A recursive scheme for computing autocorrelation functions of decimated complex wavelet subbands

This paper deals with the problem of the exact computation of the autocorrelation function of a real or complex discrete wavelet subband of a signal, when the autocorrelation function (or Power Spectral Density, PSD) of the signal in the time domain (or spatial domain) is either known or estimated using a separate technique. The solution to this problem allows us to couple time domain noise estimation techniques to wavelet domain denoising algorithms, which is crucial for the development of blind wavelet-based denoising techniques. Specifically, we investigate the Dual-Tree complex wavelet transform (DT-CWT), which has a good directional selectivity in 2-D and 3-D, is approximately shift-invariant, and yields better denoising results than a discrete wavelet transform (DWT). The proposed scheme gives an analytical relationship between the PSD of the input signal/image and the PSD of each individual real/complex wavelet subband which is very useful for future developments. We also show that a more general technique, that relies on Monte-Carlo simulations, requires a large number of input samples for a reliable estimate, while the proposed technique does not suffer from this problem

Variational multi-image stereo matching

In two-view stereo matching, the disparity of occluded pixels cannot accurately be estimated directly: it needs to be inferred through, e.g., regularisation. When capturing scenes using a plenoptic camera or a camera dolly on a track, more than two input images are available, and - contrary to the two-view case -pixels in the central view will only very rarely be occluded in all of the other views. By explicitly handling occlusions, we can limit the depth estimation of pixel (P) over right arrow to only use those cameras that actually observe (p) over right arrow. We do this by extending variational stereo matching to multiple views, and by explicitly handling occlusion on a view-by-view basis. Resulting depth maps are illustrated to be sharper and less noisy than typical recent techniques working on light fields

Reconstruction of high dynamic range images with poisson noise modeling and integrated denoising

In this paper, we present a new method for High Dynamic Range (HDR) reconstruction based on a set of multiple photographs with different exposure times. While most existing techniques take a deterministic approach by assuming that the acquired low dynamic range (LDR) images are noise-free, we explicitly model the photon arrival process by assuming sensor data corrupted by Poisson noise. Taking the noise characteristics of the sensor data into account leads to a more robust way to estimate the non-parametric camera response function (CRF) compared to existing techniques. To further improve the HDR reconstruction, we adopt the split-Bregman framework and use Total Variation for regularization. Experimental results on real camera images and ground-truth data show the effectiveness of the proposed approach

Bayesian demosaicing using Gaussian scale mixture priors with local adaptivity in the dual tree complex wavelet packet transform domain

In digital cameras and mobile phones, there is an ongoing trend to increase the image resolution, decrease the sensor size and to use lower exposure times. Because smaller sensors inherently lead to more noise and a worse spatial resolution, digital post-processing techniques are required to resolve many of the artifacts. Color filter arrays (CFAs), which use alternating patterns of color filters, are very popular because of price and power consumption reasons. However, color filter arrays require the use of a post-processing technique such as demosaicing to recover full resolution RGB images. Recently, there has been some interest in techniques that jointly perform the demosaicing and denoising. This has the advantage that the demosaicing and denoising can be performed optimally (e.g. in the MSE sense) for the considered noise model, while avoiding artifacts introduced when using demosaicing and denoising sequentially. ABSTRACT In this paper, we will continue the research line of the wavelet-based demosaicing techniques. These approaches are computationally simple and very suited for combination with denoising. Therefore, we will derive Bayesian Minimum Squared Error (MMSE) joint demosaicing and denoising rules in the complex wavelet packet domain, taking local adaptivity into account. As an image model, we will use Gaussian Scale Mixtures, thereby taking advantage of the directionality of the complex wavelets. Our results show that this technique is well capable of reconstructing fine details in the image, while removing all of the noise, at a relatively low computational cost. In particular, the complete reconstruction (including color correction, white balancing etc) of a 12 megapixel RAW image takes 3.5 sec on a recent mid-range GPU

Fast and robust variational optical flow for high-resolution images using SLIC superpixels

We show how pixel-based methods can be applied to a sparse image representation resulting from a superpixel segmentation. On this sparse image representation we only estimate a single motion vector per superpixel, without working on the full-resolution image. This allows the accelerated processing of high-resolution content with existing methods. The use of superpixels in optical flow estimation was studied before, but existing methods typically estimate a dense optical flow field - one motion vector per pixel - using the full-resolution input, which can be slow. Our novel approach offers important speed-ups compared to dense pixel-based methods, without significant loss of accuracy

Locally adaptive complex wavelet-based demosaicing for color filter array images

A new approach for wavelet-based demosaicing of color filter array (CFA) images is presented. It is observed that conventional wavelet-based demosaicing results in demosaicing artifacts in high spatial frequency regions of the image. By proposing a framework of locally adaptive demosaicing in the wavelet domain, the presented method proposes computationally simple techniques to avoid these artifacts. In order to reduce computation time and memory requirements even more, we propose the use of the dual tree complex wavelet transform. The results show that wavelet-based demosaicing, using the proposed locally adaptive framework, is visually comparable with state-of-the-art pixel based demosaicing. This result is very promising when considering a low complexity wavelet-based demosaicing and denoising approach

Realistic camera noise modeling with application to improved HDR synthesis

Abstract Due to the ongoing miniaturization of digital camera sensors and the steady increase of the “number of megapixels”, individual sensor elements of the camera become more sensitive to noise, even deteriorating the final image quality. To go around this problem, sophisticated processing algorithms in the devices, can help to maximally exploit the knowledge on the sensor characteristics (e.g., in terms of noise), and offer a better image reconstruction. Although a lot of research focuses on rather simplistic noise models, such as stationary additive white Gaussian noise (AWGN), only limited attention has gone to more realistic digital camera noise models. In this paper, we first present a digital camera noise model that takes several processing steps in the camera into account, such as sensor signal amplification, clipping, post-processing, ... We then apply this noise model to the reconstruction problem of high dynamic range (HDR) images from a small set of low dynamic range exposures of a static scene. In literature, HDR reconstruction is mostly performed by computing a weighted average, in which the weights are directly related to the observer pixel intensities of the LDR image. In this work, we derive a Bayesian probabilistic formulation of a weighting function that is near-optimal in the MSE sense (or SNR sense) of the reconstructed HDR image, by assuming exponentially distributed irradiance values. We define the weighting function as the probability that the observed pixel intensity is approximately unbiased. The weighting function can be directly computed based on the noise model parameters, which gives rise to different symmetric and asymmetric shapes when electronic noise or photon noise is dominant. We also explain how to deal with the case that some of the noise model parameters are unknown and explain how the camera response function can be estimated using the presented noise model. Finally, experimental results are provided to support our findings