Ramakrishna Kakarala

Signal analysis using a multiresolution form of the singular value decomposition

This paper proposes a multiresolution form of the singular value decomposition (SVD) and shows how it may be used for signal analysis and approximation. It is well-known that the SVD has optimal decorrelation and subrank approximation properties. The multiresolution form of SVD proposed here retains those properties, and moreover, has linear computational complexity. By using the multiresolution SVD, the following important characteristics of a signal may he measured, at each of several levels of resolution: isotropy, sphericity of principal components, self-similarity under scaling, and resolution of mean-squared error into meaningful components. Theoretical calculations are provided for simple statistical models to show what might be expected. Results are provided with real images to show the usefulness of the SVD decomposition.

Adaptive demosaicing with the principal vector method

Demosaicing is the process of interpolating the missing colors in an image that is acquired from a digital image sensor equipped with a color filter array. This paper describes a spatially adaptive demosaicing algorithm that is based on the Jacobian matrix of the color map and neighborhood voting. The algorithm requires only additions, subtractions and shifts, and is therefore attractive from a computational point of view. Comparisons are provided to show that the algorithm improves on published algorithms in terms of complexity or image quality.

Compression-aware demosaicing methods

In many digital color-image systems, most notably digital cameras, raw data from the sensor is processed to produce a pleasing image. One of the main steps in this process is demosaicing, which is the process of interpolating the raw data into a full color image. The resulting image is in turn compressed to enable compact storage. Each of these two steps, namely the demosaicing and compression, creates its own artifacts on the final image. In this work we consider the two stages together, and design a demosaicing algorithm which takes into account the fact that the final image is to be compressed. Examples are given to demonstrate the above ideas.

Shape reconstruction from noisy surface slope information using a multiresolution Bayesian method

Many optical inspection systems today can capture surface slope information directly or indirectly. For these systems, it is possible to perform a 3-D surface reconstruction which converts surface slopes to surface heights. Since the slope information obtained in such systems tend to be noisy and sometimes heavily quantized, a noise-tolerant reconstruction method is needed. We used a simple bayes reconstruction method to improve noise tolerance, and multi-resolution processing to improve the speed of calculations. For each resolution level, the surface slopes between pixels are first calculated from the original surface slopes. Then the height reconstruction for this resolution level is calculated by solving the linear equations that relate relative heights of each point and its related surface slopes. This is done through a Bayesian method which makes it easier to incorporate prior knowledge about height ranges and noise levels. The reconstructions are done for a small window of pixels at a time for each resolution level to make the linear equations manageable. The relative height solutions from all resolution levels are then combined to generate the final height map. This method has been used in optical inspection applications where slope data are quite noisy.