, that are anisotropic and characterized by geometrical regularity along different directions. In our previous work, we proposed a construction of critically sampled perfect reconstruction anisotropic transform with directional vanishing moments (DVM) imposed in the corresponding basis functions, called directionlets. Here, we show that the computational complexity of our transform is comparable to the complexity of the standard 2-D WT and substantially lower than the complexity of other similar approaches. We also present a zerotree-based image compression algorithm using directionlets that strongly outperforms the corresponding method based on the standard wavelets at low bit rates.
Sampling Schemes for Multidimensional Signals With Finite Rate of Innovation

In this paper, we consider the problem of sampling signals that are nonband-limited but have finite number of degrees of freedom per unit of time and call this number the rate of innovation. Streams of Diracs and piecewise polynomials are the examples of such signals, and thus are known as signals with finite rate of innovation (FRI). We know that the classical ("band-limited sine") sampling theory does not enable perfect reconstruction of such signals from their samples since they are not band-limited. However, the recent results on FRI sampling suggest that it is possible to sample and perfectly reconstruct such nonband-limited signals using a rich class of kernels. In this paper, we extend those results in higher dimensions using compactly supported kernels that reproduce polynomials (satisfy Strang-Fix conditions). In fact, the polynomial reproduction property of the kernel makes it possible to obtain the continuous moments of the signal from its samples. Using these moments and the annihilating filter method (Prony's method), the innovative part of the signal, and therefore, the signal itself is perfectly reconstructed. In particular, we present local (directional-derivatives-based) and global (complex-moments-based, Radon-transform-based) sampling schemes for classes of FRI signals such as sets of Diracs, bilevel, and planar polygons, quadrature domains (e.g., circles, ellipses, and cardioids), 2D polynomials with polygonal boundaries, and n-dimensional Diracs and convex polytopes. This work has been explored in a promising way in super-resolution algorithms and distributed compression, and might find its applications in photogrammetry, computer graphics, and machine vision.
Wavelet and footprint sampling of signals with a finite rate of innovation

We consider classes of not bandlimited signals, namely streams of Diracs and piecewise polynomial signals, and show that these signals can be sampled and perfectly reconstructed using wavelets as sampling kernel. Due to the multiresolution structure of the wavelet transform, these new sampling theorems naturally lead to the development of a new resolution enhancement algorithm based on wavelet footprints (Dragotti, P.L. and Vetterli, M.,  2003). Preliminary results show the potentiality of this algorithm.
Centralized and Distributed Semiparametric Compression of Piecewise Smooth Functions

This paper introduces novel wavelet-based semiparametric centralized and distributed compression methods for a class of 1-D piecewise smooth functions. Classical centralized compression schemes are based on a relatively complex, nonlinear encoder and a simple, linear decoder. Recently, a new paradigm in compression called distributed source coding has emerged. This setup involves multiple encoders, where each one partially observes the source, and a centralized decoder. First, we focus on the dual situation of the centralized compression with a simple encoder and a complex decoder. We show that, by incorporating parametric estimation into the decoding procedure, it is possible to achieve the same rate-distortion performance as that of a conventional wavelet-based compression scheme. Second, we consider the distributed compression scenario, where each independent encoder partially observes the 1-D piecewise smooth function. We propose a new wavelet-based distributed compression scheme that uses parametric estimation to perform joint decoding. Our analysis shows that it is possible for the proposed scheme to achieve the same compression performance as that of a joint encoding scheme.
Multichannel Sampling of Signals With Finite Rate of Innovation

In this letter, we present a possible extension of the theory of sampling signals with finite rate of innovation (FRI) to the case of multichannel acquisition systems. The essential issue of a multichannel system is that each channel introduces different unknown delays and gains that need to be estimated for the calibration of the channels. We pose both the synchronization stage and the signal reconstruction stage as a parametric estimation problem and demonstrate that a simultaneous exact synchronization of the channels and reconstruction of the FRI signal is possible. We also consider the case of noisy measurements and evaluate the Cramér-Rao bounds (CRB) of the proposed system. Numerical results as well as the CRB show clearly that multichannel systems are more resilient to noise than the single-channel ones.
On Sparse Representation in Fourier and Local Bases

We consider the classical problem of finding the sparse representation of a signal in a pair of bases. When both bases are orthogonal, it is known that the sparse representation is unique when the sparsity K of the signal satisfies K <; 1/μ(D), where μ(D) is the mutual coherence of the dictionary. Furthermore, the sparse representation can be obtained in polynomial time by basis pursuit (BP), when K <; 0.91/μ(D). Therefore, there is a gap between the unicity condition and the one required to use the polynomial-complexity BP formulation. For the case of general dictionaries, it is also well known that finding the sparse representation under the only constraint of unicity is NP-hard. In this paper, we introduce, for the case of Fourier and canonical bases, a polynomial complexity algorithm that finds all the possible K-sparse representations of a signal under the weaker condition that K <; √2/μ(D). Consequently, when K <; 1/μ(D), the proposed algorithm solves the unique sparse representation problem for this structured dictionary in polynomial time. We further show that the same method can be extended to many other pairs of bases, one of which must have local atoms. Examples include the union of Fourier and local Fourier bases, the union of discrete cosine transform and canonical bases, and the union of random Gaussian and canonical bases.
Transform coder identification with double quantized data

The analysis of chains of double transform coders has been recently addressed in the image forensic literature, especially for the case of double JPEG compression. In that case, the transform is assumed to be known a priori (e.g., 2D-DCT), whereas the quantization steps of the first coder need to be determined. In this work, we generalize the analysis to the challenging case in which nothing is known about the first coder, but that the transform is orthonormal. Given a set of vectors observed as output of a chain of two transform coders, we identify both the transform and the quantizer of the first. The key idea is to denoise the observed vectors exploiting the constraints imposed by the first quantizer and then apply our previously proposed method, which successfully performs transform identification in the case of noiseless observations. Experiments on real images validate the proposed approach.
Segmentation of Epipolar-Plane Image Volumes with Occlusion and Disocclusion Competition

Consider a dense array of cameras uniformly distributed along a line. A solid block of 3D data can be constructed by arranging the images into a stack. This volume, also known as the epipolar-plane image volume, contains highly structured data that can be segmented for object removal, insertion and compression. In this paper, we propose a segmentation scheme that takes fully advantage of the known geometry in order to model occlusions explicitly as a result of disparity. Moreover, we include this knowledge into an energy minimization scheme based on region competition with active contours. Instead of extracting layers sequentially from front to back, each layer is made to compete with the regions it is going to occlude and the ones it is going to disocclude. This enables a virtually unsupervised segmentation
Accurate non-iterative depth layer extraction algorithm for image based rendering

Image based rendering is an attractive alternative for generating novel views compared to model based rendering due to its lower complexity and potential for photo-realistic results. We present a fast unsupervised method for synthesising arbitrary viewpoints of a scene from a set of existing views. Our novel improvements include optimising the placement of depth layers to take advantage of the composition of real world scenes and hierarchically building our simple geometric model to maximise its accuracy.
Prosparse denoise: Prony's based sparse pattern recovery in the presence of noise

We present a novel algorithm - ProSparse Denoise - that can solve the sparsity recovery problem in the presence of noise when the dictionary is the union of Fourier and identity matrices. The algorithm is based on a proper use of Cadzow routine and Prony's method and exploits the duality of Fourier and identity matrices. The algorithm has low complexity compared to state of the art algorithms for sparse recovery since it relies on the Fast Fourier Transform (FFT) algorithm. We provide conditions on the noise that guarantees the correct recovery of the sparsity pattern. Our approach outperforms state of the art algorithms such as Basis Pursuit De-noise and Subspace Pursuit when the dictionary is the union of Fourier and identity matrices.
FRI Sampling With Arbitrary Kernels

This paper addresses the problem of sampling non-bandlimited signals within the Finite Rate of Innovation (FRI) setting. We had previously shown that, by using sampling kernels whose integer span contains specific exponentials (generalized Strang-Fix conditions), it is possible to devise non-iterative, fast reconstruction algorithms from very low-rate samples. Yet, the accuracy and sensitivity to noise of these algorithms is highly dependent on these exponential reproducing kernels - actually, on the exponentials that they reproduce. Hence, our first contribution here is to provide clear guidelines on how to choose the sampling kernels optimally, in such a way that the reconstruction quality is maximized in the presence of noise. The optimality of these kernels is validated by comparing with Cramér-Rao's lower bounds (CRB). Our second contribution is to relax the exact exponential reproduction requirement. Instead, we demonstrate that arbitrary sampling kernels can reproduce the “best” exponentials within quite a high accuracy in general, and that applying the exact FRI algorithms in this approximate context results in near-optimal reconstruction accuracy for practical noise levels. Essentially, we propose a universal extension of the FRI approach to arbitrary sampling kernels. Numerical results checked against the CRB validate the various contributions of the paper and in particular outline the ability of arbitrary sampling kernels to be used in FRI algorithms.
Wavelet footprints: theory, algorithms, and applications

Wavelet-based algorithms have been successful in different signal processing tasks. The wavelet transform is a powerful tool because it manages to represent both transient and stationary behaviors of a signal with few transform coefficients. Discontinuities often carry relevant signal information, and therefore, they represent a critical part to analyze. We study the dependency across scales of the wavelet coefficients generated by discontinuities. We start by showing that any piecewise smooth signal can be expressed as a sum of a piecewise polynomial signal and a uniformly smooth residual (Theorem 1). We then introduce the notion of footprints, which are scale space vectors that model discontinuities in piecewise polynomial signals exactly. We show that footprints form an overcomplete dictionary and develop efficient and robust algorithms to find the exact representation of a piecewise polynomial function in terms of footprints. This also leads to efficient approximation of piecewise smooth functions. Finally, we focus on applications and show that algorithms based on footprints outperform standard wavelet methods in different applications such as denoising, compression, and (nonblind) deconvolution. In the case of compression, we also prove that at high rates, footprint-based algorithms attain optimal performance (Theorem 3).
Rate-distortion optimized tree based coding algorithms

This paper addresses the problem of efficient coding of an important class of signals, namely piecewise polynomials. For this signal class, we develop a coding algorithm, which achieves oracle like rate-distortion (R-D) behavior in the high bit rate regime and with a reasonable computational complexity. For the 1-D case, our scheme is based on the binary tree segmentation of the signal and an optimal bit allocation strategy among the different signal segments. The scheme further encodes the similar neighbors jointly to achieve the right exponentially decaying R-D behavior (D(R) /spl sim/ c/sub 0/2/sup -c1R/). We have also shown that the computational cost of the scheme is of the order O(N log N). We then show that the scheme can be easily extended to the 2-D case, as the quadtree based coding scheme, with the similar R-D behavior and computational cost. Finally, we conclude with some numerical results.
Universal sampling of signals with finite rate of innovation

Recently it has been shown that specific classes of non-bandlimited signals known as signals with finite rate of innovation (FRI) can be perfectly reconstructed by using appropriate sampling kernels and reconstruction schemes. This exact FRI framework was later extended to an approximate FRI framework that works with any kernel. Reconstruction is achieved by recovering all the parameters in the parametric model of the incoming signal, hence it is essential to know the model order (the rate of innovation) to ensure recovery. In view of this, we devise an algorithm for identifying the rate of innovation in order to extend the current sampling scheme to a universal one which enables sampling signals with arbitrary FRI using any acquisition device. Our proposed algorithm can effectively identify the rate of innovation prior to the signal reconstruction using arbitrary kernels and in different noise levels where we also show that it achieves the performance predicted by the Cramèr-Rao bounds.
Wide-baseline image change detection

We present a fully automated method for the detection of changes within a scene between a reference and a sample image whose viewing angles differ by up to 30°. We also describe an extension to the SIFT technique that allows extracted feature points to be matched over wider viewing angles. Matched correspondences between reference and sample images are used to construct a Delaunay triangulation and changes are detected by comparing triangles after affine compensation using a dense SIFT metric. False positives are reduced by using a novel technique introduced as local plane matching (LPM) to match mean-shift segments in unmatched areas using the homographies of local planes to compensate for perspective distortions. The method is shown to achieve pixel-level equal error rates of 5% at a 10° azimuth view angle difference.
The distributed, partial, and conditional Karhunen-Loeve transforms

The Karhunen-Loeve transform (KLT) is a key element of many signal processing tasks, including approximation, compression, and classification. Many recent applications involve distributed signal processing where it is not generally possible to apply the KLT to the signal; the KLT must be approximated in a distributed fashion. Investigations were carried out on the distributed approximations to the KLT. First, explicit solutions to special cases were presented including a partial KLT, a conditional KLT, and the combination of these two special cases. These results were used to derive an algorithm that finds the best distributed approximation to the KLT. Applications of the results from sensor networks and distributed databases were discussed.
Estimating Localized Sources of Diffusion Fields Using Spatiotemporal Sensor Measurements

We consider diffusion fields induced by a finite number of spatially localized sources and address the problem of estimating these sources using spatiotemporal samples of the field obtained with a sensor network. Within this framework, we consider two different time evolutions: the case where the sources are instantaneous, as well as, the case where the sources decay exponentially in time after activation. We first derive novel exact inversion formulas, for both source distributions, through the use of Green's second theorem and a family of sensing functions to compute generalized field samples. These generalized samples can then be inverted using variations of existing algebraic methods such as Prony's method. Next, we develop a novel and robust reconstruction method for diffusion fields by properly extending these formulas to operate on the spatiotemporal samples of the field. Finally, we present numerical results using both synthetic and real data to verify the algorithms proposed herein.
Image restoration using a sparse quadtree decomposition representation

Techniques based on sparse and redundant representations are at the heart of many state of the art denoising and deconvolution algorithms. A very sparse representation of piecewise polynomial images can be obtained by using a quadtree decomposition to adaptively select a basis. We have recently exploited this to restore images of this form, however the same model can also provide very good sparse approximations of real world images. In this paper we take advantage of this to develop both image denoising and deconvolution algorithms suitable for real world images. We present results on the cameraman image showing comparable performance with iterative soft thresholding using the undecimated wavelet transform.
The distributed Karhunen-Loeve transform

The Karhunen-Loeve transform is a key element of many signal processing tasks, including classification and compression. In this paper, we consider distributed signal processing scenarios with limited communication between correlated sources, and we investigate a distributed Karhunen-Loeve transform (KLT). In particular, a partial (where only a subset of sources are observed) and a conditional KLT (where some sources act as side information) are posed and solved in a rate-distortion sense. The partial KLT leads to an original bit allocation problem, while the conditional KLT leads to a Wyner-Ziv solution which is separable at the sources. These two cases can be seen as extreme cases of a distributed KLT.
Consensus for the distributed estimation of point diffusion sources in sensor networks

In this contribution, we implement a fully distributed diffusion field estimation algorithm based on the use of average consensus schemes. We show that the field reconstruction problem is equivalent to estimating the sources of the field, and then derive an exact inversion formula for jointly recovering these sources when they are localized and instantaneous. Next we adapt this formula to the sensor network setting when only spatiotemporal samples of the field are available, and only local interactions between the sensors are allowed. To this end, we propose a robust distributed algorithm for reconstructing two-dimensional diffusion fields, sampled with a network of arbitrarily placed sensors. The proposed distributed algorithm is validated through numerical simulations in the noisy, multiple source setting.
Quantisation Invariants for Transform Parameter Estimation in Coding Chains

We examine the case of a signal going through a processing chain consisting of two transform coding stages, with the aim of recovering the unknown parameters of the first encoder. Through number theoretical considerations, we identify a lattice of quantisation invariant points, whose coordinates are not affected by the double quantisation and whose parameters are closely related to the unknown transform. The conditions for this lattice to exist are then discussed, and its uniqueness properties analysed. Finally, an algorithmic procedure to recover the invariants from a sparse set of points is shown together with numerical results.
Distributed Compression of Multi-View Images using a Geometrical Coding Approach

In this paper, we propose a distributed compression approach for multi-view images, where each camera efficiently encodes its visual information locally without requiring any collaboration with the other cameras. Such a compression scheme can be necessary for camera sensor networks, where each camera has limited power and communication resources and can only transmit data to a central base station. The correlation in the multi-view data acquired by a dense multi-camera system can be extremely large and should therefore be exploited at each encoder in order to reduce the amount of data transmitted to the receiver. Our distributed source coding approach is based on a quadtree decomposition method and uses some geometrical information about the scene and the position of the cameras to estimate this multi-view correlation. We assume that the different views can be modelled as 2D piecewise polynomial functions with ID linear boundaries and show how our approach applies in this context. Our simulation results show that our approach outperforms independent encoding of real multi-view images.