The usual paradigm for signal processing is to model a signal as a bandlimited function and capture the signal by
means of its time samples. The Shannon-Nyquist theory says that the sampling rate needs to be at least twice
the bandwidth. For broadbanded signals, such high sampling rates may be impossible to implement in circuitry.
Compressed Sensing is a new area of signal processing whose aim is to circumvent this dilemma by sampling
signals closer to their information rate instead of their bandwidth. Rather than model the signal as bandlimited,
Compressed Sensing, assumes the signal can be represented or approximated by a few suitably chosen terms
from a basis expansion of the signal. It also enlarges the concept of sample to include the application of any
linear functional applied to the signal. In this paper, we shall give a brief introduction to compressed sensing
that centers on the effectiveness and implementation of random sampling.
We present a method for automatically registering images based on nonlinear compression. The method involves three steps: (i) analysis of the complexity of the images, (ii) high level compression for extracting control points in the images, (iii) registration of the images by matching control points. The first step analyzes the complexity of the given images. It numerically computes from any image a complexity index which determines the efficiency at which the image can be compressed. This index is used in the second step of the algorithm to select coefficients in the wavelet representation of the image to produce a highly compressed image. The wavelet coefficients of the highly compressed image are then transformed to pixel values. Only a few pixel values are nontrivial. The third stage of the algorithm uses a point alignment technique to identify matching control points and to erect the registering transformations. The algorithm is tested on two quite different scenes: a portrait, representing an uncomplicated scene, and a Landsat TM image of the Pacific Northwest. In both cases, images are tested which differ by a rotation and which differ by a rigid transformation. The algorithm allows a choice of different metrics in which to do the compression and selection of control points.
Independent Component Analyses, Wavelets, Neural Networks, Biosystems, and Nanoengineering VIII
7 April 2010 | Orlando, Florida, United States
Independent Component Analyses, Wavelets, Neural Networks, Biosystems, and Nanoengineering VII
13 April 2009 | Orlando, Florida, United States
Independent Component Analyses, Wavelets, Unsupervised Nano-Biomimetic Sensors and Neural Networks VI
17 March 2008 | Orlando, Florida, United States
4 August 2003 | San Diego, California, United States
SC902: Compressive Sensing: Theory and Applications
Sensors and signal processing hardware and algorithms are under increasing pressure to accommodate ever larger and higher-dimensional data sets; ever faster capture, sampling, and processing rates; ever lower power consumption; communication over ever more difficult channels; and radically new sensing modalities. This four-hour course presents the fundamental theory and selected applications of Compressive Sensing, a new approach to data acquisition in which analog signals are digitized for processing not via uniform sampling but via inner products with random test functions. Unlike Nyquist-rate sampling, which completely describes a signal by exploiting its bandlimitedness, Compressive Sensing reduces the number of measurements required to completely describe a signal by exploiting its compressibility. The implications are promising for many applications and enable the design of new kinds of analog-to-digital converters, imaging systems and cameras, and radar systems, among others.
SC714: From FFTs to Wavelets for Image & Signal Processing
Wavelets and conventional filter banks have become popular because of their convenient representation and ability to isolate characteristic elements of an input in a compact subband form, often for the purposes of analysis, denoising, and compression. Recent research in this area has focused on perceptually relevant feature extraction, curve and shape characterizations, orientation selective processing, and efficient analysis-reconstruction. This four-hour course presents the fundamentals of wavelets and filter banks from a vector space point of view (in the first 2 hours) followed by a discussion of applications to image/signal processing and terrain modeling. History from FFTs evolving to treat non-stationary signal processing such as second order Time-Frequency joint representation instantaneous frequency representation and recently to the first order linear wavelet representation will be briefly reviewed. Prototypical algorithms for compression, denoising, and registration of images will be discussed and evaluated. Application of multiscale methods to terrain
modeling and surface compression will be presented.