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Abstrak :
Compressive sensing (CS) adalah teknik yang menghasilkan pengurangan dimensi pada akuisisi sinyal dengan cara mengalikan suatu matriks proyeksi dengan sinyal. Sparse Synthesis Model Based (SSMB) memodelkan sebuah sinyal sebagai kombinasi linier kolom-kolom pada matriks synthesis dictionary menggunakan sedikit koefisien. Cosparse Analysis Model Based (CAMB) memberikan model alternatif di mana koefisien cosparse didapatkan dengan mengalikan analysis dictionary (operator) dengan sinyal. Matriks proyeksi yang digunakan pada CS dapat dioptimasi untuk meningkatkan kualitas sinyal rekonstruksi. Optimasi matriks proyeksi banyak dilakukan pada SSMB-CS sedangkan optimasi matriks proyeksi pada CAMB-CS sejauh yang diketahui sampai saat ini belum ada yang mengusulkan. Di dalam penelitian ini diusulkan metode optimasi matriks proyeksi pada CAMB- CS dengan memperhitungkan parameter amplified Cosparse Representation Error (CSRE) dan relative amplified CSRE, di samping parameter mutual coherence. Matriks proyeksi teroptimasi pada CAMB-CS diperoleh menggunakan algoritma alternating minimization dan metode nonlinear conjugate gradient. Matriks acak Gaussian digunakan sebagai matriks proyeksi mula-mula dalam algoritma optimasi tersebut. Matriks proyeksi teroptimasi yang dihasilkan menurunkan average mutual coherence rata-rata sebesar 35,62% dari matriks acak Gaussian. Matriks proyeksi teroptimasi pada CAMB-CS memiliki average mutual coherence rata-rata sebesar 12,47% lebih kecil dari matriks proyeksi teroptimasi pada SSMB-CS. Matriks proyeksi teroptimasi pada CAMB-CS juga memberikan relative amplified CSRE berorde 10-6 – 10-5, lebih kecil dibandingkan dengan matriks acak Gaussian CAMB-CS (10-4 – 10-2) dan relative amplified Sparse Representation Error (SRE) matriks proyeksi teroptimasi SSMB-CS (10-3 – 10-1). Penurunan average mutual coherence dibarengi dengan relative amplified CSRE yang kecil akan meningkatkan kualitas citra rekonstruksi yang diukur menggunakan Peak Signal to Noise Ratio (PSNR) dan Structural Similarity Index Measure (SSIM). Hasil-hasil simulasi menunjukkan peningkatan PSNR dan SSIM citra rekonstruksi masing-masing sampai dengan 15,22% dan 9,24%, dibandingkan matriks acak Gaussian. Dibandingkan matriks proyeksi teroptimasi SSMB-CS, metode yang dikembangkan meningkatkan PSNR dan SSIM citra rekonstruksi masing-masing sampai dengan 23,66% dan 17,11%. ......The Compressive Sensing (CS) technique provides a signal acquisition dimensional reduction by multiplying a projection matrix with the signal. Sparse Synthesis Model Based (SSMB) models a signal as a linear combination of columns on the synthesis dictionary matrix using a few coefficients. The projection matrix used in CS can be optimized to improve the quality reconstructed signal. The projection matrix optimization is mostly done in SSMB-CS, while the optimization of the projection matrix in CAMB-CS as far as is known has not yet been proposed. In this research, the projection matrix optimization method in CAMB-CS is proposed by taking into account the amplified Cosparse Representation Error (CSRE) parameter and the relative amplified CSRE to optimize the projection matrix, in addition to the mutual coherence parameter. The optimized projection matrix in CAMB-CS is obtained using an alternating minimization algorithm and nonlinear conjugation gradient method. In the optimization algorithm, the Gaussian random matrix is used as the initial projection matrix. The resulting optimized projection matrix reduces average mutual coherence by 35.62% from the Gaussian random matrix. The optimized projection matrix in CAMB-CS has average mutual coherence, 12.47% less than the optimized projection matrix in SSMB- CS. The optimized projection matrix in CAMB-CS also provides a relative amplified CSRE of order 10-6 – 10-5, which is smaller than the Gaussian random matrix in CAMB-CS (10-4 – 10-2) and relative amplified Sparse Representation Error (SRE) of the optimized projection matrix in SSMB-CS (10-3 – 10-1). The decrease in average mutual coherence and a small relative amplified CSRE will improve the reconstructed image quality as measured using the Peak Signal to Noise Ratio (PSNR) and the Structural Similarity Index Measure (SSIM). The simulation results showed an increase in the PSNR and SSIM of the reconstructed image up to 15.22% and 9.24%, respectively, compared to the Gaussian random matrix. Compared to the SSMB-CS optimized projection matrix, the developed method increases the PSNR and SSIM of the reconstructed image up to 23.66% and 17.11%, respectively.

Abstrak :
ABSTRAK

Synthetic aperture radar (SAR) adalah sebuah teknologi remote sensing yang dapat memproduksi citra dengan resolusi yang tinggi terhadap sebuah objek tanpa bergantung dengan waktu akuisisi, jarak dan cuaca. Hal itu menyebabkan tingginya laju akuisisi, besarnya volume raw data, besarnya daya yang harus digunakan dan dibutuhkannya filter yang cocok (Match Filter). Metode konvensional SAR memiliki kekurangan yang salah satunya yaitu munculnya permasalahan side lobes sehingga mengurangi kualitas dari citra. Compressed Sensing (CS) adalah sebuah paradigma baru untuk merekonstruksi sinyal/data dari jumlah sampling yang sedikit sehingga memperoleh hasil yang lebih efisien. CS dapat menghapus fungsi match filter, mengurangi laju akuisisi dan mengurangi sidelobe pada data SAR. Dalam penelitian ini, akan membahas simulasi pengolahan citra SAR buatan pada lima jumlah target sparse dengan metode CS dan melakukan optimasi matriks pengukuran dengan menggunakan metode Gradient-Based Minimization yang dapat meningkatkan kualitas rekonstruksi dengan menurunkan nilai koherensi matriks pengukuran. Alat ukur yang digunakan yaitu dengan parameter kualitatif dan kuantitatif RMSE dan PSNR. Hasil menunjukkan dengan menggunakan optimasi terhadap matriks pengukuran pada kondisi noise-free terdapat perbaikan hasil rekonstruksi setelah optimasi terjadi pada jumlah sampling dibawah 39. Sedangkan pada kondisi noise, terjadi perbaikan nilai yang signifikan pada derau yang tinggi pada nilai SNR di bawah 30 dB

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ABSTRACT

Synthetic aperture radar (SAR) is a remote sensing technology which can generate images with high resolution on an object without having to depend on the time of acquisition, the distance, and the weather. It causes a high rate of acquisition, the large volume of raw data, high power consumption that should be used, and it also requires Match Filter. The conventional method of SAR has some lacks, one of which is the happening of side lobes problem which causes it to reduce the quality of the image. Compressed Sensing (CS) is a new paradigm to reconstruct the signal/data from few numbers of sampling in order to obtain more efficient results. CS can eliminate the match filter, reduce the acquisition rate, and minimize the effects of side lobes on SAR data. This research will discuss the image processing simulation of artificial SAR on the target amount (K=5) by using CS method and do the optimization of measurement matrix by using Gradient-Based Minimization which can improve the quality of reconstruction by decreasing the coherence value of measurement matrix. The used measuring tools are the qualitative and quantitative parameters of RMSE and PSNR. The result shows that, in using optimization for measurement matrix in noise free condition, there is improvement in the reconstruction result after the optimization occurs in the number of sampling M≤38. Meanwhile, in noise condition, there is significant movement in the value of high noise (SNR<30 dB).

Abstrak :


ABSTRAK
Akusisi sinyal adalah hal yang penting dalam teknologi modern. Compressive sensing dapat membuat proses akusisi sinyal atau data lebih cepat dan efektif. Compressive sensing memungkinkan jumlah pengukuran atau sampling yang jauh lebih sedikit dibandingkan sinyal asli. Compressive sensing digunakan secara luas pada berbagai bidang, seperti radar, kamera, pencitraan medis, seismic imaging, cognitive radio hingga wireless sensor network WSN . Hal penting dalam compressive sensing adalah memilih matriks proyeksi dan kamus basis sparse yang memenuhi Restricted Isometry Property RIP . Namun pengujian RIP sulit untuk dilakukan sehingga digunakan parameter lain yang lebih mudah untuk dihitung, yaitu mutual coherence. Berbeda dengan RIP, mutual coherence memerikan jaminan rekonstruksi yang lebih lemah. Sehingga dilakukan analisis hubungan antara mutual coherence terhadap hasil rekonstruksi citra. Didapatkan bahwa pada sistem kompresi, mutual coherence memiliki hubungan yang kuat terhadap citra hasil rekonstruksi. Sedangkan pada sistem pencitraan ECVT, mutual coherence hanya memiliki hubungan yang sangat lemah terhadap citra hasil ECVT.

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ABSTRAK
In modern technology, signal acquisition is important. Compressive sensing can make the process of acquiring signals or data to be more quickly and effectively. Compressive sensing allows a much smaller number of measurements or sampling than the original signal. Compressive sensing is widely used in various fields, such as radar, cameras, medical imaging, seismic imaging, cognitive radio to wireless sensor networks WSN . An important point in compressive sensing is to choose a projection matrix and a dictionary that meets Restricted Isometry Property RIP . But RIP testing is difficult to do, so that other parameter is used because it is easier to calculate, namely mutual coherence. Unlike RIP, mutual coherence only provides a weaker reconstruction guarantee. So that this research do analysis of relation between mutual coherence and reconstructed image. It was found that in the compression system, mutual coherence has a strong relationship to the reconstructed image. While in ECVT imaging systems, mutual coherence has only a very weak relationship to the ECVT image results.

Abstrak :
"The text is organized into concise chapters, each discussing an important point relevant to clinical MR and illustrated with images from routine patient exams. The topics covered encompass the breadth of the field, from imaging basics and pulse sequences to advanced topics including contrast-enhanced MR angiography, spectroscopy, perfusion, and advanced parallel imaging techniques. Discussion of the latest hardware and software innovations--for example, MR-PET, interventional MR, compressed sensing, and multishot EPI--is included because these topics are critical to current and future advances. Included in the third edition are a large number of new topics, keeping the text up-to-date in this increasingly complex field. The text has also been revised to include additional relevant clinical images, to improve the clarity of descriptions, and to increase the depth of content"--Provided by publisher.

Abstrak :
This book presents a comprehensive review of the recent developments in fast L1-norm regularization-based compressed sensing (CS) magnetic resonance image reconstruction algorithms. Compressed sensing magnetic resonance imaging (CS-MRI) is able to reduce the scan time of MRI considerably as it is possible to reconstruct MR images from only a few measurements in the k-space; far below the requirements of the Nyquist sampling rate. L1-norm-based regularization problems can be solved efficiently using the state-of-the-art convex optimization techniques, which in general outperform the greedy techniques in terms of quality of reconstructions. Recently, fast convex optimization based reconstruction algorithms have been developed which are also able to achieve the benchmarks for the use of CS-MRI in clinical practice. This book enables graduate students, researchers, and medical practitioners working in the field of medical image processing, particularly in MRI to understand the need for the CS in MRI, and thereby how it could revolutionize the soft tissue imaging to benefit healthcare technology without making major changes in the existing scanner hardware. It would be particularly useful for researchers who have just entered into the exciting field of CS-MRI and would like to quickly go through the developments to date without diving into the detailed mathematical analysis. Finally, it also discusses recent trends and future research directions for implementation of CS-MRI in clinical practice, particularly in Bio and Neuro-informatics applications.