Xianbiao Shu | University of Illinois at Urbana-Champaign (original) (raw)

Papers by Xianbiao Shu

journal homepage: www.elsevier.com/locate/cviu

Handbook of Robust Low-Rank and Sparse Matrix Decomposition, 2016

Computer Vision – ECCV 2010, 2010

Compressive sampling (CS) is aimed at acquiring a signal or image from data which is deemed insuf... more Compressive sampling (CS) is aimed at acquiring a signal or image from data which is deemed insufficient by Nyquist/Shannon sampling theorem. Its main idea is to recover a signal from limited measurements by exploring the prior knowledge that the signal is sparse or compressible in some domain. In this paper, we propose a CS approach using a new total-variation measure TVL1, or equivalently TV 1 , which enforces the sparsity and the directional continuity in the gradient domain. Our TV 1 based CS is characterized by the following attributes. First, by minimizing the 1-norm of partial gradients, it can achieve greater accuracy than the widely-used TV 1 2 based CS. Second, it, named hybrid CS, combines low-resolution sampling (LRS) and random sampling (RS), which is motivated by our induction that these two sampling methods are complementary. Finally, our theoretical and experimental results demonstrate that our hybrid CS using TV 1 yields sharper and more accurate images.

2011 International Conference on Computer Vision, 2011

Compressive sampling (CS) aims at acquiring a signal at a sampling rate that is significantly bel... more Compressive sampling (CS) aims at acquiring a signal at a sampling rate that is significantly below the Nyquist rate. Its main idea is that a signal can be decoded from incomplete linear measurements by seeking its sparsity in some domain. Despite the remarkable progress in the theory of CS, little headway has been made in the compressive imaging (CI) camera. In this paper, a three-dimensional compressive sampling (3DCS) approach is proposed to reduce the required sampling rate of the CI camera to a practical level. In 3DCS, a generic three-dimensional sparsity measure (3DSM) is presented, which decodes a video from incomplete samples by exploiting its 3D piecewise smoothness and temporal low-rank property. In addition, an efficient decoding algorithm is developed for this 3DSM with guaranteed convergence. The experimental results show that our 3DCS requires a much lower sampling rate than the existing CS methods without compromising recovery accuracy.

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Guang pu xue yu guang pu fen xi = Guang pu, 2007

Reflectance spectra in the visible and near-infrared wavelength region provide a rapid and inexpe... more Reflectance spectra in the visible and near-infrared wavelength region provide a rapid and inexpensive means for determining the mineralogy of samples and obtaining information on chemical composition. Hydrocarbon microseepage theory establishes a cause-and-effect relation between oil and gas reservoirs and some special surface anomalies. Therefore the authors can explore for oil and gas by determining the reflectance spectra of surface anomalies. This determination can be fulfilled by means of field work and hyperspectral remote sensing. In the present paper, based on the analysis of reflectance spectra determined in the field of Qinghai X X area, firstly, a macroscopic feature of the reflectance spectra of typical observation points in the gas fields is presented. Secondly, absorption-band parameters of spectra such as the position, depth, width, and asymmetry are extracted. Based on the spectral absorption features of the spectra of 144 samples collected from the field, a spectra...

2014 IEEE International Conference on Computational Photography (ICCP), 2014

Compressive sampling (CS) aims at acquiring a signal at a sampling rate below the Nyquist rate by... more Compressive sampling (CS) aims at acquiring a signal at a sampling rate below the Nyquist rate by exploiting prior knowledge that a signal is sparse or correlated in some domain. Despite the remarkable progress in the theory of CS, the sampling rate on a single image required by CS is still very high in practice. In this paper, a non-local compressive sampling (NLCS) recovery method is proposed to further reduce the sampling rate by exploiting non-local patch correlation and local piecewise smoothness present in natural images. Two non-local sparsity measures, i.e., non-local wavelet sparsity and non-local joint sparsity, are proposed to exploit the patch correlation in NLCS. An efficient iterative algorithm is developed to solve the NLCS recovery problem, which is shown to have stable convergence behavior in experiments. The experimental results show that our NLCS significantly improves the state-of-the-art of image compressive sampling.

2012 IEEE Conference on Computer Vision and Pattern Recognition, 2012

Computer Vision and Image Understanding, 2012

Many computational imaging applications involve manipulating the incoming light beam in the apert... more Many computational imaging applications involve manipulating the incoming light beam in the aperture and image planes. However, accessing the aperture, which conventionally stands inside the imaging lens, is still challenging. In this paper, we present an approach that allows access to the aperture plane and enables dynamic control of its transmissivity, position, and orientation. Specifically, we present two kinds of compound imaging systems (CIS), CIS1 and CIS2, to reposition the aperture in front of and behind the imaging lens respectively. CIS1 repositions the aperture plane in front of the imaging lens and enables the dynamic control of the light beam coming to the lens. This control is quite useful in panoramic imaging at the single viewpoint. CIS2 uses a rear-attached relay system (lens) to replace the aperture plane behind the imaging lens, and enables the dynamic control of the imaging light jointly formed by the imaging lens and the relay lens. In this way, the common imaging beam can be coded or split in the aperture plane to achieve many imaging functions, such as coded aperture imaging, high dynamic range (HDR) imaging and light field sampling. In addition, CIS2 repositions the aperture behind, instead of inside, the relay lens, which allows the employment of the optimized relay lens to preserve the high imaging quality. Finally, we present the physical implementations of CIS1 and CIS2, to demonstrate (1) their effectiveness in providing access to the aperture and (2) the advantages of aperture manipulation in computational imaging applications.

Advances in Space Research, 2008

Reflectance spectra in the visible and near-infrared wavelengths provide a rapid and inexpensive ... more Reflectance spectra in the visible and near-infrared wavelengths provide a rapid and inexpensive means for determining the mineralogy of samples and obtaining information on chemical composition. Hydrocarbon microseepage theory establishes a cause-and-effect relation between oil and gas reservoirs and some special surface anomalies, which mainly include surface hydrocarbon microseepage and related alterations. Therefore, we can explore for oil, gas by determining reflectance spectra of surface anomalies. This idea has been applied to the R&D project of exploring for natural gas in Qinghai province of China using NASA EO-1 satellite with the Hyperion sensor (June 2005 to June 2006). In this project, in order to improve the accuracy of exploration targets of natural gas mapped in the field studied, an integrated practical system of exploration of oil and gas was built by the analysis of not only hyperspectral remote sensing data but also data provided from field work. In this paper, our efforts were focused on the analysis of the 799 reflectance spectra provided from the field work. In order to properly define the typical form of hydrocarbon microseepage with spectroscopy and fulfill the data analysis, it was necessary to build a spectral model. In this spectral model the most important features of hydrocarbon microseepage in the surface of our study area, i.e., diagnostic spectral macroscopic features and diagnostic spectral absorption features, were proposed and extracted, respectively. The distribution of coexisting anomalies, which results from both alteration minerals and hydrocarbons, is estimated by the diagnostic macroscopic features mainly using Spectral Angle Mapper (SAM) classifier. On the other hand, the diagnostic absorption features of two main absorption bands presented abundant local information, based on deep analysis of which, we are able to map the anomalies of alteration minerals and hydrocarbons, respectively. Additionally, a general framework of analysis and key classification algorithms applied to the Hyperion data have been introduced briefly. In our work, three exploration targets of natural gas were identified from the study area which covers 2100 km 2. In the three exploration targets, three wildcats have been drilled by China National Petroleum Corporation (CNPC) since July 2006, and all the three wells have been proven some industrial reserves.

2014 IEEE Conference on Computer Vision and Pattern Recognition, 2014

Low-rank matrix recovery from a corrupted observation has many applications in computer vision. C... more Low-rank matrix recovery from a corrupted observation has many applications in computer vision. Conventional methods address this problem by iterating between nuclear norm minimization and sparsity minimization. However, iterative nuclear norm minimization is computationally prohibitive for large-scale data (e.g., video) analysis. In this paper, we propose a Robust Orthogonal Subspace Learning (ROSL) method to achieve efficient low-rank recovery. Our intuition is a novel rank measure on the low-rank matrix that imposes the group sparsity of its coefficients under orthonormal subspace. We present an efficient sparse coding algorithm to minimize this rank measure and recover the low-rank matrix at quadratic complexity of the matrix size. We give theoretical proof to validate that this rank measure is lower bounded by nuclear norm and it has the same global minimum as the latter. To further accelerate ROSL to linear complexity, we also describe a faster version (ROSL+) empowered by random sampling. Our extensive experiments demonstrate that both ROSL and ROSL+ provide superior efficiency against the state-of-the-art methods at the same level of recovery accuracy.

ABSTRACT This dissertation works on advanced imaging systems using multiplexed sensing and compre... more ABSTRACT This dissertation works on advanced imaging systems using multiplexed sensing and compressive sensing (CS). Conventional cameras (e.g., pin-hole and lens cameras) follow the one-object-point-to-one-image-point or one-to-one (OTO) mapping model. Multipled sensing and compressive sensing attempt to improve conventional OTO cameras by exploring other object-to-image mapping models, such as one-to-multiple (OTM) divergent mapping, multiple-to-one (MTO) convergent mapping and multiple-to-multiple (MTM) random mapping, and respectively achieve two different advanced imaging functions. On one hand, multiplexed sensing attempts to acquire multi-modality information from the outside scene by multi-channel sensing and fuses a more informative image. On the other hand, compressive sensing, also called compressive sampling, aims at acquiring a signal/image at a lower sampling rate (below the Nyquist rate) by exploiting (1) the MTM random sampling and (2) the prior knowledge that a signal/image is sparse or correlated in some domain. The first design is a multiplexed imaging system that accesses and manipulates the lens aperture for many computational imaging applications. Multiplexed imaging often involves manipulating the incoming light beam on the aperture, which is located inside the lens housing and thus is challenging to access or modulate. In this system, a novel approach is proposed to provide an external aperture that enables dynamic control of its transmission, position and orientation. Specifically, a rear-attached relay system (lens) is mounted behind the imaging lens to reposition the aperture plane outside the imaging lens. The physical implementation of the multiplexed imaging system is presented to show (1) the effectiveness of providing access to the aperture and (2) the advantages of aperture manipulation in computational imaging applications. The second design is a hybrid compressive sensing camera for image acquisition. First, this hybrid compressive sensing camera further reduces the sampling rate of compressive sensing by combining the traditional MTM random sampling with MTO low-resolution sampling. In addition, we propose a new L1-norm based total-variation measure TVL1, which enforces the sparsity and the directional continuity in the partial gradient domain. Theoretical and experimental results show that this new TVL1 achieves higher recovery accuracy than the previous TV measure TVL1L2 in decoding images from compressive measurements. The third design is a three-dimensional compressive sensing (3DCS) camera for video acquisition. Despite the remarkable progress in the compressive sensing theory, little headway has been made in the compressive imaging (CI) camera and the required sampling rate for acquiring an image or video is still high. We propose a three-dimensional compressive sensing (3DCS) approach, which decodes a video from incomplete random samples by exploiting its 3D piecewise smoothness and temporal low-rank property. Experimental results show that 3DCS can reduce the required sampling rate for video acquisition to a practical level (i.e., 10%). In addition, an efficient decoding algorithm is developed for this 3DCS with guaranteed convergence. Finally, a promising physical implementation of the 3DCS camera using circulant sampling (or random convolution) is presented and a new random lens is presented to simplify the traditional random convolution implementation, i.e., four-dimensional correlator in Fourier optics. This random lens has much higher light-gathering power and higher imaging quality than other simple implementations, such as coded aperture, random pinhole array and random mirror array. In addition to sparsity and total variation, low-rankness is another new and encouraging measure in compressive sensing. However, robust low-rank recovery from compressive measurements is a time-consuming process and even its state-of-the-art (robust principal component analysis or RPCA) has a cubic complexity. The fourth design is an efficient low-rank recovery approach, called robust orthonormal subspace learning (ROSL). Compared with RPCA using nuclear norm, ROSL presents a novel rank measure that imposes the group sparsity under orthonormal subspace, which enables it to recover a low-rank matrix by fast sparse coding. Theoretical bounds are given to prove that minimizing this rank measure has the same global minimum as the nuclear norm minimization. In addition, an efficient algorithm (alternating direction method and block coordinate descent) is developed for ROSL and a random sampling algorithm is introduced to further accelerate ROSL such that ROSL+ has linear complexity of the matrix size. Extensive evaluations demonstrate that ROSL and ROSL+ achieve the state-of-art efficiency in low-rank recovery without compromising the accuracy. The fifth design is a non-local compressive sensing (NLCS) camera for image acquisition. While 3DCS achieves a low required sampling rate…

This dissertation works on advanced imaging systems using multiplexed sensing and compressive sen... more This dissertation works on advanced imaging systems using multiplexed sensing and compressive sensing (CS). Conventional cameras (e.g., pin-hole and lens cameras) follow the one-object-point-to-one-image-point or one-to-one (OTO) mapping model. Multipled sensing and compressive sensing attempt to improve conventional OTO cameras by exploring other object-to-image mapping models, such as one-to-multiple (OTM) divergent mapping, multiple-to-one (MTO) convergent mapping and multiple-to-multiple (MTM) random mapping, and respectively achieve two different advanced imaging functions. On one hand, multiplexed sensing attempts to acquire multi-modality information from the outside scene by multi-channel sensing and fuses a more informative image. On the other hand, compressive sensing, also called compressive sampling, aims at acquiring a signal/image at a lower sampling rate (below the Nyquist rate) by exploiting (1) the MTM random sampling and (2) the prior knowledge that a signal/image is sparse or correlated in some domain. The first design is a multiplexed imaging system that accesses and manipulates the lens aperture for many computational imaging applications. Multiplexed imaging often involves manipulating the incoming light beam on the aperture, which is located inside the lens housing and thus is challenging to access or modulate. In this system, a novel approach is proposed to provide an external aperture that enables dynamic control of its transmission, position and orientation. Specifically, a rear-attached relay system (lens) is mounted behind the imaging lens to reposition the aperture plane outside the imaging lens. The physical implementation of the multiplexed imaging system is presented to show (1) the effectiveness of providing access to the aperture and (2) the advantages of aperture manipulation in computational imaging applications. The second design is a hybrid compressive sensing camera for image acquisition. First, this hybrid compressive sensing camera further reduces the sampling rate of compressive sensing by combining the traditional MTM random sampling with MTO low-resolution sampling. In addition, we propose a new L1-norm based total-variation measure TVL1, which enforces the sparsity and the directional continuity in the partial gradient domain. Theoretical and experimental results show that this new TVL1 achieves higher recovery accuracy than the previous TV measure TVL1L2 in decoding images from compressive measurements. The third design is a three-dimensional compressive sensing (3DCS) camera for video acquisition. Despite the remarkable progress in the compressive sensing theory, little headway has been made in the compressive imaging (CI) camera and the required sampling rate for acquiring an image or video is still high. We propose a three-dimensional compressive sensing (3DCS) approach, which decodes a video from incomplete random samples by exploiting its 3D piecewise smoothness and temporal low-rank property. Experimental results show that 3DCS can reduce the required sampling rate for video acquisition to a practical level (i.e., 10%). In addition, an efficient decoding algorithm is developed for this 3DCS with guaranteed convergence. Finally, a promising physical implementation of the 3DCS camera using circulant sampling (or random convolution) is presented and a new random lens is presented to simplify the traditional random convolution implementation, i.e., four-dimensional correlator in Fourier optics. This random lens has much higher light-gathering power and higher imaging quality than other simple implementations, such as coded aperture, random pinhole array and random mirror array. In addition to sparsity and total variation, low-rankness is another new and encouraging measure in compressive sensing. However, robust low-rank recovery from compressive measurements is a time-consuming process and even its state-of-the-art (robust principal component analysis or RPCA) has a cubic complexity. The fourth design is an efficient low-rank recovery approach, called robust orthonormal subspace learning (ROSL). Compared with RPCA using nuclear norm, ROSL presents a novel rank measure that imposes the group sparsity under orthonormal subspace, which enables it to recover a low-rank matrix by fast sparse coding. Theoretical bounds are given to prove that minimizing this rank measure has the same global minimum as the nuclear norm minimization. In addition, an efficient algorithm (alternating direction method and block coordinate descent) is developed for ROSL and a random sampling algorithm is introduced to further accelerate ROSL such that ROSL+ has linear complexity of the matrix size. Extensive evaluations demonstrate that ROSL and ROSL+ achieve the state-of-art efficiency in low-rank recovery without compromising the accuracy. The fifth design is a non-local compressive sensing (NLCS) camera for image acquisition. While 3DCS achieves a low required sampling rate for video acquisition, image CS still requires a high sampling rate. Motivated by the non-local mean approaches in image restoration, a non-local compressive sensing (NLCS) recovery method is proposed, which further reduces the sampling rate by exploiting the non-local patch correlation and the local piecewise smoothness in natural images. Two non-local sparsity measures, i.e., non-local wavelet sparsity and non-local joint sparsity, are proposed to obtain patch correlation in NLCS. In addition, an efficient iterative algorithm is developed to solve the NLCS recovery problem, which is shown to have stable convergence behavior in experiments. The experimental results show that our NLCS significantly improves the state-of-the-art image CS and that non-local joint sparsity is better than non-local wavelet sparsity in terms of recovery accuracy.