Wieghted Compressive Sensing

Sparse representation has a significant effect on various image processing applications such as image denoising, restoration, detection, etc. Existed inherent sparsity of natural images in some domains helps to reconstruct the signal with a lower number of measurements. To benefit from the sparsity, one should solve the L0-norm minimization problem which is NP-hard. However, it is proved that the L1-norm minimization techniques could reconstruct the signal exactly. It is also proved that in many cases, recovery performance can be enhanced by replacing the L1-norm with reweighted L1-norm. Here, our aim is to design novel weighted compressive sensing methods. Moreover, we develop our proposed algorithms on the block-based compressed sensing (BCS) to make it applicable to large size images. Currently, we have done two works; one based on the human visuality of natural images and the other using the singular value decomposition (SVD) of the images.

  • Weighted Compressive Sensing Based on The Human Visuality of Images

    The human eye is good at seeing small differences in brightness over a relatively large area, but not so good at distinguishing the exact strength of a high frequency brightness variation. This allows one to greatly reduce the amount of information in the high frequency components. Here, we design a weighting coefficients in reweighted L1-norm minimization based on the human visuality of images. We showed that this approach outperform existed state-of-the-art methods. Furthermore, our proposed approach is non-iterative and as a result very fast compared to other methods.

    Publications:

    • S.H. Safavi, F. Torkamani-Azar, “Cube-Based Perceptual Weighted Kronecker Compressive Sensing: Can we avoid non-visible redundancies acquisition?”, Elsevier J. Vis. Commun. Image R., vol. 49, pp. 338-350, 2017. [PDF] [DOI] [Code]

    • S.H. Safavi, F. Torkamani-Azar, “Perceptual Compressive Sensing based on Contrast Sensitivity Function: Can we avoid non-visible redundancies acquisition?”, The 25th Iranian Conference on Electrical Engineering (ICEE), pp. 2041-2046, 2017. [PDF] [DOI] [Code]

    • S.H. Safavi, F. Torkamani-Azar, “A novel Adaptive weighted Kronecker Compressive Sensing”, The 42nd IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2017), Ph.D. Forum. [PDF] [DOI] [Code]

    Some visualization results for the Forman video sequence:

    We reconstruct the video sequences when the subrate is equal to 0.2.

    Top Left: Original Video, Top Center: KCS, Top Right: Proposed Cube-based WKCS using standard JPEG quantization matrix.
    Bottom Left: Proposed Cube-based WKCS using Daly's quantization matrix, Bottom Center: Proposed Cube-based WKCS using CSF, Bottom Right: Proposed Cube-based WKCS using Spatio-temporal CSF.

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    Top Left: Original Video, Top Center: 3D KCS, Top Right: Proposed Cube-based 3D WKCS using standard JPEG quantization matrix.
    Bottom Left: Proposed Cube-based 3D WKCS using Daly's quantization matrix, Bottom Center: Proposed Cube-based 3D WKCS using CSF, Bottom Right: Proposed Cube-based 3D WKCS using Spatio-temporal CSF.

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  • Weighted Compressive Sensing Using Singular Value Decomposition

    In this work, our aim is to define some better transform domain in which the reweighted minimization problem work well. To find this transform domain, we propose to use the vectorized representation of the SVD of the signal. Note that the motivation behind the reweighted L1 minimization approach was that the larger coefficients of the signal are penalized more than smaller coefficients. Now, in this work, we propose to penalize the magnitude of the singular values of the multidimensional signal in a similar way. We compared the proposed approach with four state-of-the-art algorithms and showed that our method outperfomes their performance.

    Publication:

    • N. Abaei, S.H. Safavi , F. Torkamani-Azar, “Reweighted Block-Based Compressed Sensing Using Singular Value Decomposition” submitted to IET Signal Processing, 2016. [PDF] [Code]

    • N. Abaei, S.H. Safavi, F. Torkamani-Azar, “Reweighted Block-Based Compressed Sensing Using Singular Value Decomposition”, The 42nd IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2017), Ph.D. Forum. [PDF] [DOI] [Code]