Laplacian Scale Mixture Research Articles

Nonconvex $$\gamma $$-norm and Laplacian scale mixture with salient map for moving object detection

Nonconvex $$\gamma $$-norm and Laplacian scale mixture with salient map for moving object detection

Weighted Schatten p-norm and Laplacian scale mixture-based low-rank and sparse decomposition for foreground–background separation

Low-rank and sparse decomposition (LRSD) plays a vital role in foreground–background separation. The existing LRSD methods have the drawback: imprecise surrogate functions of rank and sparsity. We propose the weighted Schatten p-norm (WSN) and Laplacian scale mixture (LSM) method based on LRSD for foreground–background separation, which introduces the WSN and LSM to improve this drawback. To demonstrate the performance of the proposed method, it is applied to foreground–background separation and gets the highest average F-measure score.

Hyper RPCA: Joint Maximum Correntropy Criterion and Laplacian Scale Mixture Modeling on-the-Fly for Moving Object Detection

Moving object detection is critical for automated video analysis in many vision-related tasks, such as surveillance tracking, video compression coding, etc. Robust Principal Component Analysis (RPCA), as one of the most popular moving object modelling methods, aims to separate the temporally-varying (i.e., moving) foreground objects from the static background in video, assuming the background frames to be low-rank while the foreground to be spatially sparse. Classic RPCA imposes sparsity of the foreground component using <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\ell _1$</tex-math></inline-formula> -norm, and minimizes the modeling error via <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\ell _2$</tex-math></inline-formula> -norm. We show that such assumptions can be too restrictive in practice, which limits the effectiveness of the classic RPCA, especially when processing videos with dynamic background, camera jitter, camouflaged moving object, etc. In this paper, we propose a novel RPCA-based model, called Hyper RPCA, to detect moving objects on the fly. Different from classic RPCA, the proposed Hyper RPCA jointly applies the maximum correntropy criterion (MCC) for the modeling error, and Laplacian scale mixture (LSM) model for foreground objects. Extensive experiments have been conducted, and the results demonstrate that the proposed Hyper RPCA has competitive performance for foreground detection to the state-of-the-art algorithms on several well-known benchmark datasets.

Transformed Structured Sparsity With Smoothness for Hyperspectral Image Deblurring

Due to the influence of imaging equipment or environment, a hyperspectral image (HSI) is often unavoidably blurred in the acquisition process, which results in the spatial and spectral information loss of the HSI. The existing HSI deblurring methods can address the problem, however, they neglect the intrinsic structured sparsity and thus reduce the deblurring performance. Aiming at this issue, we propose a new HSI deblurring method based on transformed structured sparsity with smoothness (TSSS). We first use the local piecewise smoothness to obtain the spatial and spectral sparsity of an HSI in the gradient domain. Then, to capture the refined sparsity, we exploit the transform sparsity learning framework to encode the structured sparsity self-adaptively in transform space, where the sparse structures of transformed operators can be depicted by Laplacian scale mixture (LSM), i.e., the sparsity can be expressed as the product of a hidden positive scalar multiplier and a Laplacian vector. The visual and quantitative comparisons of experimental results on three HSI datasets indicate that our method outperforms state-of-the-arts.

When Laplacian Scale Mixture Meets Three-Layer Transform: A Parametric Tensor Sparsity for Tensor Completion.

Recently, tensor sparsity modeling has achieved great success in the tensor completion (TC) problem. In real applications, the sparsity of a tensor can be rationally measured by low-rank tensor decomposition. However, existing methods either suffer from limited modeling power in estimating accurate rank or have difficulty in depicting hierarchical structure underlying such data ensembles. To address these issues, we propose a parametric tensor sparsity measure model, which encodes the sparsity for a general tensor by Laplacian scale mixture (LSM) modeling based on three-layer transform (TLT) for factor subspace prior with Tucker decomposition. Specifically, the sparsity of a tensor is first transformed into factor subspace, and then factor sparsity in the gradient domain is used to express the local similarity in within-mode. To further refine the sparsity, we adopt LSM by the transform learning scheme to self-adaptively depict deeper layer structured sparsity, in which the transformed sparse matrices in the sense of a statistical model can be modeled as the product of a Laplacian vector and a hidden positive scalar multiplier. We call the method as parametric tensor sparsity delivered by LSM-TLT. By a progressive transformation operator, we formulate the LSM-TLT model and use it to address the TC problem, and then the alternating direction method of multipliers-based optimization algorithm is designed to solve the problem. The experimental results on RGB images, hyperspectral images (HSIs), and videos demonstrate the proposed method outperforms state of the arts.

Mixed noise removal based on Stokes residual noise removal for division of focal plane polarimetric images

The division of focal plane (DoFP) polarimeter has the advantages of simultaneous imaging and compact optical structure. It is inevitable to introducing the noise in the process of micro-polarizer array integration, polarization image acquisition and transmission. In this paper, we propose a novel mixed noise suppression method based on Stokes residual noise removal (SRNR) for mixed additive white Gaussian noise (AWGN) and impulse noise (IN) removal in DoFP polarimetric images. The Laplacian scale mixture (LSM) model is introduced to estimate the IN and the nonlocal low-rank regularization (NLR) is adopted to enhance the denoising performance. The residual noise of the Stokes parameters is taken into consideration. This crucial processing achieves the acquisition of high-quality polarization data. The experiments demonstrate the superior denoising performance for polarimetric imagery in terms of objective assessment and visual evaluation.

Modified complex multitask Bayesian compressive sensing using Laplacian scale mixture prior

Bayesian compressive sensing (BCS) is an important sub-class of sparse signal reconstruction algorithms. In this paper, a modified complex multitask Bayesian compressive sensing (MCMBCS) algorithm using the Laplacian scale mixture (LSM) prior is proposed. The LSM prior is first introduced into the complex BCS framework by exploiting its better sparse characteristic and flexibility than traditional Laplacian prior. Furthermore, by integrating out the noise variance analytically, the MCMBCS algorithm significantly improves the signal recovery performance than the original CMBCS. More importantly, the authors not only present the iterative algorithm but also develop the sub-optimal fast implementation method based on the marginal likelihood maximisation, which dramatically reduce the computational complexity. Finally, sufficient numerical simulations validate the better performance of the proposed algorithm in reconstruction accuracy and computational effectiveness than existing work. It is revealed that the proposed algorithm has great potential in the complex-valued signal processing field.

Hyperspectral Image Restoration via Subspace-Based Nonlocal Low-Rank Tensor Approximation

In this letter, we present a subspace-based nonlocal low-rank tensor approximation framework (SNLRTA) for hyperspectral image (HSI) restoration. The proposed method consists of a subspace learning method to achieve an accurate subspace characterization of HSI and a nonlocal low-rank tensor approximation to take spatial nonlocal self-similarity into consideration. Specifically, the HSI first exploits residual statistics on median filtered image to estimate a robust subspace. Laplacian scale mixture (LSM) modeling is then investigated to model tensor coefficients from overlapping cubes in low-rank subspace. Both the hidden scale parameters and the sparse coefficients therein are adaptively shrink, characterizing the sparsity of similar patches. Meanwhile, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ell _{1}$ </tex-math></inline-formula> data fidelity facilitates the implicit detection of outliers after median filtering. Substantiated by extensive experimental results, the proposed method outperforms several state-of-the-art approaches on mixed noise removal, qualitatively and quantitatively.

Block Sparse Bayesian Recovery with Correlated LSM Prior

Compressed sensing can recover sparse signals using a much smaller number of samples than the traditional Nyquist sampling theorem. Block sparse signals (BSS) with nonzero coefficients occurring in clusters arise naturally in many practical scenarios. Utilizing the sparse structure can improve the recovery performance. In this paper, we consider recovering arbitrary BSS with a sparse Bayesian learning framework by inducing correlated Laplacian scale mixture (LSM) prior, which can model the dependence of adjacent elements of the block sparse signal, and then a block sparse Bayesian learning algorithm is proposed via variational Bayesian inference. Moreover, we present a fast version of the proposed recovery algorithm, which does not involve the computation of matrix inversion and has robust recovery performance in the low SNR case. The experimental results with simulated data and ISAR imaging show that the proposed algorithms can efficiently reconstruct BSS and have good antinoise ability in noisy environments.

Multiband fusion inverse synthetic aperture radar imaging based on variational Bayesian inference

Images from high-resolution inverse synthetic aperture radar (ISAR) can provide more information about the targets. Multiband fusion imaging techniques can achieve higher range resolution without increasing hardware costs. A multiband fusion imaging algorithm based on variational Bayesian inference (VBI) is proposed to improve the range resolution of ISAR images. First, a multiband fusion ISAR imaging model is established based on sparse representation. Second, the scattering coefficients and noise are assumed to be the Laplacian scale mixture distribution and the complex Gaussian distribution, respectively. Finally, the fusion image is directly reconstructed in the complex domain by the VBI based on Laplace approximation method. The effectiveness and robustness of the proposed algorithm are verified by the experimental fusion results of one-dimensional signals and two-dimensional ISAR images.

Enhancing flaw detection in aluminum castings by two different mixed noise removal methods

Aluminum casting is utilized for making complex objects. Different defects may, however, be introduced during the casting process; the detection of which relies on radiography testing as a standard inspection method. To improve information extraction from the acquired X-ray images, image processing methods are often necessary to improve the contrast of the image features and to increase detection success of hidden defects. In this study, two methods based on the sparse regularization were used to enhance the contrast and defect(s) visualization from the radiographs of different casting objects. The Weighted Encoding with Sparse Nonlocal Regularization (WESNR) and Laplacian Scale Mixture (LSM) with a Nonlocal Low-rank Regularizer (NLR) was used to remove Gaussian and impulse noises from the low contrast images. The proposed algorithms were successfully implemented to radiographic images of the cast objects. The results show that improvements in the visualization of internal structure and defect regions were significant, usually by factors of between two and three. Quantitative data supported the outcome of radiography operators’ evaluation that in general, the image features from reconstructed images using the LSM-NLR reconstructed images were better visualized than the WESNR enhanced images.

A Novel ISAR Imaging Method Using Pattern-Coupled Laplacian Scale Mixture Prior

We develop a novel method for high-resolution inverse synthetic aperture radar (ISAR) imaging by exploring the block-sparse structure inherent in the ISAR image. First, the Laplacian scale mixture (LSM) prior is utilized to encode the sparsity of the ISAR image. Then, a 2-D pattern-coupled scale prior for sparse coefficients that encourage dependencies among neighboring coefficients is utilized to capture the block-sparse structure of the target scene. Finally, the Laplace approximation-based variational Bayesian inference (VBI) is employed to infer the posterior of the ISAR image along with hyperparameters. Numerical results based on simulated and measured data are provided to validate the effectiveness of the proposed algorithm.

Generalized nuclear norm and Laplacian scale mixture based low-rank and sparse decomposition for video foreground-background separation

Low-rank and sparse decomposition (LRSD) poses a big challenge problem in video foreground-background separation and many other fields due to its difficulties in approximations of low-rank and sparse parts. The rank and sparsity may not be well approximated in practice since these conventional approaches suffer from the suboptimal issues in many cases. In this paper, we adopt the generalized nuclear norm (GNN) and the Laplacian scale mixture (LSM) modeling to approximate the low-rank and sparse matrices, respectively, and propose a generalized formulation which called GNNLSM for nonconvex low-rank and sparse decomposition based on the GNN and the LSM. And then, we adopt the alternating direction method of multipliers (ADMM) to solve our proposed problem. Simulation results and discussions on video foreground-background separation are given to validate the superiority and the effectiveness of our proposed method.

A Probabilistic Model-Based Method With Nonlocal Filtering for Robust Magnetic Resonance Imaging Reconstruction

Existing model-based or data-driven methods have achieved a high-quality reconstruction in compressive sensing magnetic resonance imaging (CS-MRI). However, most methods are designed for a specific type of sampling mask or sampling rate while ignoring the existence of external noise, resulting in poor robustness. In this work, we propose a probabilistic model-based method based on Laplacian scale mixture (LSM) modeling and denoising based approximate message passing (D-AMP) algorithm to address this issue. Sparse coefficients of similar packed patches are modeled with LSM distribution to exploit the nonlocal self-similarity prior of MR image, and a maximum a posterior estimation problem for sparse coding is formulated. It is shown that both hidden scale parameters i.e. variances of sparse coefficients and location parameters can be jointly estimated along with the unknown sparse coefficients via the method of alternating optimization. Moreover, the variance of noise is also iteratively updated based on maximum likelihood estimation. With plug-and-play prior method, the above structured sparse coding procedure can be regarded as a nonlocal filtering operation and be incorporated into D-AMP for MR image reconstruction. Owing to the power of our nonlocal filtering which takes both signal and noise estimation into account, the proposed method not only outperforms many state-of-the-art methods for most situations of observation, but also delivers the best qualitative reconstruction results with finer details and less artifacts in experiments.

Bayesian High Resolution Range Profile Reconstruction of High-speed Moving Target from Under-sampled Data.

Obtained by wide band radar system, high resolution range profile (HRRP) is the projection of scatterers of target to the radar line-of-sight (LOS). HRRP reconstruction is unavoidable for inverse synthetic aperture radar (ISAR) imaging, and of particular usage for target recognition, especially in cases that the ISAR image of target is not able to be achieved. For the high-speed moving target, however, its HRRP is stretched by the high order phase error. To obtain well-focused HRRP, the phase error induced by target velocity should be compensated, utilizing either measured or estimated target velocity. Noting in case of under-sampled data, the traditional velocity estimation and HRRP reconstruction algorithms become invalid, a novel HRRP reconstruction of high-speed target for under-sampled data is proposed. The Laplacian scale mixture (LSM) is used as the sparse prior of HRRP, and the variational Bayesian inference is utilized to derive its posterior, so as to reconstruct it with high resolution from the under-sampled data. Additionally, during the reconstruction of HRRP, the target velocity is estimated via joint constraint of entropy minimization and sparseness of HRRP to compensate the high order phase error brought by the target velocity to concentrate HRRP. Experimental results based on both simulated and measured data validate the effectiveness of the proposed Bayesian HRRP reconstruction algorithm.

An Entropy-Based Algorithm with Nonlocal Residual Learning for Image Compressive Sensing Recovery

Image recovery from compressive sensing (CS) measurement data, especially noisy data has always been challenging due to its implicit ill-posed nature, thus, to seek a domain where a signal can exhibit a high degree of sparsity and to design an effective algorithm have drawn increasingly more attention. Among various sparsity-based models, structured or group sparsity often leads to more powerful signal reconstruction techniques. In this paper, we propose a novel entropy-based algorithm for CS recovery to enhance image sparsity through learning the group sparsity of residual. To reduce the residual of similar packed patches, the group sparsity of residual is described by a Laplacian scale mixture (LSM) model, therefore, each singular value of the residual of similar packed patches is modeled as a Laplacian distribution with a variable scale parameter, to exploit the benefits of high-order dependency among sparse coefficients. Due to the latent variables, the maximum a posteriori (MAP) estimation of the sparse coefficients cannot be obtained, thus, we design a loss function for expectation–maximization (EM) method based on relative entropy. In the frame of EM iteration, the sparse coefficients can be estimated with the denoising-based approximate message passing (D-AMP) algorithm. Experimental results have shown that the proposed algorithm can significantly outperform existing CS techniques for image recovery.

Joint Sparse Aperture ISAR Autofocusing and Scaling via Modified Newton Method-Based Variational Bayesian Inference

For sparse aperture (SA) radar echoes, the coherence between the undersampled pulses is destroyed, which challenges the effectiveness of the traditional autofocusing and scaling in inverse synthetic aperture radar (ISAR) imaging. A novel Bayesian ISAR autofocusing and scaling algorithm for sparse aperture is proposed, which utilizes Laplacian scale mixture, as the sparse prior of ISAR image, and variational Bayesian inference based on the Laplacian approximation to derive its posterior. In addition, it learns the phase error, rotational velocity, and center of target from radar echo automatically during the reconstruction of ISAR image, so as to achieve ISAR autofocusing and scaling for SA. Because the parameters learning is not easy to converge with the undersampled data, a modified Newton method based on joint constraint of entropy and sparsity is proposed to guarantee fast convergence in a right direction. Experimental results based on both simulated and measured data validate the robustness of the proposed ISAR imaging algorithm against SA and noise.

Robust Tensor Approximation With Laplacian Scale Mixture Modeling for Multiframe Image and Video Denoising

Sparse and low-rank models have been widely studied in the literature of signal processing and computer vision. However, as the dimensionality of dataset increases (e.g., multispectral images, dynamic MRI images, and video sequences), the optimality of vector and matrix-based data representations and modeling tools becomes questionable. Inspired by recent advances in sparse and low-rank tensor analysis, we propose a novel robust tensor approximation (RTA) framework with the Laplacian Scale Mixture (LSM) modeling for three-dimensional (3-D) data and beyond. Our technical contributions are summarized as follows: first, conceptually similar to robust PCA, we consider its tensor extension here—i.e., low-rank tensor approximation in the presence of outliers modeled by sparse noise; second, built upon previous work on tensor sparsity, we propose to model tensor coefficients with an LSM prior and formulate a maximum a posterior estimation problem for noisy observations. Both unknown sparse coefficients and hidden LSM parameters can be efficiently estimated by the method of alternating optimization; and third, we have derived closed-form solutions for both subproblems and developed computationally efficient denoising techniques for multiframe images and video. Experimental results on three datasets have shown that the proposed algorithm can better preserve the sharpness of important image structures and outperform several existing state-of-the-art image/video denoising methods (e.g., BM4D/VBM4D and tensor dictionary learning).

Simultaneous sparse coding with Laplacian scale mixture prior for image restoration

Group-based sparse representation modeling of natural images codes each patch in a group as a sparse linear combination from an over-complete dictionary and assumes that the coding coefficients of each patch have a common set of nonzero support. This model has shown great success in image restoration (IR) applications; however, current group-based sparse models are simple extensions of traditional L0 or L1 sparse models and lack spatial adaption and principled fashion. We propose a group-based sparse model named as simultaneously sparse coding with Laplacian scale mixture (LSM) prior through probabilistic approach. In this model, the representation coefficients of each patch in group are characterized by the same LSM prior, which is dominated by the shared scale variables. By imposing a hyperprior distribution over the scale variables, the sparse coefficients and shared scale variables can be jointly estimated via alternating optimization. Furthermore, we generalize this model to process more general IR problems under the plug-and-play alternating direction method of multipliers framework. Extensive experiments on image denoising, deblurring, and single-image super-resolution demonstrate that the proposed method achieves notable objective and subjective improvements over many state-of-the-art restored methods.

Image Denoising via Improved Simultaneous Sparse Coding with Laplacian Scale Mixture

Image denoising is a well-studied problem closely related to sparse coding. Noticing that the Laplacian distribution has a strong sparseness, we use Laplacian scale mixture to model sparse coefficients. With the observation that prior information of an image is relevant to the estimation of sparse coefficients, we introduce the prior information into maximum a posteriori (MAP) estimation of sparse coefficients by an appropriate estimate of the probability density function. Extending to structured sparsity, a nonlocal image denoising model: Improved Simultaneous Sparse Coding with Laplacian Scale Mixture (ISSC-LSM) is proposed. The centering preprocessing, which admits biased-mean of sparse coefficients and saves expensive computation, is done firstly. By alternating minimization and learning an orthogonal PCA dictionary, an efficient algorithm with closed-form solutions is proposed. When applied to noise removal, our proposed ISSC-LSM can capture structured image features, and the adoption of image prior information leads to highly competitive denoising performance. Experimental results show that the proposed method often provides higher subjective and objective qualities than other competing approaches. Our method is most suitable for processing images with abundant self-repeating patterns by effectively suppressing undesirable artifacts while maintaining the textures and edges.