Statistical modelling for wavelet-domain image fusion

Achim, Alin; Loza, AT; Bull,; Canagarajah, N.

doi:10.1016/b978-0-12-372529-5.00001-9

Cited by 10 publications

(8 citation statements)

References 22 publications

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“…Such algorithms endeavor to create a fused image containing the salient information from each source image without introducing artefacts or inconsistencies. Existing pixel-level fusion schemes range from simple averaging of the pixel values of registered images to more complex multiresolution (MR) pyramids and sparse methods [13,14]. In this paper, we pose the image fusion problem as an inverse one and develop an algorithm based on sparse representations and convex regularization that uses non-convex penalty functions.…”

Section: Introductionmentioning

confidence: 99%

Image fusion via sparse regularization with non-convex penalties

Anantrasirichai

Zheng

Selesnick

et al. 2020

Pattern Recognition Letters

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The L 1 norm regularized least squares method is often used for finding sparse approximate solutions and is widely used in 1-D signal restoration. Basis pursuit denoising (BPD) performs noise reduction in this way. However, the shortcoming of using L1 norm regularization is the underestimation of the true solution. Recently, a class of non-convex penalties have been proposed to improve this situation. This kind of penalty function is non-convex itself, but preserves the convexity property of the whole cost function. This approach has been confirmed to offer good performance in 1-D signal denoising. This paper demonstrates the aforementioned method to 2-D signals (images) and applies it to multisensor image fusion. The problem is posed as an inverse one and a corresponding cost function is judiciously designed to include two data attachment terms. The whole cost function is proved to be convex upon suitably choosing the non-convex penalty, so that the cost function minimization can be tackled by convex optimization approaches, which comprise simple computations. The performance of the proposed method is benchmarked against a number of state-of-the-art image fusion techniques and superior performance is demonstrated both visually and in terms of various assessment measures.

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Section: Introductionmentioning

confidence: 99%

Image fusion via sparse regularization with non-convex penalties

Anantrasirichai

Zheng

Selesnick

et al. 2020

Pattern Recognition Letters

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“…By taking the limit as s → 1 of the first and second derivatives of the logarithm of Φ SαS (s), we obtain the following results for the second-kind cumulants of the SαS model [11],…”

Section: B Alpha-stable Distributions For Modelling Ultrasound Datamentioning

confidence: 98%

Compressive sensing for ultrasound RF echoes using a-Stable Distributions

Achim

Buxton

Tzagkarakis

et al. 2010

2010 Annual International Conference of the IEEE Engineering in Medicine and Biology

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This paper introduces a novel framework for compressive sensing of biomedical ultrasonic signals based on modelling data with stable distributions. We propose an approach to ℓ(p) norm minimisation that employs the iteratively reweighted least squares (IRLS) algorithm but in which the parameter p is judiciously chosen by relating it to the characteristic exponent of the underlying alpha-stable distributed data. Our results show that the proposed algorithm, which we prefer to call S ± S-IRLS, outperforms previously proposed ℓ(1) minimisation algorithms, such as basis pursuit or orthogonal matching pursuit, both visually and in terms of PSNR.

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“…By taking the limit as s → 1 of the first and second derivatives of the logarithm of Φ SαS (s), we obtain the following results for the second-kind cumulants of the SαS model [28] …”

Section: ) Model Parameter Estimation For Sαs Distributionsmentioning

confidence: 99%

Reconstruction of Ultrasound RF Echoes Modeled as Stable Random Variables

Achim

Basarab

Tzagkarakis

et al. 2015

IEEE Trans. Comput. Imaging

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OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. Abstract-This paper introduces a new technique for reconstruction of biomedical ultrasound images from simulated compressive measurements, based on modeling data with stable distributions. The proposed algorithm exploits two types of prior information: on one hand, our proposed approach is based on the observation that ultrasound RF echoes are best characterized statistically by alpha-stable distributions. On the other hand, through knowledge of the acquisition process, the support of the RF echoes in the Fourier domain can be easily inferred. Together, these two facts form the basis of an p minimization approach that employs the iteratively reweighted least squares (IRLS) algorithm, but in which the parameter p is judiciously chosen, by relating it to the characteristic exponent of the underlying alpha-stable distributed data. We demonstrate, through Monte Carlo simulations, that the optimal value of the parameter p is just below that of the characteristic exponent α, which we estimate from the data. Our reconstruction results show that the proposed algorithm outperforms previously proposed reconstruction techniques, both visually and in terms of two objective evaluation measures.

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Statistical modelling for wavelet-domain image fusion

Cited by 10 publications

References 22 publications

Image fusion via sparse regularization with non-convex penalties

Image fusion via sparse regularization with non-convex penalties

Compressive sensing for ultrasound RF echoes using a-Stable Distributions

Reconstruction of Ultrasound RF Echoes Modeled as Stable Random Variables

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