Tomographic X-Ray Data Of A Walnut

Hämäläinen, K.; Harhanen, Lauri; Kallonen, Aki; Kujanpää, Antti; Niemi, Esa; Siltanen, Samuli

doi:10.5281/zenodo.1254206

Cited by 6 publications

(12 citation statements)

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“…For each of the 3 cases shown in Figure 5, starting with K = 665 modulo samples acquired with sampling rate T = 75 µs, the signal's effective bandwidth is observed to be approximately 1000 Hz. Note that this band-limitation is not due to the ADC that we apply when sampling ρ θ , but already present in the original data set [27]. Using our recovery method, we obtain an HDR reconstruction with mean squared error of at most 10 −3 (in each case).…”

Section: Experimental Demonstration For Synthetic Datamentioning

confidence: 99%

“…As we derive for a benchmark signal model, our method can also lead to large savings in the number of samples as compared to adjusted existing approaches. To show the applicability of our approach we finally provide numerical experiments in Section 4, where we in addition to the classical Shepp-Logan phantom also consider the open-source walnut dataset [27] and show hardware demonstrations using our custom designed prototype modulo ADC.…”

Section: Towards High-dynamic-range Tomographymentioning

confidence: 99%

“…The purpose of our numerical experiments is to demonstrate the single shot, HDR reconstruction approach based on the MRT. Starting with the benchmark "Shepp-Logan Phantom" that serves as a simulation study, we use the open source "Walnut Dataset" [27] that includes realistic uncertainties arising from the tomography hardware. This dataset is then used in two different configurations.…”

Section: Towards High-dynamic-range Tomographymentioning

confidence: 99%

“…Our findings confirm that our approach is robust to realistic uncertainties added in the sampling pipeline due to a practical implementation. To this end, we consider the Walnut dataset from [27], which is transformed to parallel beam geometry with M = 600 and K = 1128 corresponding to T = 1 /1128. Moreover, the Radon data is normalized to the dynamical range [0, 1] so that Rf ∞ = 1, see Figure 4 The reconstructions with our proposed US-FBP method are shown in Figures 4(e) and 4(f), where we again use the cosine reconstruction filter.…”

Section: Experimental Demonstration For Synthetic Datamentioning

confidence: 99%

“…Hardware Experiment with Prototype ADC. To further evaluate the feasibility of our work in a realistic setting, we consider the Walnut dataset from [27] from the previous subsection and physically digitize it using our prototype modulo ADC that converts a continuous function into modulo samples. To set up our experiment, we start with the Walnut Radon Transform projections p θ = R θ f at a given angle θ and physically interpolate these measurements using an electronic function generator to obtain a continuous-time analog signal ρ θ .…”

Section: Experimental Demonstration For Synthetic Datamentioning

confidence: 99%

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The Modulo Radon Transform: Theory, Algorithms and Applications

Beckmann¹,

Bhandari²,

Krahmer³

2021

Preprint

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Recently, experiments have been reported where researchers were able to perform high dynamic range (HDR) tomography in a heuristic fashion, by fusing multiple tomographic projections. This approach to HDR tomography has been inspired by HDR photography and inherits the same disadvantages. Taking a computational imaging approach to the HDR tomography problem, we here suggest a new model based on the Modulo Radon Transform (MRT), which we rigorously introduce and analyze. By harnessing a joint design between hardware and algorithms, we present a singleshot HDR tomography approach, which to our knowledge, is the only approach that is backed by mathematical guarantees. On the hardware front, instead of recording the Radon Transform projections that my potentially saturate, we propose to measure modulo values of the same. This ensures that the HDR measurements are folded into a lower dynamic range. On the algorithmic front, our recovery algorithms reconstruct the HDR images from folded measurements. Beyond mathematical aspects such as injectivity and inversion of the MRT for different scenarios including band-limited and approximately compactly supported images, we also provide a first proof-of-concept demonstration. To do so, we implement MRT by experimentally folding tomographic measurements available as an open source data set using our custom designed modulo hardware. Our reconstruction clearly shows the advantages of our approach for experimental data. In this way, our MRT based solution paves a path for HDR acquisition in a number of related imaging problems.

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Section: Experimental Demonstration For Synthetic Datamentioning

confidence: 99%

Section: Towards High-dynamic-range Tomographymentioning

confidence: 99%

Section: Towards High-dynamic-range Tomographymentioning

confidence: 99%

Section: Experimental Demonstration For Synthetic Datamentioning

confidence: 99%

Section: Experimental Demonstration For Synthetic Datamentioning

confidence: 99%

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The Modulo Radon Transform: Theory, Algorithms and Applications

Beckmann¹,

Bhandari²,

Krahmer³

2021

Preprint

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A content-adaptive unstructured grid based regularized CT reconstruction method with a SART-type preconditioned fixed-point proximity algorithm

Chen¹,

Lu²,

Ma³

et al. 2022

Inverse Problems

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The goal of this study is to develop a new computed tomography (CT) image reconstruction method, aiming at improving the quality of the reconstructed images of existing methods while reducing computational costs. Existing CT reconstruction is modeled by pixel-based piecewise constant approximations of the integral equation that describes the CT projection data acquisition process. Using these approximations imposes a bottleneck model error and results in a discrete system of a large size. We propose to develop a content-adaptive unstructured grid (CAUG) based regularized CT reconstruction method to address these issues. Speciﬁcally, we design a CAUG of the image domain to sparsely represent the underlying image, and introduce a CAUG-based piecewise linear approximation of the integral equation by employing a collocation method. We further apply a regularization deﬁned on the CAUG for the resulting illposed linear system, which may lead to a sparse linear representation for the underlying solution. The regularized CT reconstruction is formulated as a convex optimization problem, whose objective function consists of a weighted least square norm based fidelity term, a regularization term and a constraint term. Here, the corresponding weighted matrix is derived from the simultaneous algebraic reconstruction technique (SART). We then develop a SART-type preconditioned fixed-point proximity algorithm to solve the optimization problem. Convergence analysis is provided for the resulting iterative algorithm. Numerical experiments demonstrate the outperformance of the proposed method over several existing methods in terms of both suppressing noise and reducing computational costs. These methods include the SART without regularization and with quadratic regularization on the CAUG, the traditional total variation (TV) regularized reconstruction method and the TV superiorized conjugate gradient method on the pixel grid.

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Controlling Neural Networks via Energy Dissipation

Moeller

Moellenhoff

Cremers³

2019

2019 IEEE/CVF International Conference on Computer Vision (ICCV)

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The last decade has shown a tremendous success in solving various computer vision problems with the help of deep learning techniques. Lately, many works have demonstrated that learning-based approaches with suitable network architectures even exhibit superior performance for the solution of (ill-posed) image reconstruction problems such as deblurring, super-resolution, or medical image reconstruction. The drawback of purely learning-based methods, however, is that they cannot provide provable guarantees for the trained network to follow a given data formation process during inference. In this work we propose energy dissipating networks that iteratively compute a descent direction with respect to a given cost function or energy at the currently estimated reconstruction. Therefore, an adaptive step size rule such as a line-search, along with a suitable number of iterations can guarantee the reconstruction to follow a given data formation model encoded in the energy to arbitrary precision, and hence control the model's behavior even during test time. We prove that under standard assumptions, descent using the direction predicted by the network converges (linearly) to the global minimum of the energy. We illustrate the effectiveness of the proposed approach in experiments on single image super resolution and computed tomography (CT) reconstruction, and further illustrate extensions to convex feasibility problems.

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Tomographic X-Ray Data Of A Walnut

Cited by 6 publications

References 1 publication

The Modulo Radon Transform: Theory, Algorithms and Applications

The Modulo Radon Transform: Theory, Algorithms and Applications

A content-adaptive unstructured grid based regularized CT reconstruction method with a SART-type preconditioned fixed-point proximity algorithm

Controlling Neural Networks via Energy Dissipation

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