## Implementing Algorithms for Signal and Image Reconstruction on Graphical Processing Units

Citations: | 6 - 2 self |

### BibTeX

@MISC{Lee_implementingalgorithms,

author = {Sangkyun Lee and Stephen J. Wright},

title = {Implementing Algorithms for Signal and Image Reconstruction on Graphical Processing Units},

year = {}

}

### OpenURL

### Abstract

Several highly effective algorithms that have been proposed recently for compressed sensing and image processing applications can be implemented efficiently on commodity graphical processing units (GPUs). The properties of algorithms and application that make for efficient GPU implementation are discussed, and computational results for several algorithms are presented that show large speedups over CPU implementations.

### Citations

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Citation Context ...y concerning the effectiveness of these formulations for finding sparse solutions of Ax = y can be found in the papers of Donoho [12, 11], Candès and Tao [5], and Candès, Romberg, and Tao [4]. Donoho =-=[10]-=- and Candès [6] give introductions to compressed sensing and discuss the various contexts in which these problems arise. 3.2. Algorithms. The optimization formulations above are conceptually simple — ... |

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Citation Context ... is x = 0, where τmax := ‖A T y‖∞. (3.3) Theory concerning the effectiveness of these formulations for finding sparse solutions of Ax = y can be found in the papers of Donoho [12, 11], Candès and Tao =-=[5]-=-, and Candès, Romberg, and Tao [4]. Donoho [10] and Candès [6] give introductions to compressed sensing and discuss the various contexts in which these problems arise. 3.2. Algorithms. The optimizatio... |

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Citation Context ... effectiveness of these formulations for finding sparse solutions of Ax = y can be found in the papers of Donoho [12, 11], Candès and Tao [5], and Candès, Romberg, and Tao [4]. Donoho [10] and Candès =-=[6]-=- give introductions to compressed sensing and discuss the various contexts in which these problems arise. 3.2. Algorithms. The optimization formulations above are conceptually simple — (3.1) can be wr... |

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Citation Context ...ly drawn from a discrete Fourier transform (DFT). As a sample of the vast algorithmic literature, we mention the iterative thresholding / shrinking (IST) approach [9, 13]; extensions of this approach =-=[21, 2]-=- based on the optimal first-order methodology of Nesterov [19, 20]; a variant of IST that uses a “continuation” strategy of successively reducing the parameter τ in (3.2) [16]; interiorpoint methods [... |

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Citation Context ...strategy of successively reducing the parameter τ in (3.2) [16]; interiorpoint methods [27, 18, 3]; and gradient projection applied to the bound-constrained quadratic programming formulation of (3.2) =-=[14]-=-. We focus in this paper on the SpaRSA approach of [33], which can be viewed as an accelerated variant of IST. From the current iterate xk , SpaRSA obtains the newSIGNAL AND IMAGE RECONSTRUCTION ALGO... |

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Citation Context ...s), where A consists of m rows randomly drawn from a discrete Fourier transform (DFT). As a sample of the vast algorithmic literature, we mention the iterative thresholding / shrinking (IST) approach =-=[9, 13]-=-; extensions of this approach [21, 2] based on the optimal first-order methodology of Nesterov [19, 20]; a variant of IST that uses a “continuation” strategy of successively reducing the parameter τ i... |

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Citation Context ...s), where A consists of m rows randomly drawn from a discrete Fourier transform (DFT). As a sample of the vast algorithmic literature, we mention the iterative thresholding / shrinking (IST) approach =-=[9, 13]-=-; extensions of this approach [21, 2] based on the optimal first-order methodology of Nesterov [19, 20]; a variant of IST that uses a “continuation” strategy of successively reducing the parameter τ i... |

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Citation Context ....2) [16]; interiorpoint methods [27, 18, 3]; and gradient projection applied to the bound-constrained quadratic programming formulation of (3.2) [14]. We focus in this paper on the SpaRSA approach of =-=[33]-=-, which can be viewed as an accelerated variant of IST. From the current iterate xk , SpaRSA obtains the newSIGNAL AND IMAGE RECONSTRUCTION ALGORITHMS ON GPUS 5 iterate x k+1 by solving the following... |

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Citation Context ...d in [35]. These first-order methods are shown to be effective for finding solutions of low to moderate accuracy, though they tend to be overtaken by second-order methods such as the one described in =-=[8]-=- when high accuracy is demanded. The first order methods require at each calculation of the gradient residual r := Ax − λg and the gradient of (4.8), which is A T r. Multiplication by A T is the diffe... |

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Citation Context ...] based on the optimal first-order methodology of Nesterov [19, 20]; a variant of IST that uses a “continuation” strategy of successively reducing the parameter τ in (3.2) [16]; interiorpoint methods =-=[27, 18, 3]-=-; and gradient projection applied to the bound-constrained quadratic programming formulation of (3.2) [14]. We focus in this paper on the SpaRSA approach of [33], which can be viewed as an accelerated... |

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Citation Context ...ing GPUs to run critical numerical computing tasks in various applications, including pattern analysis [7, 15], biomedical imaging [17], DNA sequence alignment [28], molecular modeling and simulation =-=[29, 32]-=-, multibody dynamics [30], and quantum chemistry [31]. Our focus in this paper is on GPU implementations of algorithms that have been proposed recently for reconstruction of sparse signals from random... |

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Citation Context ... units than those on CPUs. Many recent studies have reported significant performance boosts by using GPUs to run critical numerical computing tasks in various applications, including pattern analysis =-=[7, 15]-=-, biomedical imaging [17], DNA sequence alignment [28], molecular modeling and simulation [29, 32], multibody dynamics [30], and quantum chemistry [31]. Our focus in this paper is on GPU implementatio... |

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Citation Context ...preserving edges. We report here on TV-regularized denoising and deblurring formulations, solved with a particularly effective primal-dual gradient descent approach described recently by Zhu and Chan =-=[34]-=-. The main computational operations in this algorithm include a difference operation (needed to calculate the TV-norm), DFTs and inverse DFTs (needed in the deblurring application), and various Level ... |

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Citation Context ...] based on the optimal first-order methodology of Nesterov [19, 20]; a variant of IST that uses a “continuation” strategy of successively reducing the parameter τ in (3.2) [16]; interiorpoint methods =-=[27, 18, 3]-=-; and gradient projection applied to the bound-constrained quadratic programming formulation of (3.2) [14]. We focus in this paper on the SpaRSA approach of [33], which can be viewed as an accelerated... |

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Citation Context ...ions of this approach [21, 2] based on the optimal first-order methodology of Nesterov [19, 20]; a variant of IST that uses a “continuation” strategy of successively reducing the parameter τ in (3.2) =-=[16]-=-; interiorpoint methods [27, 18, 3]; and gradient projection applied to the bound-constrained quadratic programming formulation of (3.2) [14]. We focus in this paper on the SpaRSA approach of [33], wh... |

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Citation Context ... units than those on CPUs. Many recent studies have reported significant performance boosts by using GPUs to run critical numerical computing tasks in various applications, including pattern analysis =-=[7, 15]-=-, biomedical imaging [17], DNA sequence alignment [28], molecular modeling and simulation [29, 32], multibody dynamics [30], and quantum chemistry [31]. Our focus in this paper is on GPU implementatio... |

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Citation Context ...ted significant performance boosts by using GPUs to run critical numerical computing tasks in various applications, including pattern analysis [7, 15], biomedical imaging [17], DNA sequence alignment =-=[28]-=-, molecular modeling and simulation [29, 32], multibody dynamics [30], and quantum chemistry [31]. Our focus in this paper is on GPU implementations of algorithms that have been proposed recently for ... |

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Citation Context ...any recent studies have reported significant performance boosts by using GPUs to run critical numerical computing tasks in various applications, including pattern analysis [7, 15], biomedical imaging =-=[17]-=-, DNA sequence alignment [28], molecular modeling and simulation [29, 32], multibody dynamics [30], and quantum chemistry [31]. Our focus in this paper is on GPU implementations of algorithms that hav... |

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Citation Context ...for τ ≥ τmax the solution is x = 0, where τmax := ‖A T y‖∞. (3.3) Theory concerning the effectiveness of these formulations for finding sparse solutions of Ax = y can be found in the papers of Donoho =-=[12, 11]-=-, Candès and Tao [5], and Candès, Romberg, and Tao [4]. Donoho [10] and Candès [6] give introductions to compressed sensing and discuss the various contexts in which these problems arise. 3.2. Algorit... |

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Citation Context ...rical computing tasks in various applications, including pattern analysis [7, 15], biomedical imaging [17], DNA sequence alignment [28], molecular modeling and simulation [29, 32], multibody dynamics =-=[30]-=-, and quantum chemistry [31]. Our focus in this paper is on GPU implementations of algorithms that have been proposed recently for reconstruction of sparse signals from random observations (compressed... |

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Citation Context ...ious applications, including pattern analysis [7, 15], biomedical imaging [17], DNA sequence alignment [28], molecular modeling and simulation [29, 32], multibody dynamics [30], and quantum chemistry =-=[31]-=-. Our focus in this paper is on GPU implementations of algorithms that have been proposed recently for reconstruction of sparse signals from random observations (compressed sensing) and for image deno... |

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Citation Context ...ly drawn from a discrete Fourier transform (DFT). As a sample of the vast algorithmic literature, we mention the iterative thresholding / shrinking (IST) approach [9, 13]; extensions of this approach =-=[21, 2]-=- based on the optimal first-order methodology of Nesterov [19, 20]; a variant of IST that uses a “continuation” strategy of successively reducing the parameter τ in (3.2) [16]; interiorpoint methods [... |

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Citation Context ...the vast algorithmic literature, we mention the iterative thresholding / shrinking (IST) approach [9, 13]; extensions of this approach [21, 2] based on the optimal first-order methodology of Nesterov =-=[19, 20]-=-; a variant of IST that uses a “continuation” strategy of successively reducing the parameter τ in (3.2) [16]; interiorpoint methods [27, 18, 3]; and gradient projection applied to the bound-constrain... |

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Citation Context ...] based on the optimal first-order methodology of Nesterov [19, 20]; a variant of IST that uses a “continuation” strategy of successively reducing the parameter τ in (3.2) [16]; interiorpoint methods =-=[27, 18, 3]-=-; and gradient projection applied to the bound-constrained quadratic programming formulation of (3.2) [14]. We focus in this paper on the SpaRSA approach of [33], which can be viewed as an accelerated... |

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Citation Context ... but since such techniques are well understood, we do not investigate them in this paper. 2.2. Software Platform. The Compute Unified Device Architecture (CUDA) is NVIDIA’s software platform for GPUs =-=[24]-=-. It is an extension to the the C++ language that allows users to write thread execution configurations, manage device memory, and do thread synchronization. CUDA splits a task into a grid of blocks, ... |

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Citation Context ...the vast algorithmic literature, we mention the iterative thresholding / shrinking (IST) approach [9, 13]; extensions of this approach [21, 2] based on the optimal first-order methodology of Nesterov =-=[19, 20]-=-; a variant of IST that uses a “continuation” strategy of successively reducing the parameter τ in (3.2) [16]; interiorpoint methods [27, 18, 3]; and gradient projection applied to the bound-constrain... |

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Citation Context ... recommended in [24] to have at least one hundred blocks per task to ensure overlapped execution of threads. A convenient way to monitor the factors described above is to use the CUDA Visual Profiler =-=[25]-=-, which shows the numbers of uncoalesced global memory loads/stores, the number of divergence branches, GPU utilization, and other important information.18 S. LEE AND S. J. WRIGHT Use page-locked mem... |

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Citation Context ...ing GPUs to run critical numerical computing tasks in various applications, including pattern analysis [7, 15], biomedical imaging [17], DNA sequence alignment [28], molecular modeling and simulation =-=[29, 32]-=-, multibody dynamics [30], and quantum chemistry [31]. Our focus in this paper is on GPU implementations of algorithms that have been proposed recently for reconstruction of sparse signals from random... |