A New Method for Superresolution Image Reconstruction Based on Surveying Adjustment

A new method for superresolution image reconstruction based on surveying adjustment method is described in this paper. The main idea of such new method is that a sequence of low-resolution images are taken firstly as observations, and then observation equations are established for the superresolution image reconstruction. The gray function of the object surface can be found by using surveying adjustment method from the observation equations. High-resolution pixel value of the corresponding area can be calculated by using the gray function. The results show that the proposed algorithm converges much faster than that of conventional superresolution image reconstruction method. By using the new method, the visual feeling of reconstructed image can be greatly improved compared to that of iterative back projection algorithm, and its peak signal-to-noise ratio can also be improved by nearly 1 dB higher than the projection onto convex sets algorithm. Furthermore, this method can successfully avoid the ill-posed problems in reconstruction process

Image reconstruction/synthesis from nonuniform data and zero/threshold crossings

We address the problem of reconstructing functions from their nonuniform data and zero/threshold crossings. We introduce a deterministic process via the Gram-Schmidt orthonormalization procedure to reconstruct functions from their nonuniform data and zero/threshold crossings. This is achieved by first introducing the nonorthogonal basis functions in a chosen 2-D domain (e.g., for a band-limited signal, a possible choice is the 2-D Fourier domain of the image) that span the signal subspace of the nonuniform data. We then use the Gram-Schmidt procedure to construct a set of orthogonal basis functions that span the linear signal subspace defined by the nonorthogonal basis functions. Next, we project the N-dimensional measurement vector (N is the number of nonuniform data or threshold crossings) onto the newly constructed orthogonal basis functions. Finally, the function at any point can be reconstructed by projecting the representation with respect to the newly constructed orthonormal basis functions onto the reconstruction basis functions that span the signal subspace of the evenly spaced sampled data. The reconstructed signal gives the minimum mean square error estimate of the original signal. This procedure gives error-free reconstruction provided that the nonorthogonal basis functions that span the signal subspace of the nonuniform data form a complete set in the signal subspace of the original band-limited signal. We apply this algorithm to reconstruct functions from their unevenly spaced sampled data and zero crossings and also apply it to solve the problem of synthesis of a 2-D band-limited function with the prescribed level crossings

Partition-based Interpolation for Color Filter Array Demosaicking and Super-Resolution Reconstruction

A class of partition-based interpolators that addresses a variety of image interpolation applications are proposed. The proposed interpolators first partition an image into a finite set of partitions that capture local image structures. Missing high resolution pixels are then obtained through linear operations on neighboring pixels that exploit the captured image structure. By exploiting the local image structure, the proposed algorithm produces excellent performance on both edge and uniform regions. The presented results demonstrate that partition-based interpolation yields results superior to traditional and advanced algorithms in the applications of color filter array (CFA) demosaicking and super-resolution reconstruction

Bandwidth-based mesh adaptation in multiple dimensions

Spectral methods are becoming increasingly prevalent in solving time-varying partial differential equations due to their fast convergence properties. However, they typically use regular computational meshes that do not account for spatially varying resolution requirements. This can significantly increase the overall grid density when resolution requirements vary sharply over the modelled domain. Moving mesh methods offer a remedy for this, by allowing the position of mesh nodes to adapt to the simulated model solution. In this paper, a mesh specification is presented that is based on a local measure of the spatial bandwidth of the model solution. This addresses the rate of decay of the model solution's frequency components by producing high-sampling rates when this decay is slow. The spatial bandwidth is computed using a combination of the original solution and its Riesz transformed counterparts. It is then integrated into a Fourier spectral moving mesh method, using the parabolic Monge–Ampère equation for mesh control. This method is used to solve a multidimensional version of the viscous Burgers equation, and a heterogeneous advection equation. The performance of bandwidth-based mesh adaptation is compared with arclength- and curvature-based adaptation, and against a static mesh. These numerical experiments show that the bandwidth-based approach produces superior convergence rates, and hence requires fewer mesh nodes for a given level of solution accuracy

Programación del algoritmo POCS para mejorar la resolución de imágenes de campos de cultivo

El presente trabajo de tesis surgió debido a la necesidad de obtener imágenes de campos de cultivo de alta resolución a partir de un conjunto de imágenes de baja resolución capturadas por un dispositivo óptico. La propiedad de desplazamiento sub-pixel existente entre las imágenes de baja resolución capturadas por el dispositivo óptico hace posible la obtención de imágenes digitales de alta resolución mediante la aplicación de un algoritmo de reconstrucción de imágenes. Con el fin de poder incrementar la resolución de las imágenes de campos de cultivo, de tal modo que estas puedan ser procesadas y analizadas con mayor precisión, se seleccionó y programó el algoritmo POCS (Projections Onto Convex Sets) debido a su robustez, simplicidad y flexibilidad para incorporar información conocida a priori de las imágenes deseadas al proceso de reconstrucción. El presente trabajo se desarrolla en cuatro capítulos. En el primer capítulo se presenta el concepto de Agricultura de Precisión y la necesidad de aplicar técnicas que mejoren la resolución de imágenes de campos de cultivo. En el segundo capítulo se describen los principales problemas que presentan los dispositivos ópticos para aumentar la resolución de imágenes, se presenta el modelo que describe el proceso de degradación de imágenes y se realiza un recuento de los principales algoritmos que aumentan la resolución de las mismas. En el tercer capítulo se presentan los objetivos del presente trabajo de tesis, se detalla el marco teórico del algoritmo POCS y se muestra la programación del mismo. En el cuarto capítulo se definen las métricas usadas para evaluar el algoritmo y se presentan los resultados de diversas pruebas aplicadas a las imágenes de campos de cultivo. Finalmente, se concluyó que el algoritmo POCS incrementa la resolución de imágenes de campos de cultivo de manera satisfactoria, además, se concluyó que POCS presentó mejor desempeño con respecto a los algoritmos de interpolación y de deconvolución que formaron parte de las pruebas.Tesi