500 research outputs found
Bayesian Robust Tensor Factorization for Incomplete Multiway Data
We propose a generative model for robust tensor factorization in the presence
of both missing data and outliers. The objective is to explicitly infer the
underlying low-CP-rank tensor capturing the global information and a sparse
tensor capturing the local information (also considered as outliers), thus
providing the robust predictive distribution over missing entries. The
low-CP-rank tensor is modeled by multilinear interactions between multiple
latent factors on which the column sparsity is enforced by a hierarchical
prior, while the sparse tensor is modeled by a hierarchical view of Student-
distribution that associates an individual hyperparameter with each element
independently. For model learning, we develop an efficient closed-form
variational inference under a fully Bayesian treatment, which can effectively
prevent the overfitting problem and scales linearly with data size. In contrast
to existing related works, our method can perform model selection automatically
and implicitly without need of tuning parameters. More specifically, it can
discover the groundtruth of CP rank and automatically adapt the sparsity
inducing priors to various types of outliers. In addition, the tradeoff between
the low-rank approximation and the sparse representation can be optimized in
the sense of maximum model evidence. The extensive experiments and comparisons
with many state-of-the-art algorithms on both synthetic and real-world datasets
demonstrate the superiorities of our method from several perspectives.Comment: in IEEE Transactions on Neural Networks and Learning Systems, 201
Variational semi-blind sparse deconvolution with orthogonal kernel bases and its application to MRFM
We present a variational Bayesian method of joint image reconstruction and point spread function (PSF) estimation when the PSF of the imaging device is only partially known. To solve this semi-blind deconvolution problem, prior distributions are specified for the PSF and the 3D image. Joint image reconstruction and PSF estimation is then performed within a Bayesian framework, using a variational algorithm to estimate the posterior distribution. The image prior distribution imposes an explicit atomic measure that corresponds to image sparsity. Importantly, the proposed Bayesian deconvolution algorithm does not require hand tuning. Simulation results clearly demonstrate that the semi-blind deconvolution algorithm compares favorably with previous Markov chain Monte Carlo (MCMC) version of myopic sparse reconstruction. It significantly outperforms mismatched non-blind algorithms that rely on the assumption of the perfect knowledge of the PSF. The algorithm is illustrated on real data from magnetic resonance force microscopy (MRFM)
Variational semi-blind sparse deconvolution with orthogonal kernel bases and its application to MRFM
We present a variational Bayesian method of joint image reconstruction and point spread function (PSF) estimation when the PSF of the imaging device is only partially known. To solve this semi-blind deconvolution problem, prior distributions are specified for the PSF and the 3D image. Joint image reconstruction and PSF estimation is then performed within a Bayesian framework, using a variational algorithm to estimate the posterior distribution. The image prior distribution imposes an explicit atomic measure that corresponds to image sparsity. Importantly, the proposed Bayesian deconvolution algorithm does not require hand tuning. Simulation results clearly demonstrate that the semi-blind deconvolution algorithm compares favorably with previous Markov chain Monte Carlo (MCMC) version of myopic sparse reconstruction. It significantly outperforms mismatched non-blind algorithms that rely on the assumption of the perfect knowledge of the PSF. The algorithm is illustrated on real data from magnetic resonance force microscopy (MRFM)
ISTA-Net: Interpretable Optimization-Inspired Deep Network for Image Compressive Sensing
With the aim of developing a fast yet accurate algorithm for compressive
sensing (CS) reconstruction of natural images, we combine in this paper the
merits of two existing categories of CS methods: the structure insights of
traditional optimization-based methods and the speed of recent network-based
ones. Specifically, we propose a novel structured deep network, dubbed
ISTA-Net, which is inspired by the Iterative Shrinkage-Thresholding Algorithm
(ISTA) for optimizing a general norm CS reconstruction model. To cast
ISTA into deep network form, we develop an effective strategy to solve the
proximal mapping associated with the sparsity-inducing regularizer using
nonlinear transforms. All the parameters in ISTA-Net (\eg nonlinear transforms,
shrinkage thresholds, step sizes, etc.) are learned end-to-end, rather than
being hand-crafted. Moreover, considering that the residuals of natural images
are more compressible, an enhanced version of ISTA-Net in the residual domain,
dubbed {ISTA-Net}, is derived to further improve CS reconstruction.
Extensive CS experiments demonstrate that the proposed ISTA-Nets outperform
existing state-of-the-art optimization-based and network-based CS methods by
large margins, while maintaining fast computational speed. Our source codes are
available: \textsl{http://jianzhang.tech/projects/ISTA-Net}.Comment: 10 pages, 6 figures, 4 Tables. To appear in CVPR 201
Salient Object Detection via Structured Matrix Decomposition
Low-rank recovery models have shown potential for salient object detection, where a matrix is decomposed into a low-rank
matrix representing image background and a sparse matrix identifying salient objects. Two deficiencies, however, still exist. First,
previous work typically assumes the elements in the sparse matrix are mutually independent, ignoring the spatial and pattern relations
of image regions. Second, when the low-rank and sparse matrices are relatively coherent, e.g., when there are similarities between the
salient objects and background or when the background is complicated, it is difficult for previous models to disentangle them. To
address these problems, we propose a novel structured matrix decomposition model with two structural regularizations: (1) a
tree-structured sparsity-inducing regularization that captures the image structure and enforces patches from the same object to have
similar saliency values, and (2) a Laplacian regularization that enlarges the gaps between salient objects and the background in feature
space. Furthermore, high-level priors are integrated to guide the matrix decomposition and boost the detection. We evaluate our model
for salient object detection on five challenging datasets including single object, multiple objects and complex scene images, and show
competitive results as compared with 24 state-of-the-art methods in terms of seven performance metrics
Bayesian Linear Regression with Cauchy Prior and Its Application in Sparse MIMO Radar
In this paper, a sparse signal recovery algorithm using Bayesian linear
regression with Cauchy prior (BLRC) is proposed. Utilizing an approximate
expectation maximization(AEM) scheme, a systematic hyper-parameter updating
strategy is developed to make BLRC practical in highly dynamic scenarios.
Remarkably, with a more compact latent space, BLRC not only possesses essential
features of the well-known sparse Bayesian learning (SBL) and iterative
reweighted l2 (IR-l2) algorithms but also outperforms them. Using sparse array
(SPA) and coprime array (CPA), numerical analyses are first performed to show
the superior performance of BLRC under various noise levels, array sizes, and
sparsity levels. Applications of BLRC to sparse multiple-input and
multiple-output (MIMO) radar array signal processing are then carried out to
show that the proposed BLRC can efficiently produce high-resolution images of
the targets.Comment: 22 page
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