Improved Total Variation based Image Compressive Sensing Recovery by Nonlocal Regularization

Recently, total variation (TV) based minimization algorithms have achieved great success in compressive sensing (CS) recovery for natural images due to its virtue of preserving edges. However, the use of TV is not able to recover the fine details and textures, and often suffers from undesirable staircase artifact. To reduce these effects, this letter presents an improved TV based image CS recovery algorithm by introducing a new nonlocal regularization constraint into CS optimization problem. The nonlocal regularization is built on the well known nonlocal means (NLM) filtering and takes advantage of self-similarity in images, which helps to suppress the staircase effect and restore the fine details. Furthermore, an efficient augmented Lagrangian based algorithm is developed to solve the above combined TV and nonlocal regularization constrained problem. Experimental results demonstrate that the proposed algorithm achieves significant performance improvements over the state-of-the-art TV based algorithm in both PSNR and visual perception.Comment: 4 Pages, 1 figures, 3 tables, to be published at IEEE Int. Symposium of Circuits and Systems (ISCAS) 201

Combined First- and Second-Order Variational Model for Image Compressive Sensing

A hybrid variational model combined first- and second-order total variation for image reconstruction from its finite number of noisy compressive samples is proposed in this paper. Inspired by majorization-minimization scheme, we develop an efficient algorithm to seek the optimal solution of the proposed model by successively minimizing a sequence of quadratic surrogate penalties. Both the nature and magnetic resonance (MR) images are used to compare its numerical performance with four state-of-the-art algorithms. Experimental results demonstrate that the proposed algorithm obtained a significant improvement over related state-of-the-art algorithms in terms of the reconstruction relative error (RE) and peak signal to noise ratio (PSNR)

Sparse variational regularization for visual motion estimation

The computation of visual motion is a key component in numerous computer vision tasks such as object detection, visual object tracking and activity recognition. Despite exten- sive research effort, efficient handling of motion discontinuities, occlusions and illumina- tion changes still remains elusive in visual motion estimation. The work presented in this thesis utilizes variational methods to handle the aforementioned problems because these methods allow the integration of various mathematical concepts into a single en- ergy minimization framework. This thesis applies the concepts from signal sparsity to the variational regularization for visual motion estimation. The regularization is designed in such a way that it handles motion discontinuities and can detect object occlusions

Informative sensing : theory and applications

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2012.Cataloged from PDF version of thesis.Includes bibliographical references (p. 145-156).Compressed sensing is a recent theory for the sampling and reconstruction of sparse signals. Sparse signals only occupy a tiny fraction of the entire signal space and thus have a small amount of information, relative to their dimension. The theory tells us that the information can be captured faithfully with few random measurement samples, even far below the Nyquist rate. Despite the successful story, we question how the theory would change if we had a more precise prior than the simple sparsity model. Hence, we consider the settings where the prior is encoded as a probability density. In a Bayesian perspective, we see the signal recovery as an inference, in which we estimate the unmeasured dimensions of the signal given the incomplete measurements. We claim that good sensors should somehow be designed to minimize the uncertainty of the inference. In this thesis, we primarily use Shannon's entropy to measure the uncertainty and in effect pursue the InfoMax principle, rather than the restricted isometry property, in optimizing the sensors. By approximate analysis on sparse signals, we found random projections, typical in the compressed sensing literature, to be InfoMax optimal if the sparse coefficients are independent and identically distributed (i.i.d.). If not, however, we could find a different set of projections which, in signal reconstruction, consistently outperformed random or other types of measurements. In particular, if the coefficients are groupwise i.i.d., groupwise random projections with nonuniform sampling rate per group prove asymptotically Info- Max optimal. Such a groupwise i.i.d. pattern roughly appears in natural images when the wavelet basis is partitioned into groups according to the scale. Consequently, we applied the groupwise random projections to the sensing of natural images. We also considered designing an optimal color filter array for single-chip cameras. In this case, the feasible set of projections is highly restricted because multiplexing across pixels is not allowed. Nevertheless, our principle still applies. By minimizing the uncertainty of the unmeasured colors given the measured ones, we could find new color filter arrays which showed better demosaicking performance in comparison with Bayer or other existing color filter arrays.by Hyun Sung Chang.Ph.D