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Study On The Ultrasonic Detection And Image Restoration Technologies Based On The Theory Of Convex Optimization

Posted on:2015-03-08Degree:DoctorType:Dissertation
Country:ChinaCandidate:C Y ChenFull Text:PDF
GTID:1108330464968881Subject:Circuits and Systems
Abstract/Summary:PDF Full Text Request
Traditional signal processing methods, including signal-domain methods such as linear filters and transform-domain methods such as Fourier analysis, are widely applied in solving well-posed problems in the engineering field. However, with the increasingly deep study and the rapid technique development, more and more ill-posed problems have arised in the engineering field. The framework of traditional signal processing can hardly meet the requirement of high performance. With the growth of the convex optimization theory, many new signal processing methods based on convex optimization are applied in the engineering field. Due to the flexibility and the stability of the convex optimization framework, these new methods can handle some ill-posed problems that traditional methods cannot handle, and achieve better performance compared to the traditional methods. Since the convex optimization theory is still developing, it is necessary to learn and utilize the emerging theory of convex optimization to solve practical engineering problems.Compressed sensing(CS), low-rank and sparse decomposition(LRSD) of matrices, and cross-modality filters are three new signal processing methods that developed rapidly in recent years, which have been used in many engineering applications and achieved great success. As a result, this paper will firstly give an analysis for these methods in the viewpoint of convex optimization, which reveals the connection between these methods and convex optimization and summarizes the common idea of utilizing these methods to solve practical problems. Then, considering that pulse signal, image, and video are representative multidimensional signals, this paper concentrates on the processing of these three types of signals. In particular, a high-resolution detection technique using narrowband transmitted signals, a restoration method for depth images, and a scheme for improving the compression performance of videos in this paper. The main researches and contributions of this paper are:1. We have proposed an ultrasonic detection technique that is able to use narrowband transmitted signals to achieve high-resolution detection. To solve the problem of highly overlapping echoes in narrowband ultrasonic detection, we propose a decoupling method based on convex optimization by combining CS theory and singular value decomposition, which improves the resolution of narrowband signal detection. First, we formulate the separation of pulse signals in ultrasonic detection as a non-convex optimization problem. Then, we convert it to a convex optimization problem with the guidance of the CS theory. Moreover, we employ singular value decomposition to extract the dominant components of transmitted pulse and echo signals, so that we can compress the dictionary and solve the high-dimensional optimization in a low-dimensional subspace. Because there is no constraint on the bandwidth in the CS theory, the proposed method can separate the narrowband signals that cannot be separated by the traditional methods. Simulations show that the proposed method can handle several types of signal distortions, including additional noise, loss of frequency components, and phase variations, and obtain better signal separation performance compared to other existing methods. Experimental results on real ultrasonic data show that the proposed method can also improve the range resolution of ultrasonic imaging systems.2. We have proposed an unified framework for the recovery of structure-light depth and its corresponding local filters. To handle the special noise and edge misalignments of Kinect depth data, we propose a formulation of convex optimzation which integrates local filtering and depth regularization term. We also develop an approximate solution for it, which enables fast and accurate Kinect depth recovery. First, from the perspective of convex optimization, we formulate depth recovery as an energy minimization problem whose fidelity term takes into account the characteristics of sensor data and regularization term involves the improvement of existing cross-modality filters, resulting in a framework that can simultaneously do the depth denoising and depth hole-filling. Based on this framework, we propose local filters that approximate the solving procedures by analyzing the solution to the proposed optimization problem. To quantitatively evaluate the quality of depth recovery, we generate a specific database that simulates the characteristics of real devices. Numerous evaluations for different features of depth recovery are done for the existing mainstream methods of depth recovery. The experimental results show that, the proposed depth recovery method outperforms other methods in terms of recovery accuracy.3. We have proposed a scheme that can improve the compression performance of the existing video codecs for videos captured by fixed cameras. Because the efficiency in compressing videos with fixed backgrounds is to be improved, we use the low-rank property to utilize the temporal redundancy of such videos and propose a LRSD based video coding scheme, which improves the coding efficiency. We also propose an optimization model for incremental decomposition, which reduces the memory cost. Considering there is large amount of background redundancy in these videos, and low-rank and sparse properties can compactly represent the background and foreground components respectively, we formulate the separation of foreground and background as the LRSD of a matrix. Then, after solving the decomposition via convex optimization, we obtain the low-rank background and sparse foreground, which are compressed by the existing codecs. Experimental results show that the proposed scheme can efficiently improve the mainstream video codecs. In particular, at the relatively low bitrates, the proposed method can achieve up to 5 d B of performance gain. In addition, to reduce the memory requirement of the existing LRSD algorithms and enable large-scale video processing, we propose an incremental LRSD algorithm consisting of two steps, incremental low-rank decomposition and incremental sparse decomposition. These two steps efficiently reduce the memory requirement of LRSD, and can be used individually or simultaneously according to different video compression scenarios, resulting in very high flexibilities. Therefore, compared to the typical LRSD algorithms, the proposed incremental algorithm is more suitable for the compression of practical videos.
Keywords/Search Tags:Convex optimization, Compressed sensing, LRSD, Cross-modality filtering
PDF Full Text Request
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