Pointwise Shape-Adaptive DCT Image Filtering and Signal-Dependent Noise Estimation

When an image is acquired by a digital imaging sensor, it is always degraded by some noise. This leads to two basic questions: What are the main characteristics of this noise? How to remove it? These questions in turn correspond to two key problems in signal processing: noise estimation and noise removal (so-called denoising). This thesis addresses both abovementioned problems and provides a number of original and effective contributions for their solution. The first part of the thesis introduces a novel image denoising algorithm based on the low-complexity Shape-Adaptive Discrete Cosine Transform (SA-DCT). By using spatially adaptive supports for the transform, the quality of the filtered image is high, with clean edges and without disturbing artifacts. We further present extensions of this approach to image deblurring, deringing and deblocking, as well as to color image filtering. For all these applications, the proposed SA-DCT approach demonstrates a state-of-the-art filtering performance, which is achieved at a very competitive computational cost. The second part of the thesis addresses the problem of noise estimation. In particular, we consider noise estimation for raw-data, i.e. the unprocessed digital output of the imaging sensor. We introduce a method for nonparametric estimation of the standard-deviation curve which can be used with non-uniform targets under non-uniform illumination. Thus, we overcome key limitations of the existing approaches and standards, which typically assume the use of specially calibrated uniform targets. Further, we propose a noise model for the raw-data. The model is composed of a Poissonian part, for the photon sensing, and a Gaussian part, for the remaining stationary disturbances in the output data. The model explicitly takes into account the clipping of the data, faithfully reproducing the nonlinear response of the sensor when parts of the image are over- or under-exposed. This model allows for the parametric estimation of the noise characteristics from a single image. For this purpose, a fully automatic algorithm is presented. Numerous experiments with synthetic as well as with real data are presented throughout the thesis, proving the efficiency of the proposed solutions. Finally, illustrative examples, which show how the methods proposed in the first and in the second part can be integrated within a single procedure, conclude the thesis