CS: dental CT, Fast MRI, Joint-sparse recovery from multiple measurements, Counting the Scaled +1/-1 Matrices with RIP, Sparse Event Detection in SN

Compressed sensing metal artifact removal in dental CT by JiYoung Choi, Min Woo Kim, W. Seong and Jong Chul Ye, The abstract reads;

Metal artifact removal (MAR) has been an important issue in dental X-ray CT due to the presence of metal implant and fillings. The practical use of most existing MAR methods have limitations due to their inherent drawbacks. In this research, we propose a novel MAR algorithm in dental CT. Based on the sparse volume occupation of the metallic inserts, we can formulate the MAR problem as a sparse recovery problem within the compressed sensing framework. One of the main advantages of employing compressed sensing theory in MAR problem is that the sparseness of the metallic objects allows us to reduce the view samples significantly without loss of image quality, accelerating the proposed MAR algorithm drastically. Experimental results using real dental CT scanner measurements show that our algorithm can perform accurate metallic artifact removal very quickly.

I like what I see near the end, emphasis are mine:

Even though most of MAR methods have been evaluated based on the reconstruction quality of axial sections, in diagnosis of teethridge infection, sagittal and coronal sections are, however, important as much as axial sections. Especially, the dark shadow between metallic inserts are often misdiagnosed as inflammation. So the removal of such artifacts are one of the most important criteria from a clinical perspective. In Figure 5, we can confirm that CS-MAR outperforms conventional MAR method for the sagittal and coronal sections, as well as axial sections.

I don't think that I have seen that the main reason for undersampling is to reduce the radiation dose to the patient, which as a nuclear engineer I am always sensitive to.

Performance evalution of accelerated functional MRI acquisition using compressed sensing by Hong Jung and Jong Chul Ye. The abstract reads:

Functional MRI (fMRI) has been widely accepted as a standard tool to study the function of brain. However, because of the limited temporal resolution of MR scanning, researchers have experienced difficulties in various event related cognitive studies which usually require higher temporal resolution than the current acquisition protocol. Even if several accelerated fMRI methods have been proposed to overcome the limited temporal resolution, the results have not been widely accepted since there were concerns whether the result came from blood oxygen level-dependent (BOLD) signal or artifacts due to down sampling. The main contribution of this paper is to propose a new high spatio-temporal resolution fMRI technique based on compressed sensing theory and to justify the performance using receiver operating characteristic (ROC) curve.

Joint-sparse recovery from multiple measurements by Ewout van den Berg and Michael Friedlander. The abstract reads:

The joint-sparse recovery problem aims to recover, from sets of compressed measurements, unknown sparse matrices with nonzero entries restricted to a subset of rows. This is an extension of the single-measurement-vector (SMV) problem widely studied in compressed sensing. We analyze the recovery properties for two types of recovery algorithms. First, we show that recovery using sum-of-norm minimization cannot exceed the uniform recovery rate of sequential SMV using L1 minimization, and that there are problems that can be solved with one approach but not with the other. Second, we analyze the performance of the ReMBo algorithm [M. Mishali and Y. Eldar, IEEE Trans. Sig. Proc., 56 (2008)] in combination with L1 minimization, and show how recovery improves as more measurements are taken. From this analysis it follows that having more measurements than number of nonzero rows does not improve the potential theoretical recovery rate.

The attendant code allowing one to reproduce the figures of this paper can be found here.


The Rice repository added two new additions:

Counting the Scaled +1/-1 Matrices that Satisfy the Restricted Isometry Property by Gilles Gnacadja. The abstract reads:

An mxn real matrix \phi is said to satisfy the Restricted Isometry Property (RIP) of order k if it nearly preserves the l2-norm of all vectors in Rn that have no more than k nonzero entries. Matrices that satisfy the RIP are useful in compressed sensing, a fast-expanding eld of mathematics and signal processing. The mxn matrices with entries +1 and -1 and scaled by 1/sqrt(m) are often mentioned as an example of matrices that satisfy the RIP with high probability. We show that if n \lt 2^m-1, then the precise count of these matrices that satisfy the RIP of order k = 2 is

\rho(m,n) = 2^n Product( 2^(m-1) -j)

and the restricted isometry constants do not exceed 1 - 2/m. If n ¡\gt 2^(m-1), then there are no scaled +1/-1 matrices of size mxn that satisfy the RIP, except for the order k = 1.

and Sparse Event Detection in Wireless Sensor Networks using Compressive Sensing by Jia Meng, Husheng Li, and Zhu Han, The abstract reads:

Compressive sensing is a revolutionary idea proposed recently to achieve much lower sampling rate for sparse signals. For large wireless sensor networks, the events are relatively sparse compared with the number of sources. Because of deployment cost, the number of sensors is limited, and due to energy constraint, not all the sensors are turned on all the time. In this paper, the first contribution is to formulate the problem for sparse event detection in wireless sensor networks asa compressive sensing problem. The number of (wake-up) sensors can be greatly reduced to the similar level of the number of sparse events, which is much smaller than the total number of sources. Second, we suppose the event has the binary nature, and employ the Bayesian detection using this prior information. Finally, we analyze the performance of the compressive sensing algorithms under the Gaussian noise. From the simulation results, we show that the sampling rate can reduce to 25% without sacrificing performance. With further decreasing the sampling rate, the performance is gradually reduced until 10% of sampling rate. Our proposed detection algorithm has much better performance than the l1-magic algorithm proposed in the literature.

Image Credit: NASA/JPL/Space Science Institute, Saturn Moon shadow as explained here.