Nonnegative Reconstruction Research Articles

Smooth non-negative sparse representation for face and handwritten recognition

In sparse representation problem, there is always interest to reduce the solution space by introducing additional constraints. This can lead to efficient application-specific algorithms. Despite known advantages of sparsity and non-negativity for image data representation, limited studies have addressed these characteristics simultaneously, due to the challenges involved. In this paper, we propose a novel inexpensive sparse non-negative reconstruction method. We utilise a non-negativity penalty term within a convex function while imposing sparsity at the same time. Our method, termed as SnSA (smooth non-negative sparse approximation) applies a novel thresholding strategy on the sparse coefficients during the minimisation of the proposed convex function. The main advantage of SnSA algorithm is that hard zeroing the negative samples which leads to unstable and non-optimal sparse solution is avoided. Instead, a differentiable smoothing function is proposed that allows gradual suppression of negative samples leading to a sparse non-negative solution. This way, the algorithm is driven towards a solution with a balance in maximising the sparsity and minimising the reconstruction error. Our numerical and experimental results on both synthetic signals and well-established face and handwritten image databases, indicate higher classification performance of the proposed method compared to the state-of-the-art techniques.

Superiorized Photo-Acoustic Non-NEgative Reconstruction (SPANNER) for Clinical Photoacoustic Imaging.

Photoacoustic (PA) imaging can revolutionize medical ultrasound by augmenting it with molecular information. However, clinical translation of PA imaging remains a challenge due to the limited viewing angles and imaging depth. Described here is a new robust algorithm called Superiorized Photo-Acoustic Non-NEgative Reconstruction (SPANNER), designed to reconstruct PA images in real-time and to address the artifacts associated with limited viewing angles and imaging depth. The method utilizes precise forward modeling of the PA propagation and reception of signals while accounting for the effects of acoustic absorption, element size, shape, and sensitivity, as well as the transducer's impulse response and directivity pattern. A fast superiorized conjugate gradient algorithm is used for inversion. SPANNER is compared to three reconstruction algorithms: delay-and-sum (DAS), universal back-projection (UBP), and model-based reconstruction (MBR). All four algorithms are applied to both simulations and experimental data acquired from tissue-mimicking phantoms, ex vivo tissue samples, and in vivo imaging of the prostates in patients. Simulations and phantom experiments highlight the ability of SPANNER to improve contrast to background ratio by up to 20 dB compared to all other algorithms, as well as a 3-fold increase in axial resolution compared to DAS and UBP. Applying SPANNER on contrast-enhanced PA images acquired from prostate cancer patients yielded a statistically significant difference before and after contrast agent administration, while the other three image reconstruction methods did not, thus highlighting SPANNER's performance in differentiating intrinsic from extrinsic PA signals and its ability to quantify PA signals from the contrast agent more accurately.

Unsupervised Saliency Detection of Rail Surface Defects using Stereoscopic Images

Visual information is increasingly recognized as a useful method to detect rail surface defects due to its high efficiency and stability. However, it cannot sufficiently detect a complete defect in the complex background information. The addition of surface profiles can effectively improve this by including a 3-D information of defects. However, in high-speed detection, the traditional 3-D profile acquisition is difficult and separate from the image acquisition, which cannot satisfy the above-mentioned requirements effectively. Therefore, an unsupervised stereoscopic saliency detection method based on a binocular line-scanning system is proposed in this article. This method can simultaneously obtain a highly precise image as well as profile information while also avoids the decoding distortion of the structured light reconstruction method. In our method, a global low-rank nonnegative reconstruction algorithm with a background constraint is proposed. Unlike the low-rank recovery model, the algorithm has a more comprehensive low rank and background clustering properties. Furthermore, outlier detection based on the geometric properties of the rail surface is also proposed in this method. Finally, the image saliency results and depth outlier detection results are associated with the collaborative fusion, and a dataset (RSDDS-113) containing the rail surface defects is established for the experimental verification. The experimental results demonstrate that our method can obtain a mean absolute error of 0.09 and area under the ROC curve of 0.94, better than 15 state-of-the-art algorithms.

A well-balanced positivity preserving two-dimensional shallow flow model with wetting and drying fronts over irregular topography

This paper presents an improved well-balanced Godunov-type 2-D finite volume model with structured grids to simulate shallow flows with wetting and drying fronts over an irregular topography. The intercell flux is computed using a central upwind scheme, which is a Riemann-problem-solver-free method for hyperbolic conservation laws. The nonnegative reconstruction method for the water depth is implemented to resolve the stationary or wet/dry fronts. The bed slope source term is discretized using a central difference method to capture the static flow state over the irregular topography. Second-order accuracy in space is achieved by using the slope limited linear reconstruction method. With the proposed method, the model can avoid the partially wetting/drying cell problem and maintain the mass conservation. The proposed model is tested and verified against three theoretical benchmark tests and two experimental dam break flows. Further, the model is applied to predict the maximum water level and the flood arrival time at different gauge points for the Malpasset dam break event. The predictions agree well with the numerical results and the measurement data published in literature, which demonstrates that with the present model, a well-balanced state can be achieved and the water depth can be nonnegative when the Courant number is kept less than 0.25.

Identification of regional activation by factorization of high-density surface EMG signals: A comparison of Principal Component Analysis and Non-negative Matrix factorization

In this study, we investigated whether principal component analysis (PCA) and non-negative matrix factorization (NMF) perform similarly for the identification of regional activation within the human vastus medialis. EMG signals from 64 locations over the VM were collected from twelve participants while performing a low-force isometric knee extension. The envelope of the EMG signal of each channel was calculated by low-pass filtering (8 Hz) the monopolar EMG signal after rectification. The data matrix was factorized using PCA and NMF, and up to 5 factors were considered for each algorithm. Association between explained variance, spatial weights and temporal scores between the two algorithms were compared using Pearson correlation. For both PCA and NMF, a single factor explained approximately 70% of the variance of the signal, while two and three factors explained just over 85% or 90%. The variance explained by PCA and NMF was highly comparable (R > 0.99). Spatial weights and temporal scores extracted with non-negative reconstruction of PCA and NMF were highly associated (all p < 0.001, mean R > 0.97). Regional VM activation can be identified using high-density surface EMG and factorization algorithms. Regional activation explains up to 30% of the variance of the signal, as identified through both PCA and NMF.

Image regularization by nonnegatively constrained Conjugate Gradient

In the image reconstruction context the nonnegativity of the computed solution is often required. Conjugate Gradient (CG), used as a reliable regularization tool, may give solutions with negative entries, particularly when large nearly zero plateaus are present. The active constraints set, detected by projection onto the nonnegative orthant, turns out to be largely incomplete leading to poor effects on the accuracy of the reconstructed image. In this paper an inner-outer method based on CG is proposed to compute nonnegative reconstructed images with a strategy which enlarges subsequently the active constraints set. This method appears to be especially suitable for the reconstruction of images having large nearly zero backgrounds. The numerical experimentation validates the effectiveness of the proposed method when compared to other strategies for nonnegative reconstruction.

Modeling of Breaching Due to Overtopping Flow and Waves Based on Coupled Flow and Sediment Transport

Breaching of earthen or sandy dams/dunes by overtopping flow and waves is a complicated process with strong, unsteady flow, high sediment transport, and rapid bed changes in which the interactions between flow and morphology should not be ignored. This study presents a depth-averaged two-dimensional (2D) coupled flow and sediment transport model to investigate the flow and breaching processes with and without waves. Bed change and variable flow density are included in the flow continuity and momentum equations to consider the impacts of sediment transport. The model adopts the non-equilibrium approach for total-load sediment transport and specifies different repose angles to handle non-cohesive embankment slope avalanching. The equations are solved using an explicit finite volume method on a rectangular grid with the improved Godunov-type central upwind scheme and the nonnegative reconstruction of the water depth method to handle mixed-regime flows near the breach. The model has been tested against two sets of experimental data which show that it well simulates the flow characteristics, bed changes, and sediment transport. It is then applied to analyze flow and morphologic changes by overtopping flow with and without waves. The simulated bed change and breach cross-section shape show a significant difference if waves are considered. Erosion by flow without waves mainly occurs at the breach and is dominated by vertical erosion at the initial stage followed by the lateral erosion. With waves, the flow overtops the entire length of the dune to cause faster erosion along the entire length. Erosion mainly takes place at the upper layer at the initial stage and gradually accelerates as the height of the dune reduces and flow discharge increases, which indicates the simulated results with waves shall be further verified by physical experimental evidence.

Unsupervised document summarization from data reconstruction perspective

Due to its wide applications in information retrieval, document summarization is attracting increasing attention in natural language processing. A large body of recent literature has implemented document summarization by extracting sentences that cover the main topics of a document with a minimum redundancy. In this paper, we take a different perspective from data reconstruction and propose a novel unsupervised framework named Document Summarization based on Data Reconstruction (DSDR). Specifically, our approach generates a summary which consist of those sentences that can best reconstruct the original document. To model the relationship among sentences, we firstly introduce the linear reconstruction which approximates the document by linear combinations of the selected sentences. We then extend it into the non-negative reconstruction which allows only additive, not subtractive, linear combinations. In order to handle the nonlinear cases and respect the geometrical structure of sentence space, we also extend the linear reconstruction in the manifold adaptive kernel space which incorporates the manifold structure by using graph Laplacian. Extensive experiments on summarization benchmark data sets demonstrate that our proposed framework outperform state of the art.

A Well-Balanced Numerical Model for the Simulation of Long Waves over Complex Domains

This paper presents a well-balanced two-dimensional (2D) finite volume model to simulate the propagation, runup and rundown of long wave. Non-staggered grid is adopted to discretize the governing equation and the intercell flux is computed using a central upwind scheme, which is a Riemann-problem-solver-free method for hyperbolic conservation laws. The nonnegative reconstruction method for water depth is implemented in the present model to treat the appearance of wet/dry fronts, and the friction term is solved by a semi-implicit scheme to ensure the stability of the model. The Euler method is applied to update flow variable to the new time level. The model is verified against two experimental cases and good agreements are observed between numerical results and observed data.

A stable 2D unstructured shallow flow model for simulations of wetting and drying over rough terrains

This paper proposes a 2D unstructured finite volume Godunov-type shallow water model to simulate complex flows involving wet–dry interfaces over irregular terrains. In this model, the MUSCL linear reconstruction is used to compute the values of variables at cell edges. These values are then modified with a non-negative reconstruction method to preserve non-negative edge water depths and the C-property. The modified values are then employed to evaluate the fluxes and the slope source terms using the Harten, Lax and van Leer approximate Riemann solver with the contact wave restored (HLLC) and the slope flux method, respectively. The friction source terms are solved by a splitting point-implicit method. The novel aspect of the model is an efficient approach to eliminate spurious edge velocities with high local extreme values caused by MUSCL reconstruction of the conservative variables near wet–dry interfaces. This approach is crucial to preserve the numerical stability of the model when simulating wetting and drying. The proposed model is tested against exact solutions, laboratory experiments and a real dam-break case. The results show that the proposed model is accurate and stable for handling complex flows with moving wet–dry interfaces over complex beds on unstructured grids.

A coupled morphodynamic model for applications involving wetting and drying

This work presents a new finite volume Godunov-type model for predicting morphological changes under the rapidly varying flood conditions with wetting and drying. The model solves the coupled shallow water and Exner equations, with the interface fluxes evaluated by an Harten-Lax-van Leer-Contact (HLLC) approximate Riemann solver. Well-balanced solution is achieved using the surface gradient method and wetting and drying are handled by a non-negative reconstruction approach. The new model is validated against several theoretical benchmark tests and promising results are obtained.

Numerical resolution of well-balanced shallow water equations with complex source terms

This paper presents a well-balanced numerical scheme for simulating frictional shallow flows over complex domains involving wetting and drying. The proposed scheme solves, in a finite volume Godunov-type framework, a set of pre-balanced shallow water equations derived by considering pressure balancing. Non-negative reconstruction of Riemann states and compatible discretization of slope source term produce stable and well-balanced solutions to shallow flow hydrodynamics over complex topography. The friction source term is discretized using a splitting implicit scheme. Limiting value of the friction force is derived to ensure stability. This new numerical scheme is validated against four theoretical benchmark tests and then applied to reproduce a laboratory dam break over a domain with irregular bed profile.

Maximum-likelihood expectation-maximization reconstruction of sinograms with arbitrary noise distribution using NEC-transformations.

The maximum-likelihood (ML) expectation-maximization (EM) [ML-EM] algorithm is being widely used for image reconstruction in positron emission tomography. The algorithm is strictly valid if the data are Poisson distributed. However, it is also often applied to processed sinograms that do not meet this requirement. This may sometimes lead to suboptimal results: streak artifacts appear and the algorithm converges toward a lower likelihood value. As a remedy, we propose two simple pixel-by-pixel methods [noise equivalent counts (NEC)-scaling and NEC-shifting] in order to transform arbitrary sinogram noise into noise which is approximately Poisson distributed (the first and second moments of the distribution match those of the Poisson distribution). The convergence speed associated with both transformation methods is compared, and the NEC-scaling method is validated with both simulations and clinical data. These new methods extend the ML-EM algorithm to a general purpose nonnegative reconstruction algorithm.