3 Computation of the shearlet transform 13 3.1 Finite discrete shearlets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3.2 A discrete shearlet frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 3.3 Inversion of the shearlet transform . . . . . . . . . . . . . . . . . . . . . . . . . 20 3.4 Smooth shearlets . . . . . . . . . . . . . . . . . . . . . . . . . ...

We develop a mathematically-motivated algorithm for image superresolution, based on the discrete shearlet transform. The shearlet transform is strongly directional, and is known to provide nearoptimally sparse representations for a broad class of images. This often leads to superior performance in edge detection and image representation, when compared to other isotropic frames. We justify the u...

Recently introduced inpainting algorithms using a combination of applied harmonic analysis and compressed sensing have turned out to be very successful. One key ingredient is a carefully chosen representation system which provides (optimally) sparse approximations of the original image. Due to the common assumption that images are typically governed by anisotropic features, directional represen...

This paper presents a novel remote sensing image fusion algorithm, which implements panchromatic sharpening of multispectral data through application of the principal component analysis (PCA) transform and the dual-tree compactly supported shearlet transform (DT CSST). Shearlet transforms provide near optimal representation of the anisotropic features of an image. The compactly supported shearl...

Since cone-beam computed tomography (CT) has been adapted for use with a C-arm system it has brought volumetric CT capabilities in the interventional suite. Although cone-beam CT image resolution is far inferior to that generated by traditional CT scanners, the system offers the ability to place an access needle into position under tomographic guidance and use the access to immediately begin a ...

The spectral sensitivity of cat retinal ganglion neurons (RGNs) was determined by means of extracellular recordings under scotopic and photopic conditions, in both receptive field center and surround. Test stimuli were presented either as square-wave single flashes or as flicker stimuli. Chromatic adaptation was achieved by a large steady monochromatic background field. In the dark-adapted stat...

PURPOSE To investigate the characteristics of the waveform generated by blue and red light stimulations in a dark-adapted electroretinogram (ERG) and those of cone responses in the dark-adapted condition. METHODS The study subjects were 52 persons (88 eyes) with no previous medical history. The author recorded b-waves (rod response) with red light stimulation and the x-waves (dark-adapted con...

Shearlet theory has become a central tool in analyzing and representing 2D data with anisotropic features. Shearlet systems are systems of functions generated by one single generator with parabolic scaling, shearing, and translation operators applied to it, in much the same way wavelet systems are dyadic scalings and translations of a single function, but including a precise control of directio...

Dark-adapted rods in the area surrounding a luminance-modulated field can suppress flicker detection. However, the characteristics of the interaction between rods and each of the cone types are unclear. To address this issue, the effect that dark-adapted rods have on specific classes of receptoral and postreceptoral signals was determined by measuring the critical fusion frequencies (CFF) for r...

In this paper, a new bivariate shrinkage denoising method is proposed to model statistics of shearlet coefficients of images. Using Bayesian estimation theory we derive from this model a simple non-linear shrinkage function for shearlet denoising, which generalizes the soft threshold approach. Experimental results show that the proposed method can remove Gaussian white noise while effectively p...