Compressive sensing of images encompasses the following stage processes: Representation of sparse signal, constructing the linear measurement and reconstructing of the image. This paper, presents the novelty of representing the sparse signal based on dictionary learning method. The choice of designing the dictionary model based on deep learning methodology, which delivers a simple and expressive structure for designing well-organized and efficient dictionaries. The norm- difference of the image is used of evaluating the performance of dictionary learning based algorithms. Experimental result shows that the matching pursuit (OMP) performance has better output when compared to Least Angle Regression (LAR) algorithm. The result indicates that the sparse modelling using dictionary learning with Orthogonal Matching Pursuit is proficient in CS of MRI images. Compressive sensing, sparse representation, dictionary learning, medical images.
Compressive sensing (CS) is plays on vital role in signal processing community. The signals can
be restored as a compressed form is called the new signal acquisition in a compressive sensing. The
signals are basic tools of processing the video clips, medical scans and natural images [
Dictionary Learning (DL) transforms data into sparse representation. The well-known DL method
is KSVD [
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large scale data. Data-driven tight frame (DDTF)is a recently developed method to gain efficient output.
By the term tight frame, we that the frame has a sound reconstruction property i.e., signal
representation by means of linear combination of atoms can be specified with products in the signal
and dictionary [
The objective of this work is to modelling the sparse matrix using dictionary learning method with a help of deep learning architectures for compressive sensing process of medical images. This requires the comparability of the reconstruction algorithms orthogonal matching pursuit (OMP) and least angle regression (LAR).This paper is organized as follows: in Section 2 we give the overview of the dictionary learning. In Section 3 sparse modelling using dictionary learning discussed. Interpretations of the results of the experimentation are shown in section 4 and conclusion is drawn in section 5.
In CS the sparse representation process is the essential for modelling the dictionary. As expected,
the signals are sparse and can be restored form the linear projection of space or time measurements
[
x = = ∑ =1 (1) b is not unique when the dictionary is over complete. This is the point where a sparsity constraint has avital role. Decrease of requirements of the sparse, higher the efficiency of sparse representation. With approximation error for bounded energy the sparse linear expansion is obtained. Our main aim is to find sparse vector b containing minimal significant coefficients, and the remaining coefficients lesser than are equal to zero. In other words, our objective is to have limited no of resources (atoms) for representing the signal.
Min|| ||0 subject to x = + and || |2|2< (2)
Where ||. || represents the l norm and the problem is non-deterministic polynomial-time (NP)
hard. In order to obtain the suboptimal solution for vector b, the method of approximation
algorithms for polynomials with respect to time are used [
The convex 1 norm is replaced by non-convex 0 norm through convex relaxation, where 0 has
nonzero elements and the term norm is used when p approaches zero. Apart from pursuit algorithms
other algorithms are also used such as focal underdetermined system solver [
In research, three main streams with three algorithm groups are used for dictionary learning. They include 1. probabilistic learning; 2. The learning methods clustering or vector quantization-based learning; 3. particular construction learning with dictionaries. The construction comprises of data structure or focus on managing dictionaries. This section provides three important principles of algorithm representation with three dictionary Learning categories. The over complete dictionary must be well examined than complete dictionary [14]. In order to define over complete dictionaries there, exist two representations namely analysis path and synthesis path. In the area of signal processing, learning is a topic whereas dictionary is referred to represent spare or signal approximation. The dictionary consists of atom collection where atoms refer to real column vectors with length. For example a dictionary with finite number k can be represented as a matrix D with size. Similarly, a sparserepresentation can be represented as a linear combo of dictionary atoms [12].
The size of the normal image is too large, it can be partition into N× image blocks and sparse modelling can be done using image blocks X = [x1, x2, x3, xL], each of size √ × √ pixels, where
√ is an integer value. Learning of dictionaries determines the vector approximation with sparse
criteria on coefficients i.e., it allows minimal nonzero coefficients. The dictionary is fit in LHS for the
reconstruction to happen on RHS. It is noticed that a better output is retrieved from an undistorted
image but here we start with a contradiction [
Since the real world image is larger we segregate it into smaller blocks and modelling is done in that particular set.
Here it deals with the medical image Cardiac [16] considered for experimentation as shown in Fig.2.Theexecution of software for this method is implemented with the language Python with help of Intel Core (R) 64-bit processor with 8.00 GB RAM, 2.60GHz clock speed on the Windows11operatingsystem. The Dictionary learning domain is applied in sparse Representation using deep learning methodology. Using dictionary model the linear measurement is also achieved to obtain the linear measurement and image reconstruction using the orthogonal matchingpursuit method and least angle regression (LAR) method is executed for the reconstruction of the enhanced image. The CAD cardiac MRI images undergo training with limited time and reconstruction achieved by norm value. The following metrices PSNR, norm value and time are measured to validate the results of CS.
The regional practice of gaining results in denoising image is obtained by comparing the original and reconstructed images. If the reconstructed image becomes perfect then it resembles the Gaussian noise.It can be notified from the plotting that the output from imp with 2 nonzero coefficients is less biased whereas with one non-zero coefficient it becomes a controversy [13].
The cardiac MRI images are initially learning from dictionaries and classified into 7076 patches
with total training time of (3.0sec.). By training the dataset in deep learning method the cardiac MRI
dataset with the single atom dictionary of orthogonal matching pursuit algorithm has obtained the
maximum norm value (5.00) with minimum computation time(0.4sec.). Secondly, the dictionary of
two atom OMP method is yielded the (4.18) with time consumption (0.8sec.). For the same, sparse
dictionary learning and least angle recursion method has shown least performance in terms of norm
(6.18), needs more computation time (5.7 sec). Threshold value is obtained the higher norm (6.85)
value with minimal time (0.1) but it doesn’t provide the desired image. The Measurement metrics
PSNR are observed that orthogonal matching pursuit algorithm with single dictionary atom are
achieved the desired results (33.02dB) orthogonal matching pursuit algorithm with two dictionary
atom performs secondly, threshold performs poor denoising in the PSNR value (25.01 dB). On the
whole, Dictionary learning with OMP method is able to accomplish near to the extreme one in terms
of all the metrics. It is obvious that, least angle recursion algorithm is the second in performance [
In addition, it is closer to F norm and LAR is strongly biased with differing intensity value of original image. Though thresholding gives efficient output and is used in other tasks such as object clarificationwith relating visuals, it is less helpful in denoising.
In this paper, the novelty of developing the sparse modelling with dictionary learning method using deep learning performs well on MRI images. The performance of the sparse modelling using dictionary learning with least angle regression method and Orthogonal matching pursuit are calculated based on the experimentation using Cardiac MRI image. Generally, to find better output performance the image of reconstructed image or difference norm image and original images are consider.MRI dataset with the single atom dictionary of orthogonal matching pursuit algorithm obtained the highest norm value with minimum time for computation. Sparse dictionary learning and least angle recursion method exhibits low performance concerning norm, which needs more computation time. Threshold value is obtained the higher norm value with minimal time but it doesn’t provide the desired image. OM achieves most suitable results compared with performance of LAR. Further work can be done by testing the methods of compressive sensing using the dictionary learning model which can be extended to medical images.