A multiplication-free framework for signal processing and applications in biomedical image analysis

A new framework for signal processing is introduced based on a novel vector product definition that permits a multiplier-free implementation. First a new product of two real numbers is defined as the sum of their absolute values, with the sign determined by product of the hard-limited numbers. This new product of real numbers is used to define a similar product of vectors in RN. The new vector product of two identical vectors reduces to a scaled version of the l1 norm of the vector. The main advantage of this framework is that it yields multiplication-free computationally efficient algorithms for performing some important tasks in signal processing. An application to the problem of cancer cell line image classification is presented that uses the notion of a co-difference matrix that is analogous to a covariance matrix except that the vector products are based on our new proposed framework. Results show the effectiveness of this approach when the proposed co-difference matrix is compared with a covariance matrix. © 2013 IEEE

Approximate Computation of DFT without Performing Any Multiplications: Applications to Radar Signal Processing

In many practical problems it is not necessary to compute the DFT in a perfect manner including some radar problems. In this article a new multiplication free algorithm for approximate computation of the DFT is introduced. All multiplications $(a\times b)$ in DFT are replaced by an operator which computes $sign(a\times b)(|a|+|b|)$. The new transform is especially useful when the signal processing algorithm requires correlations. Ambiguity function in radar signal processing requires high number of multiplications to compute the correlations. This new additive operator is used to decrease the number of multiplications. Simulation examples involving passive radars are presented

Compressively Sensed Image Recognition

Compressive Sensing (CS) theory asserts that sparse signal reconstruction is possible from a small number of linear measurements. Although CS enables low-cost linear sampling, it requires non-linear and costly reconstruction. Recent literature works show that compressive image classification is possible in CS domain without reconstruction of the signal. In this work, we introduce a DCT base method that extracts binary discriminative features directly from CS measurements. These CS measurements can be obtained by using (i) a random or a pseudo-random measurement matrix, or (ii) a measurement matrix whose elements are learned from the training data to optimize the given classification task. We further introduce feature fusion by concatenating Bag of Words (BoW) representation of our binary features with one of the two state-of-the-art CNN-based feature vectors. We show that our fused feature outperforms the state-of-the-art in both cases.Comment: 6 pages, submitted/accepted, EUVIP 201

Flexible Multi-layer Sparse Approximations of Matrices and Applications

The computational cost of many signal processing and machine learning techniques is often dominated by the cost of applying certain linear operators to high-dimensional vectors. This paper introduces an algorithm aimed at reducing the complexity of applying linear operators in high dimension by approximately factorizing the corresponding matrix into few sparse factors. The approach relies on recent advances in non-convex optimization. It is first explained and analyzed in details and then demonstrated experimentally on various problems including dictionary learning for image denoising, and the approximation of large matrices arising in inverse problems

Communication channel analysis and real time compressed sensing for high density neural recording devices

Next generation neural recording and Brain- Machine Interface (BMI) devices call for high density or distributed systems with more than 1000 recording sites. As the recording site density grows, the device generates data on the scale of several hundred megabits per second (Mbps). Transmitting such large amounts of data induces significant power consumption and heat dissipation for the implanted electronics. Facing these constraints, efficient on-chip compression techniques become essential to the reduction of implanted systems power consumption. This paper analyzes the communication channel constraints for high density neural recording devices. This paper then quantifies the improvement on communication channel using efficient on-chip compression methods. Finally, This paper describes a Compressed Sensing (CS) based system that can reduce the data rate by > 10x times while using power on the order of a few hundred nW per recording channel

Graphics processing unit accelerating compressed sensing photoacoustic computed tomography with total variation

Photoacoustic computed tomography with compressed sensing (CS-PACT) is a commonly used imaging strategy for sparse-sampling PACT. However, it is very time-consuming because of the iterative process involved in the image reconstruction. In this paper, we present a graphics processing unit (GPU)-based parallel computation framework for total-variation-based CS-PACT and adapted into a custom-made PACT system. Specifically, five compute-intensive operators are extracted from the iteration algorithm and are redesigned for parallel performance on a GPU. We achieved an image reconstruction speed 24–31 times faster than the CPU performance. We performed in vivo experiments on human hands to verify the feasibility of our developed method