Curvelet Analysis

curvelet length vs widthThis blog post is a continuation of my previous post on ridgelet analysis. Motivated by the problem of finding efficient representation of objects, people introduced yet another representation system called the curvelet transform. This is very efficient in representing objects that have discontinuities along curves, and compressing image data as well. Curvelets are a non-adaptive technique for multi-scale object representation. Why do we need this? Are they more efficient that ridgelets?   Continue reading

Ridgelet Analysis

ridgeletsThe pioneering work of researchers on signal processing paved the way to the powerful concept of multiresolution analysis. This is perhaps best known under the generic name of wavelets. Signals occur in the form of images, voice, radar, sonar, infrared etc. Different techniques have been developed over the years to understand these signals. Multiresolution provides us with tools to analyze these signals at different level of resolutions. It’s like looking at the same thing using a microscope with different magnifying powers. The formulation of multiresolution analysis moved the signal processing field away from classical Fourier analysis. But are wavelets equally efficient for all the shapes? Can we somehow take advantage of the shape of the object?   Continue reading

Wavelet Analysis

Wavelets are actually a topic of pure mathematics. But over the last couple of decades, they have shown great promise and are now being adapted for a vast number of applications. They are used in image compression, molecular dynamics, seismology, physics, DNA analysis etc. One of the main advantages of wavelet analysis is the amount of information we can extract from a signal. Wavelet transforms are extensively used to analyze many different kinds of signals. So what exactly are these wavelets? Why is this method of analysis so powerful?   Continue reading