Image blur estimation based on the average cone of ratio in the wavelet domain

In this paper, we propose a new algorithm for objective blur estimation using wavelet decomposition. The central idea of our method is to estimate blur as a function of the center of gravity of the average cone ratio (ACR) histogram. The key properties of ACR are twofold: it is powerful in estimating local edge regularity, and it is nearly insensitive to noise. We use these properties to estimate the blurriness of the image, irrespective of the level of noise. In particular, the center of gravity of the ACR histogram is a blur metric. The method is applicable both in case where the reference image is available and when there is no reference. The results demonstrate a consistent performance of the proposed metric for a wide class of natural images and in a wide range of out of focus blurriness. Moreover, the proposed method shows a remarkable insensitivity to noise compared to other wavelet domain methods

Image restoration using regularized inverse filtering and adaptive threshold wavelet denoising

Although the Wiener filtering is the optimal tradeoff of inverse filtering and noise smoothing, in the case when the blurring filter is singular, the Wiener filtering actually amplify the noise. This suggests that a denoising step is needed to remove the amplified noise .Wavelet-based denoising scheme provides a natural technique for this purpose .<br />In this paper a new image restoration scheme is proposed, the scheme contains two separate steps : Fourier-domain inverse filtering and wavelet-domain image denoising. The first stage is Wiener filtering of the input image , the filtered image is inputted to adaptive threshold wavelet denoising stage . The choice of the threshold estimation is carried out by analyzing the statistical parameters of the wavelet sub band coefficients like standard deviation, arithmetic mean and geometrical mean . The noisy image is first decomposed into many levels to obtain different frequency bands. Then soft thresholding method is used to remove the noisy coefficients, by fixing the optimum thresholding value by this method .Experimental results on test image by using this method show that this method yields significantly superior image quality and better Peak Signal to Noise Ratio (PSNR). Here, to prove the efficiency of this method in image restoration , we have compared this with various restoration methods like Wiener filter alone and inverse filter

Restauración de imágenes con desensibilización de estimaciones

El marco de esta tesis es la restauración digital de imágenes, esto es, el proceso por el cual se recupera una imagen original que ha sido degradada por las imperfecciones del sistema de adquisición: emborronamiento y ruido. Restaurar esta degradación es un problema mal condicionado pues la inversión directa por mínimos cuadrados amplifica el ruido en las altas frecuencias. Por ello, se utiliza la regularización matemática como medio para incluir información a priori de la imagen que consiga estabilizar la solución. Durante la primera parte de la memoria se hace un repaso de ciertos algoritmos del estado del arte, que se usarán posteriormente como métodos de comparación en los experimentos. Para resolver el problema de regularización, la restauración de imágenes tiene dos requisitos previos. En primer lugar, es necesario realizar hipótesis sobre el comportamiento de la imagen fuera de sus fronteras, debido a la propiedad no local de la convolución que modela la degradación. La ausencia de condiciones de frontera en la restauración da lugar al artefacto conocido como boundary ringing. En segundo lugar, los algoritmos de restauración dependen de un número importante de parámetros divididos en tres grupos: parámetros respecto al proceso de degradación, al ruido y a la imagen original. Todos ellos necesitan de una estimación a priori suficientemente precisa, pues pequeños errores respecto a sus valores reales producen importantes desviaciones en los resultados de restauración. El problema de frontera y la sensibilidad a estimaciones son los objetivos a resolver en esta tesis mediante dos algoritmos iterativos. El primero de los algoritmos afronta el problema de frontera partiendo de una imagen truncada en el campo de visión como observación real. Para resolver esta no linealidad, se utiliza una red neuronal que minimiza una función de coste definida principalmente por la regularización por variación total, pero sin incluir ningún tipo de información a priori sobre las fronteras ni requerir entrenamiento previo de la iv red. Como resultado, se obtiene una imagen restaurada sin efectos de ringing en el campo de visión y además las fronteras truncadas son reconstruidas hasta el tamaño original. El algoritmo se basa en la técnica de retro-propagación de energía, con lo que la red se convierte en un ciclo iterativo de dos procesos: forward y backward, que simulan una restauración y una degradación por cada iteración. Siguiendo el mismo concepto iterativo de restauración-degradación, se presenta un segundo algoritmo en el dominio de la frecuencia para reducir la dependencia respecto a las estimaciones de parámetros. Para ello, se diseña un nuevo filtro de restauración desensibilizado como resultado de aplicar un algoritmo iterativo sobre un filtro original. Estudiando las propiedades de sensibilidad de este filtro y estableciendo un criterio para el número de iteraciones, se llega a una expresión para el algoritmo de desensibilización particularizado a los filtros Wiener y Tikhonov. Los resultados de los experimentos demuestran el buen comportamiento del filtro respecto al error dependiente del ruido, con lo que la estimación que se hace más robusta es la correspondiente a los parámetros del ruido, si bien la desensibilización se extiende también al resto de estimaciones. Abstract The framework of this thesis is digital image restoration, that is to say, the process of recovering an original image which has been degraded due to the imperfections in the acquisition system: blurring and noise. Restoring this degradation is an ill-posed problem since the inverse solution using least-squares leads to excessive noise amplification. For that reason, mathematical regularization is used to include prior knowledge about the image which allows the stabilization of the solution in the face of noise. In the first part of the thesis, we provide a review of the state-of-the-art methods which will be used later in the experimental results. To deal with a regularization problem, image restoration imposes two main requirements. First, it is necessary to make assumptions about how the image behaves outside the field of view, as a result of the non-local property of the underlying convolution. The absence of boundary conditions in the restoration problem produces the so-called boundary ringing artifact. Secondly, the restoration methods depend on a wide set of parameters which can be largely grouped into three categories: parameters with respect to the degradation process, the noise and the original image. All parameters require an accurate prior estimation because small errors in their values lead to important deviations in the restoration results. The boundary problem and the sensitivity to estimations are the issues to resolve in this thesis by means of two iterative algorithms. The first algorithm copes with the boundary problem taking a truncated image in the field of view as a real observation. To resolve the nonlinearity in the observation, we use a neural network that minimizes a cost function mainly defined by the total variation regularization, but with neither prior assumption as regards the boundaries nor previous training in the net. It yields a restored image without ringing artifacts and, moreover, the truncated boundaries are reconstructed according to the original image size. The algorithm is based on the backpropagation method, which turns out an iterative cycle of two steps: forward and backward, simulating respectively restoration and degradation processes at each iteration. Following the same iterative concept of restoration-degradation, we present a second algorithm in the frequency domain to reduce the dependency on the estimation of parameters. Hence, a novel desensitized restoration filter is designed by applying an iterative algorithm over the original filter. Analyzing the sensitivity properties of this filter and setting a criterion to choose the number of iterations, we come up with an expression for the desensitized algorithm that is particularized to the Wiener and the Tikhonov filters. Experimental results demonstrate the desensitizing behavior with respect to the noise-dependent error and a consequent robustness to the noise parameters, although the desensitization also applies to the rest of the estimations