CS: KGG presentation, Jacket, pystream, a paradigm shift in signal processing, 3D CS for Dynamic MRI

I mentioned her yesterday, but the links were all wrong. So here we are again: Svetlana Avramov-Zamurovic presented a tutorial on Compressive Sensing in a course at the USNA. She also made a video of it. It is here. The slides and attendant paper by Richard Baraniuk on which the presentation is based. It is added to the Compressive Sensing Videos page.

Also found on the interwebs:

Compressive Sensing Theory and L1-Related Optimization Algorithms by Yin Zhang. Of interest is the mention of a recoverability proof without the use of the RIP argument.

A presentation by Albert Cohen entitled Near optimal recovery of arbitrary signals from highly incomplete measurements.

There is a summary of the Frames for the finite world: Sampling, coding and quantization workshop organized by Sinan Gunturk, Goetz Pfander, Holger Rauhut, and Ozgur Yilmaz

Jacket v1.0, a Matlab to GPU software is now available. It's not free but heavily discounted for academics it seems. There is also pystream from the project page:

PyStream combines the power and convenience of Python with the high performance of modern Graphics Processing Units (GPUs). The focus of PyStream is on NVIDIA GPUs, such as the GeForce 8800 and Tesla series, that support the Compute Unified Device Architecture (CUDA) toolkit. With PyStream, the CUDA libraries, including the CUDA BLAS and FFT libraries, can be called from directly from Python. Data can be moved back and forth seamlessly between the GPU and Python objects (NumPy arrays) on the CPU. Initial development of PyStream was done by Tech-X Corporation. Tech-X Corporation has shifted its efforts to a new GPU related project, called GPULib, that has a higher level API than PyStream and also supports other languages other than Python. Because of this change, PyStream is no longer being actively developed. However, PyStream will remain available under the BSD license.

Also found on Arxiv, Compressive sensing: a paradigm shift in signal processing by Olga V. Holtz.

The abstract reads:We survey a new paradigm in signal processing known as "compressive sensing". Contrary to old practices of data acquisition and reconstruction based on the Shannon-Nyquist sampling principle, the new theory shows that it is possible to reconstruct images or signals of scientific interest accurately and even exactly from a number of samples which is far smaller than the desired resolution of the image/signal, e.g., the number of pixels in the image. This new technique draws from results in several fields of mathematics, including algebra, optimization, probability theory, and harmonic analysis. We will discuss some of the key mathematical ideas behind compressive sensing, as well as its implications to other fields: numerical analysis, information theory, theoretical computer science, and engineering.

There is an attendant presentation entitled An Introduction to Compressive Sensing by the same author.

Finally, Three-Dimensional Compressed Sensing for Dynamic MRI by Ali Bilgin, Ted Trouard, Maria Altbach, and Natarajan Raghunand. The introduction reads:

Dynamic contrast enhanced (DCE) magnetic resonance imaging (MRI) is a valuable tool used in a number of clinical applications. However, imaging of time-varying objects is a challenging task when both high spatial resolution and high temporal resolution is desired. It has been demonstrated that radial imaging techniques can yield increased temporal resolution without sacrificing spatial resolution and are less susceptible to motion [1,2]. However, highly undersampled radial trajectories result in increased streaking artifacts and low SNR. The recently introduced Compressed Sensing (CS) theory illustrates that a small number of linear measurements can be sufficient to reconstruct sparse or compressible signals [3,4] and has the potential to significantly accelerate data acquisition in MRI [5,6,7]. In this work, we introduce a CS theory based method for reconstruction of time-varying radial k-space data by exploiting the spatio-temporal sparsity of DCE-MRI images.

Credit: NASA/JPL/Space Science Institute,Saturn's ring taken on January 28th, 2009.