Efficient design of a low redundant Discrete Shearlet Transform

Goossens, Bart; Aelterman, Jan; Luong, Hiêp; Pižurica, Aleksandra; Philips, Wilfried

doi:10.1109/lnla.2009.5278394

Cited by 28 publications

(27 citation statements)

References 33 publications

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“…In the middle of the room, a bright point light source is positioned, creating a dynamic range of 11 stops (i.e. the ratio of the brightest and smallest possible pixel intensity is about 2 11 ). Sensor signals were simulated and artificial noise was thereby generated, according to the procedure explained in Section "Camera noise modeling".…”

Section: Ground Truth Data With Simulated Noisementioning

confidence: 99%

“…A white stationary Gaussian noise assumption leads to simple and elegant denoising methods (such as wavelet shrinkage methods [1][2][3][4][5], total variation [6], anisotropic diffusion [7,8], NLMeans [9][10][11]). However, when applied to realistic problems (e.g., the suppression of noise from CCD/CMOS measures taken with mobile phones or other consumer cameras), these techniques often yield poor results [11][12][13]. The main problem is the noise model mismatch, which causes the http://asp.eurasipjournals.com/content/2012/1/171…”

Section: Introductionmentioning

confidence: 99%

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Realistic camera noise modeling with application to improved HDR synthesis

Goossens

Luong

Aelterman

et al. 2012

EURASIP J. Adv. Signal Process.

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Due to the ongoing miniaturization of digital camera sensors and the steady increase of the "number of megapixels", individual sensor elements of the camera become more sensitive to noise, even deteriorating the final image quality. To go around this problem, sophisticated processing algorithms in the devices, can help to maximally exploit the knowledge on the sensor characteristics (e.g., in terms of noise), and offer a better image reconstruction. Although a lot of research focuses on rather simplistic noise models, such as stationary additive white Gaussian noise, only limited attention has gone to more realistic digital camera noise models. In this article, we first present a digital camera noise model that takes several processing steps in the camera into account, such as sensor signal amplification, clipping, post-processing, ... We then apply this noise model to the reconstruction problem of high dynamic range (HDR) images from a small set of low dynamic range (LDR) exposures of a static scene. In literature, HDR reconstruction is mostly performed by computing a weighted average, in which the weights are directly related to the observer pixel intensities of the LDR image. In this work, we derive a Bayesian probabilistic formulation of a weighting function that is near-optimal in the MSE sense (or SNR sense) of the reconstructed HDR image, by assuming exponentially distributed irradiance values. We define the weighting function as the probability that the observed pixel intensity is approximately unbiased. The weighting function can be directly computed based on the noise model parameters, which gives rise to different symmetric and asymmetric shapes when electronic noise or photon noise is dominant. We also explain how to deal with the case that some of the noise model parameters are unknown and explain how the camera response function can be estimated using the presented noise model. Finally, experimental results are provided to support our findings.

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Section: Ground Truth Data With Simulated Noisementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Realistic camera noise modeling with application to improved HDR synthesis

Goossens

Luong

Aelterman

et al. 2012

EURASIP J. Adv. Signal Process.

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“…The most popular ones are based on total-variation (TV) or wavelets. Recently, more and more interest has been raised in sparse signal approximation using learned dictionaries [11] or multiresolution representations with better directional selectivity such as curvelets, ridgelets or shearlets [12,13,14]. Shearlets are theoretically optimal in representing images with edges, which is also referred to as optimal sparsity [13].…”

Section: Proposed Primal-dual Approachmentioning

confidence: 99%

A primal-dual algorithm for joint demosaicking and deconvolution

Luong

Goossens

Aelterman

et al. 2012

2012 19th IEEE International Conference on Image Processing

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In this paper, we present a first-order primal-dual algorithm for tackling the joint demosaicking and deconvolution problem. The proposed algorithm exploits the sparsity of both discrete gradient (TV) and shearlet coefficients as prior knowledge. In order to deal with this sparsity across the color channels, we first decorrelate the signals in color space before sparsifying them spatially, resulting in a separable transform. We demonstrate that this approach yields better results than employing group sparsity strategies. We propose to update the decorrelation operator during the image reconstruction, this approach will result in a significant improvement in PSNR. By relaxing the sparsity of the chrominance signals, we obtain both better objective and subjective image quality compared to other stateof-the-art demosaicking and deconvolution algorithms. Also, color artifacts due to demosaicking are suppressed very well.

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“…Initially, the implementations of Shearlet Transform was related to the application environment [12] [13]. Gradually, the implementations became more and more sophisticated and independent to its application [14] [15]. In general, there are two implementation types, one is in spatial domain, and the other is in frequency domain.…”

Section: Introductionmentioning

confidence: 99%

Dual Tree Complex Shearlet Transform and its Shift Invariance Properties

Chen

Zhang

Wang

2012

2012 International Conference on Industrial Control and Electronics Engineering

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In Shearlab, the publicized spatial implementation of Shearlet Transform is shift-variance because it is based on DWT, which is shift-variance. The deficiency of the spatial implementation scheme could be mitigated by the method of Dual Tree Complex Shearlet Transform (DT CST). In this paper, the definition of Complex Shearlet Transform is given, and then discussed the details of the DT CST about its theory, structure and implementation. Numerical results suggest that it is nearly shift-invariance.

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Efficient design of a low redundant Discrete Shearlet Transform

Cited by 28 publications

References 33 publications

Realistic camera noise modeling with application to improved HDR synthesis

Realistic camera noise modeling with application to improved HDR synthesis

A primal-dual algorithm for joint demosaicking and deconvolution

Dual Tree Complex Shearlet Transform and its Shift Invariance Properties

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