Total variation based convex filters for medical imaging

Keeling, Stephen L.

doi:10.1016/s0096-3003(02)00171-6

Cited by 64 publications

(45 citation statements)

References 6 publications

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“…Some of these techniques, generally developed for 2D images, have often been extended to 3D medical data, especially to MR images: anisotropic diffusion [34], [35], total variation [36], bilateral filtering and variants [37], waveletbased filtering [38]- [42], hybrid approaches [43], [44].…”

Section: State-of-the-art a General Overviewmentioning

confidence: 99%

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An Optimized Blockwise Nonlocal Means Denoising Filter for 3-D Magnetic Resonance Images

Coupé

Yger

Prima

et al. 2008

IEEE Trans. Med. Imaging

1,049

856

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Section: State-of-the-art a General Overviewmentioning

confidence: 99%

“…In practice, the TV minimization scheme tends to remove texture and small image structures as seen in Fig. 13 [36]. To solve this problem, iterative total variation schemes have been recently developed [55], [56].…”

Section: B) Total Variation Minimization Schemementioning

confidence: 99%

An Optimized Blockwise Nonlocal Means Denoising Filter for 3-D Magnetic Resonance Images

Coupé

Yger

Prima

et al. 2008

IEEE Trans. Med. Imaging

1,049

856

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show abstract

“…At the same time, Proposition 2 implies that the sequence of wavelet block-coefficient norms c (k) 2 in the null space of BH * must be sufficiently compressible and bounded by the total-variation of x. Combining these properties -flatness and tail-compressibility -produces the Sobolev-type inequality (27). …”

Section: A Sobolev Inequality For Incoherent Subspacesmentioning

confidence: 96%

“…In the setting of compressed sensing and more broadly in other imaging applications, it has been used for denoising, deblurring, and inpainting (see e.g. [8], [11], [7], [41], [14], [33], [34], [31], [38], [35], [25], [27], [49], [37] and the references therein). We consider here the TV problem in the compressed sensing setting.…”

Section: A Imaging With Csmentioning

confidence: 99%

Near-optimal compressed sensing guarantees for anisotropic and isotropic total variation minimization

Needell¹,

Ward²

2013

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Consider the problem of reconstructing a multidimensional signal from partial information, as in the setting of compressed sensing. Without any additional assumptions, this problem is ill-posed. However, for signals such as natural images or movies, the minimal total variation estimate consistent with the measurements often produces a good approximation to the underlying signal, even if the number of measurements is far smaller than the ambient dimensionality. Recently, guarantees for two-dimensional images x ∈ C linear measurements y = Ax using total variation minimization to within a factor of the best s-term approximation of its gradient. The reconstruction guarantees we provide are necessarily optimal up to polynomial factors in the spatial dimension d and a logarithmic factor in the signal dimension N d . The proof relies on bounds in approximation theory concerning the compressibility of wavelet expansions of bounded-variation functions.

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“…Este filtro es popular porque provee excelente capacidad en la reducción de ruido, particularmente es efectivo en imágenes con presencia de ruido de impulsivo bipolar ("sal y pimienta"). (Keeling 2003), han sido obtenidos a partir de la minimización de funcionales apropiados. Consideremos la funcional (Weickert 2001), 10) donde I r es la imagen observada (con ruido), u es la imagen filtrada que se pretende reconstruir a partir de I r , µ y son constantes y Ω es una región convexa de 2 que constituyen el espacio de apoyo de la superficie u(x, y), que representa la imagen.…”

Section: Filtro De Medianaunclassified

Algoritmos de detección y filtrado de imágenes para arquitecturas multicore y manycore.

Sánchez¹,

Guadalupe²

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ResumenEn esta tesis se aborda la eliminación de ruido impulsivo, gaussiano y speckle en imágenes a color y en escala de grises. Como caso particular se puede mencionar la eliminación de ruido en imágenes médicas.Algunos métodos de filtrado son costosos computacionalmente y más aún, si las imágenes son de gran tamaño. Con el fin de reducir el coste computacional de dichos métodos, en esta tesis se utiliza hardware que soporta procesamiento paralelo, como lo son los cores CPU con procesadores multicore y GPUs con procesadores manycore.En las implementaciones paralelas en CUDA, se configuran algunas características con la finalidad de optimizar el procesamiento de la aplicación en las GPUs.Esta tesis estudia por un lado, el rendimiento computacional obtenido en el proceso de eliminación de ruido impulsivo y uniforme. Por otro lado, se evalúa la calidad después de realizar el proceso de filtrado. El rendimiento computacional se ha obtenido con la paralelización de los algoritmos en CPU y/o GPU. Para obtener buena calidad en la imagen filtrada, primero se detectan los píxeles corruptos y luego se filtranúnicamente los píxeles que se han detectado como corruptos. Por lo que respecta a la eliminación de ruido gaussiano y speckle, el análisis del filtro difusivo no lineal ha demostrado ser eficaz para este caso.Los algoritmos que se utilizan para eliminar el ruido impulsivo y uniforme en las imágenes, y sus implementaciones secuenciales y paralelas se han evaluado experimentalmente en tiempo de ejecución (speedup) y eficiencia en tres equipos de cómputo de altas prestaciones. Los resultados han mostrado que las implementaciones paralelas disminuyen considerablemente los tiempos de ejecución secuenciales.Finalmente, en esta tesis se propone un método para reducir eficientemente el ruido en las imágenes sin tener información inicial del tipo de ruido contenido en ellas. AbstractThis thesis focuses on the removal of impulse noise, Gaussian and speckle in color images and grayscale. As a particular case we can mention the elimination of noise in medical images.Some filtering methods are computationally expensive and even more so, if the images are large. In order to reduce the computational cost of such methods, in this thesis we use hardware that supports parallel processing such as CPU cores with multicore processors and GPUs with manycore processor, In CUDA parallel implementations, some features are set in order to optimize the application processing on GPUs.This thesis studies on one side the computational efficiency obtained by the process of elimination of impulsive and uniform noise. On the other side the quality is evaluated after performing the filtering process. The computational performance is obtained with the parallelization of the algorithms in CPU and/or GPU. In order to obtain good quality in the filtering image, first the corrupted pixels are detected and then only the corrupted pixels that have been detected as corrupted are filtered. From which concerns to the removing of the Gaussiano and Speckle noise...

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Total variation based convex filters for medical imaging

Cited by 64 publications

References 6 publications

An Optimized Blockwise Nonlocal Means Denoising Filter for 3-D Magnetic Resonance Images

An Optimized Blockwise Nonlocal Means Denoising Filter for 3-D Magnetic Resonance Images

Near-optimal compressed sensing guarantees for anisotropic and isotropic total variation minimization

Algoritmos de detección y filtrado de imágenes para arquitecturas multicore y manycore.

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