Image resolution enhancement using dual-tree complex wavelet transform

In this letter, a complex wavelet-domain image resolution enhancement algorithm based on the estimation of wavelet coefficients is proposed. The method uses a forward and inverse dual-tree complex wavelet transform (DT-CWT) to construct a high-resolution (HR) image from the given low-resolution (LR) image. The HR image is reconstructed from the LR image, together with a set of wavelet coefficients, using the inverse DT-CWT. The set of wavelet coefficients is estimated from the DT-CWT decomposition of the rough estimation of the HR image. Results are presented and discussed on very HR QuickBird data, through comparisons between state-of-the-art resolution enhancement methods

Timeline analysis and wavelet multiscale analysis of the AKARI All-Sky Survey at 90 micron

We present a careful analysis of the point source detection limit of the AKARI All-Sky Survey in the WIDE-S 90 $\mu$m band near the North Ecliptic Pole (NEP). Timeline Analysis is used to detect IRAS sources and then a conversion factor is derived to transform the peak timeline signal to the interpolated 90 $\mu$m flux of a source. Combined with a robust noise measurement, the point source flux detection limit at S/N $>5$ for a single detector row is $1.1\pm0.1$ Jy which corresponds to a point source detection limit of the survey of $\sim$0.4 Jy. Wavelet transform offers a multiscale representation of the Time Series Data (TSD). We calculate the continuous wavelet transform of the TSD and then search for significant wavelet coefficients considered as potential source detections. To discriminate real sources from spurious or moving objects, only sources with confirmation are selected. In our multiscale analysis, IRAS sources selected above $4\sigma$ can be identified as the only real sources at the Point Source Scales. We also investigate the correlation between the non-IRAS sources detected in Timeline Analysis and cirrus emission using wavelet transform and contour plots of wavelet power spectrum. It is shown that the non-IRAS sources are most likely to be caused by excessive noise over a large range of spatial scales rather than real extended structures such as cirrus clouds.Comment: 16 pages, 19 figures, 5 tables, accepted for publication in MNRA

Sparsity and Incoherence in Compressive Sampling

We consider the problem of reconstructing a sparse signal $x^0\in\R^n$ from a limited number of linear measurements. Given $m$ randomly selected samples of $U x^0$, where $U$ is an orthonormal matrix, we show that $\ell_1$ minimization recovers $x^0$ exactly when the number of measurements exceeds $$m\geq \mathrm{Const}\cdot\mu^2(U)\cdot S\cdot\log n,$$ where $S$ is the number of nonzero components in $x^0$, and $\mu$ is the largest entry in $U$ properly normalized: $\mu(U) = \sqrt{n} \cdot \max_{k,j} |U_{k,j}|$. The smaller $\mu$, the fewer samples needed. The result holds for ``most'' sparse signals $x^0$ supported on a fixed (but arbitrary) set $T$. Given $T$, if the sign of $x^0$ for each nonzero entry on $T$ and the observed values of $Ux^0$ are drawn at random, the signal is recovered with overwhelming probability. Moreover, there is a sense in which this is nearly optimal since any method succeeding with the same probability would require just about this many samples

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

Diagnosis and decision-making for awareness during general anaesthesia

This is the post-print version of the article. The official published version can be obtained from the link below.We describe the design process of a diagnostic system for monitoring the anaesthetic state of patients during surgical interventions under general anaesthesia. Mid-latency auditory evoked potentials (MLAEPs) obtained during general anaesthesia are used to design a neuro-fuzzy system for the determination of the level of unconsciousness after feature extraction using multiresolution wavelet analysis (MRWA). The neuro-fuzzy system proves to be a useful tool in eliciting knowledge for the fuzzy system: the anaesthetist's expertise is indirectly coded in the knowledge rule-base through the learning process with the training data. The anaesthetic depth of the patient, as deduced by the anaesthetist from the clinical signs and other haemodynamic variables, noted down during surgery, is subsequently used to label the MLAEP data accordingly. This anaesthetist-labelled data, used to train the neuro-fuzzy system, is able to produce a classifier that successfully interprets unseen data recorded from other patients. This system is not limited, however, to the combination of drugs used here. Indeed, the similar effects of inhalational and analgesic anaesthetic drugs on the MLAEPs demonstrate that the system could potentially be used for any anaesthetic and analgesic drug combination. We also suggest the use of a closed-loop architecture that would automatically provide the drug profile necessary to maintain the patient at a safe level of sedation

KIC 9406652: An Unusual Cataclysmic Variable in the Kepler Field of View

KIC 9406652 is a remarkable variable star in the Kepler field of view that shows both very rapid oscillations and long term outbursts in its light curve. We present an analysis of the light curve over quarters 1 to 15 and new spectroscopy that indicates that the object is a cataclysmic variable with an orbital period of 6.108 hours. However, an even stronger signal appears in the light curve periodogram for a shorter period of 5.753 hours, and we argue that this corresponds to the modulation of flux from the hot spot region in a tilted, precessing disk surrounding the white dwarf star. We present a preliminary orbital solution from radial velocity measurements of features from the accretion disk and the photosphere of the companion. We use a Doppler tomography algorithm to reconstruct the disk and companion spectra, and we also consider how these components contribute to the object's spectral energy distribution from ultraviolet to infrared wavelengths. This target offers us a remarkable opportunity to investigate disk processes during the high mass transfer stage of evolution in cataclysmic variables.Comment: 31 pages, 13 figures, accepted for Ap