Frequency selective signal extrapolation for compensation of missing data in sinograms

Herraiz, Joaquín L.; España, Samuel; Vicente, E.; Herranz, Elena; Desco, Manuel; Vaquero, J.J.; Udías, J. M.

doi:10.1109/nssmic.2008.4774234

Cited by 11 publications

(10 citation statements)

References 10 publications

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“…While in non-rotating scanners the sinogram may have large gaps [25] of missing data, for a continuous rotating scanner such as VrPET, there are no missing data due to gaps between detector blocks.…”

Section: A Brief Description Of the Cpu Implementationmentioning

confidence: 99%

GPU-Based Fast Iterative Reconstruction of Fully 3-D PET Sinograms

Herraiz

España

Cabido

et al. 2011

IEEE Trans. Nucl. Sci.

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Abstract-This work presents a graphics processing unit (GPU)-based implementation of a fully 3-D PET iterative reconstruction code, FIRST (Fast Iterative Reconstruction Software for [PET] Tomography), which was developed by our group. We describe the main steps followed to convert the FIRST code (which can run on several CPUs using the message passing interface [MPI] protocol) into a code where the main time-consuming parts of the reconstruction process (forward and backward projection) are massively parallelized on a GPU. Our objective was to obtain significant acceleration of the reconstruction without compromising the image quality or the flexibility of the CPU implementation. Therefore, we implemented a GPU version using an abstraction layer for the GPU, namely, CUDA C. The code reconstructs images from sinogram data, and with the same System Response Matrix obtained from Monte Carlo simulations than the CPU version. The use of memory was optimized to ensure good performance in the GPU. The code was adapted for the VrPET small-animal PET scanner. The CUDA version is more than 70 times faster than the original code running in a single core of a high-end CPU, with no loss of accuracy.

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Section: A Brief Description Of the Cpu Implementationmentioning

confidence: 99%

GPU-Based Fast Iterative Reconstruction of Fully 3-D PET Sinograms

Herraiz

España

Cabido

et al. 2011

IEEE Trans. Nucl. Sci.

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“…Here, again fast orthogonality deficiency compensation is used to derive the estimate for the expansion coefficient from the projection coefficient. Finally, the update of the model in every iteration can be carried out according to (9).…”

Section: Using R (ν)mentioning

confidence: 99%

“…SE iteratively generates a model of the signal to be extrapolated as weighted superposition of basis functions. In the past years, this extrapolation algorithm also has been adopted by several others like [9,10] to solve extrapolation problems in their contexts.…”

Section: Introductionmentioning

confidence: 99%

A Fast Algorithm for Selective Signal Extrapolation with Arbitrary Basis Functions

Seiler

Kaup

2011

EURASIP J. Adv. Signal Process.

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Signal extrapolation is an important task in digital signal processing for extending known signals into unknown areas. The Selective Extrapolation is a very effective algorithm to achieve this. Thereby, the extrapolation is obtained by generating a model of the signal to be extrapolated as weighted superposition of basis functions. Unfortunately, this algorithm is computationally very expensive and, up to now, efficient implementations exist only for basis function sets that emanate from discrete transforms. Within the scope of this contribution, a novel efficient solution for Selective Extrapolation is presented for utilization with arbitrary basis functions. The proposed algorithm mathematically behaves identically to the original Selective Extrapolation but is several decades faster. Furthermore, it is able to outperform existent fast transform domain algorithms which are limited to basis function sets that belong to the corresponding transform. With that, the novel algorithm allows for an efficient use of arbitrary basis functions, even if they are only numerically defined.

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“…Due to the non-regularity, visually disturbing aliasing artifacts that conventionally occur for regular sampling can be reduced [2,3,4]. For the reconstruction, frequency selective reconstruction (FSR) has shown to be a successful reconstruction scheme for various inpainting and extrapolation tasks [5,6] and gave best results for non-regular sampling and quarter sampling in [1,7,8]. Quarter sampling, as well as any nonregular sub-sampling, can be seen as a special case of compressed sensing [9,10] as has been shown in [7,11].…”

Section: Introductionmentioning

confidence: 99%

Novel Consistency Check For Fast Recursive Reconstruction Of Non-Regularly Sampled Video Data

Grosche¹,

Seiler²,

Kaup³

2021

2021 IEEE International Conference on Image Processing (ICIP)

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Quarter sampling is a novel sensor design that allows for an acquisition of higher resolution images without increasing the number of pixels. When being used for video data, one out of four pixels is measured in each frame. Effectively, this leads to a non-regular spatio-temporal sub-sampling. Compared to purely spatial or temporal sub-sampling, this allows for an increased reconstruction quality, as aliasing artifacts can be reduced. For the fast reconstruction of such sensor data with a fixed mask, recursive variant of frequency selective reconstruction (FSR) was proposed. Here, pixels measured in previous frames are projected into the current frame to support its reconstruction. In doing so, the motion between the frames is computed using template matching. Since some of the motion vectors may be erroneous, it is important to perform a proper consistency checking. In this paper, we propose faster consistency checking methods as well as a novel recursive FSR that uses the projected pixels different than in literature and can handle dynamic masks. Altogether, we are able to significantly increase the reconstruction quality by +1.01 dB compared to the state-of-the-art recursive reconstruction method using a fixed mask. Compared to a single frame reconstruction, an average gain of about +1.52 dB is achieved for dynamic masks. At the same time, the computational complexity of the consistency checks is reduced by a factor of 13 compared to the literature algorithm.

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Frequency selective signal extrapolation for compensation of missing data in sinograms

Cited by 11 publications

References 10 publications

GPU-Based Fast Iterative Reconstruction of Fully 3-D PET Sinograms

GPU-Based Fast Iterative Reconstruction of Fully 3-D PET Sinograms

A Fast Algorithm for Selective Signal Extrapolation with Arbitrary Basis Functions

Novel Consistency Check For Fast Recursive Reconstruction Of Non-Regularly Sampled Video Data

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