CS: ICASSP CS day, related papers, a thesis and a video.

Here are probably the last blog entries on ICASSP. Thursday was mostly about Compressed Sensing and I gained some insight from these blog entries:

• Gonzalo Vazquez Vilar's Compressed sensing's day at the ICASSP
• Eric Trammel's Day 4 -- A Veritable Cornucopia of Compressed Sensing

I learned things. Thank you Eric and Gonzalo for covering ICASSP. I also found some related papers to these blog entries, here they are (see below). There is a also video at the end of this entry, so don't skip it thinking it is just a series of papers.

Empirical Quantization for Sparse Sampling Systems by Michael A. Lexa. The abstract reads;

We propose a quantization design technique (estimator) suitable for new compressed sensing sampling systems whose ultimate goal is classification or detection. The design is based on empirical divergence maximization, an approach akin to the well-known technique of empirical risk minimization. We show that the estimator’s rate of convergence to the “best in class” estimate can be as fast as n^−1, where n equals the number of training samples.

Two papers that look similar:
Concentration of Measure for Block Diagonal Measurement Matrices by Michael Wakin, Jae Young Park, Han Lun Yap, and Christopher J. Rozell. The abstract reads:

Concentration of measure inequalities are at the heart of much theoretical analysis of randomized compressive operators. Though commonly studied for dense matrices, in this paper we derive a concentration of measure bound for block diagonal matrices where the nonzero entries along the main diagonal blocks are i.i.d. subgaussian random variables. Our main result states that the concentration exponent, in the best case, scales as that for a fully dense matrix. We also identify the role that the energy distribution of the signal plays in distinguishing the best case from the worst. We illustrate these phenomena with a series of experiments.

and Concentration of Measure for Block Diagonal Matrices with Repeated Blocks by Christopher J. Rozell, Han Lun Yap, Jae Young Park, Michael Wakin. The abstract:

The theoretical analysis of randomized compressive operators often relies on the existence of a concentration of measure inequality for the operator of interest. Though commonly studied for unstructured, dense matrices, matrices with more structure are often of interest because they model constraints on the sensing system or allow more efficient system implementations. In this paper we derive a concentration of measure bound for block diagonal matrices where the nonzero entries along the main diagonal are a single repeated block of i.i.d. Gaussian random variables. Our main result states that the concentration exponent, in the best case, scales as that for a fully dense matrix. We also identify the role that the signal diversity plays in distinguishing the best and worst cases. Finally, we illustrate these phenomena with a series of experiments.

and a thesis entitled: New Sampling and Detection Approaches for Compressed Sensing and their Application to Ultra Wideband Communications by Zhongmin Wang. The abstract reads:

Compressed sensing (CS) provides an efficient way to acquire and reconstruct sparse signals from a limited number of linear projection measurements leading to sub-Nyquist sampling rates. The advantages of compressed sensing include simpler hardware design, faster acquisition time, and less power consumption. In this thesis, several important applications of compressed sensing are addressed and better performance than that of existing solutions is obtained by exploiting the theory of compressed sensing. Firstly, we focus on designing efficient sampling methods for image acquisition based on CS. A key to the success of CS is the design of the measurement ensemble. A novel variable density sampling strategy is designed, where the a priori information of the statistical distributions that natural images exhibit in the wavelet domain is exploited. The proposed variable density sampling has the following advantages: 1) the generation of the measurement ensemble is computationally efficient and requires less memory; 2) the necessary number of measurements for image reconstruction is reduced; 3) the proposed sampling method can be applied to several transform domains and leads to simple implementations. The application of our proposed method to magnetic resonance imaging (MRI) is also provided in this thesis. Secondly, we address the detection of sparse signals within the CS domain. A new family of detectors called subspace compressive detectors are developed for the detection of sparse signals based on the theory of compressed sensing. The proposed detectors reduce the number of measurements needed for a given detection performance by exploiting the fact that the sparse signal resides in a low dimension subspace. By designing random projection operators tailored to the subspace where the signal-of-interest lies, the signal energy can be captured more efficiently leading to better detection performance. The information of the signal subspace can be learned from compressive measurements of training signals and the detectors are adaptive to the signal structure. Within the compressed sensing framework, it is shown that very limited random measurements of training signals can suffice to provide valuable information of the signal subspace for detection purposes. The performance of the proposed subspace compressive detectors is analyzed and implementation issues including the waveform quantization are discussed. Subspace compressive detection under narrowband interference is also considered in this thesis.
In the last part of this dissertation, the theory of compressed sensing is exploited in the design of a new type of suboptimal impulse ultra-wideband (I-UWB) receivers where only sub-Nyquist sampling of the received UWB signal is required. However, the proposed I-UWB receivers have simple hardware implementations and, at the same time, shares the flexibility in data processing with full-resolution digital receivers based on Nqyuist sampling. An improved symbol detection method is proposed for I-UWB communications by exploiting the sparsity of the received UWB signals, where the sparsity is mainly due to the multipath diversity introduced by I-UWB channels. A compressive pilot assisted time-hopping spread-spectrum signaling is introduced and performance analysis of the proposed receivers is provided. Compared with other suboptimal I-UWB receivers, satisfactory detection performance is achieved with simple hardware implementation.

Finally, we have a video of Andrea Montanari on Iterative Algorithms. The abstract of the talk:

The problem of estimating a high dimensional vector from a set of linear observations arises in a number of engineering disciplines. It becomes particularly challenging when the underlying signal has some non-linear structure that needs to be exploited. I will present a new class of iterative algorithms inspired by probabilistic graphical models ideas, that appear to be asymptotically optimal in specific contexts. I will discuss in particular the application to compressed sensing problems. [Joint work with David L. Donoho and Arian Maleki]

Credit: NASA / JPL / SSI / color composite by Gordan Ugarkovic, Titan's ring via the planetary society blog.