Logarithmic Discrete Wavelet Transform for High-Quality Medical Image Compression

Logarithmic Discrete Wavelet Transform for High Quality Medical Image Compression

By: Mohammed IBRAHEEM

29-03-2017

Prof. YANG-SONG Fan Reviewer

Prof. RABAH Hassan Reviewer

Prof. BENSRHAIR Abdelaziz Examiner

Prof. LEMIRE Daniel Examiner

Dr. HACHICHA Khalil Supervisor

M. HOCHBERG Sylvain Supervisor

Prof. GARDA Patrick Supervisor

Jury Members

Prof. MEHREZ Habib President

Outlines

29-03-201729-03-2017 LNS-DWT Mohammed IBRAHEEM – LIP6-UMPC-CIRA 33

IntroductionPart I

State of the artPart II

Logarithmic Library for image processingPart III

Logarithmic DWT based Compression Part IV

2D-DWT Hardware ArchitecturePart V

Conclusion and Future workPart VI

Part IIntroductionIntroduction

29-03-2017 LNS-DWT Mohammed IBRAHEEM – LIP6-UMPC-CIRA 4

ContextContext


E-health systemsMedical imaging technology growthResolution/Image size

E-health systemsMedical imaging technology growthResolution/Image size

Needs ?

Archive Remote access Embedded solutions

Limitations ?

Storage cost → huge numbers dailyo Full MRI exam can produce 10 GB

Bandwidth limited resources on embedded systems

ChallengesChallenges


Trade-off between image quality/compression

Vital information → preserving quality → avoid misdiagnoses

Q: How to achieve an efficient image compression while preserving the diagnostic quality?

First Challenge

Second Challenge Speed

Q: How to achieve a high-speed compression on Embedded systems?

The compression algorithm on embedded systems/limited resources

Time is a life saver

Part IIState of the artState of the art


Original Image

CompressedImage

Original Image

CompressedImage

Original Image

CompressedImage

Image Compression Algorithms Used in Medical domain Image Compression Algorithms Used in Medical domain


JPEG

Quant.DCTEntropyEncoder

Color Space

Transform

Quant.DWTEntropyEncoder

Color Space

Transform

Quant.DWTHENUCEncoder

Color Space

Transform

Based on DCT → Block artifacts

JPEG2000

Two compression modes: lossy / lossless Based on DWT No block artifacts

WAAVES

Two compression modes: lossy / lossless Based on DWT → No block artifacts Medical certified → clinical tests Efficient encoder

Hierarchical Enumerative Coding

Image Quality Issues in Image CompressionImage Quality Issues in Image Compression


Quality

issues

Arithmetic

(Real numbers)

DWT/DCT

Quantization

(Division + rounding)

Arithmetic alternatives in state of the art

• Floating-point

• Fixed-pointo Limited accuracy

o High speed - HW

Simple div/mul operations

Accuracy near to FLP

An alternative to FLP on embedded systems

Accelerate the DSP apps

Compressed

ImageQuant.

DWT

DCTEncoder

Color

Space

Transform

Original

Image

Multiplication 𝒍𝒐𝒈𝟐 𝒙 × 𝒚 = 𝒂 + 𝒃

Division 𝒍𝒐𝒈𝟐 𝒙 ÷ 𝒚 = 𝒂 − 𝒃

Addition 𝒍𝒐𝒈𝟐 𝒙 + 𝒚 = 𝒃 + 𝒍𝒐𝒈𝟐(𝟐𝒂−𝒃 + 𝟏)

Subtraction 𝒍𝒐𝒈𝟐 𝒙 − 𝒚 = 𝒃 + 𝒍𝒐𝒈𝟐(𝟐𝒂−𝒃 − 𝟏)

a= 𝒍𝒐𝒈𝟐 𝒙 , b= 𝒍𝒐𝒈𝟐 𝒚

No existing research addressed it in the image compression domain

Recently: Logarithmic number system (LNS)

Application : Smart-EEG Project (New tool) Application : Smart-EEG Project (New tool)


Mentoring RequirementsMentoring Requirements

Fast myoclonus jerks high frame rate → 100 f/s

• Currently: 30 f/s

Why 100 f/s ?Why 100 f/s ?

Correct diagnosis Real time constraints

Exam procedureExam procedure

EEG acquisition

Video acquisition

Video compression

Sync. + Transmission

Camera

(Video acquisition)

EEG Cap

(acquisition)

Academic

Industry

Hospitals

Compression Block on Smart-EEG Compression Block on Smart-EEG


HENUC Encoder unit→ implemented in LIP6 by:

Yhui / Zahid / Laurent

DWT unit → required for integration → full compression chain

Many DWT solutions

• SW : GPU/DSP

• HW: ASIC/FPGA

High speed

Limitations

DDR RAM latency not addressed

The lack of memory optimization and compatibility with HENUC

DWT Related work

Compression algorithm choice: WAAVES

Problem Statement Problem Statement


Does the logarithmic representation has the ability to improve

the trade-off between the compression ratio and the image quality?

Q.1

How to provide a new DWT hardware architecture that can

fulfill the Smart-EEG high-speed requirement?

Q.2

Part IIILNS Library For Image Compression LNS Library For Image Compression


IntroductionIntroduction


ObjectivesObjectives

The need of a tool to study the logarithmic domain Image compression compatibility

IssuesIssues

The logarithm of a negative number is undefined The logarithm of zero is undefined log(0) = -∞ The quantization process

Sign AmbiguitySign Ambiguity


Logarithmicdomain

Lineardomain

𝒙= -16𝒙= -16 𝒙 = 16

𝒗 = 𝒍𝒐𝒈𝟐( 𝒙 )

𝒗 = 𝟒

𝒙 = 𝟐𝒗

𝒙 = 𝟏𝟔

Lineardomain

Logarithmicdomain

Lineardomain

𝒙= -16𝒙= -16 𝒙 = 16

𝒗 = 𝒍𝒐𝒈𝟐( 𝒙 )

𝒙 = −𝟏𝒔 × 𝟐𝒗

Lineardomain

𝒔 = 𝟏 𝒔 = 𝟎

𝟎 4𝒔 𝒗

𝟏 4𝒔 𝒗

𝒙= -16𝒙= -16 𝒙 = 16

Proposed Solution: Sign flag

The logarithm of ZeroThe logarithm of Zero


The importance of ZerosThe importance of Zeros

Image compatibility Efficient coding Better compression ratio

Lineardomain

Logarithmicdomain

Lineardomain

𝒙 = 𝟎𝒙 = 𝟎 Ex. L = 0 * yEx. L = 0 * y

𝒗 = 𝟎𝒗 = 𝟎

𝒙 = 𝟎𝒙 = 𝟎 𝑳 = 𝟎𝑳 = 𝟎

Proposed solution: Virtual Zero

𝒍𝒐𝒈 𝟎 = −∞

Logarithmic Quantization : LNS-QLogarithmic Quantization : LNS-Q


LNS-Q Features

Novel quantization method → scaling

Controlled Precision → 𝒏𝒇 Limited quality degradation

Smaller quantization error

𝑿𝑳𝑵𝑺−𝑸 = 𝒓𝒐𝒖𝒏𝒅 𝒙 × 𝑺𝑪

𝑺𝑪 = 𝟏𝟎𝒏𝒇 = 𝟏, 𝟏𝟎, 𝟏𝟎𝟎, 𝒆𝒕𝒄 , 𝒏𝒇 ≥ 𝟎𝒙 : un-quantized logarithmic value

𝑿𝑳𝑵𝑺−𝑸 : quantized logarithmic value

𝑺𝑪 ∶ scaling factor

𝒏𝒇 ∶ number of the fractional digits

LNS-Q

Limitation

× Quality degradation

× Large quantization error

Linear-Q

𝑿𝒒 = 𝒓𝒐𝒖𝒏𝒅𝒙

𝒒𝒔𝒕𝒆𝒑

𝒒𝒔𝒕𝒆𝒑 ≥ 𝟎 : quantization step

𝒙 : un-quantized value

𝑿𝒒 : quantized value

LNS Library StructureLNS Library Structure


LNS Library

Data

LNS-Object

𝑳 = {𝒔, 𝒗}

Sign-flag

𝑳. 𝒔𝑳. 𝒔 =

𝟎, 𝒙 ≥ 𝟎𝟏, 𝒙 < 𝟎

Value

𝑳. 𝒗𝑳. 𝒗 =

𝒍𝒐𝒈( 𝒙 ), 𝒙 ≠ 𝟎𝟎, 𝒙 = 𝟎

Operators

ADD/SUB

DIV/MUL

𝒙: linear domain

LNS Arithmetic Operators : Multiplication/DivisionLNS Arithmetic Operators : Multiplication/Division


LNSOperator

A{v,s}A{v,s} B{v,s}B{v,s}

C{v,s}C{v,s}

𝐶. 𝑣 = 0, 𝐴. 𝑣 = 0 𝑜𝑟 𝐵. 𝑣 = 0𝐴. 𝑣 + 𝐵. 𝑣, 𝑚𝑢𝑙𝐴. 𝑣 − 𝐵. 𝑣, 𝑑𝑖𝑣

𝐶. 𝑠 = 0, 𝐴. 𝑣 = 0 𝑜𝑟 𝐵. 𝑣 = 00, 𝐴. 𝑠 = 𝐵. 𝑠1, 𝐴. 𝑠 ≠ 𝐵. 𝑠

Multiplication/DivisionMultiplication/Division

LNS Arithmetic Operators : Addition/SubtractionLNS Arithmetic Operators : Addition/Subtraction


LNSOperator

A{v,s}A{v,s} B{v,s}B{v,s}

C{v,s}C{v,s}

𝐶. 𝑣 =

𝐴. 𝑣 + 𝑓_𝑎𝑑𝑑, 𝐴. 𝑠 = 𝐵. 𝑠𝐴. 𝑣 + 𝑓_𝑠𝑢𝑏, 𝐴. 𝑠 ≠ 𝐵. 𝑠𝐴. 𝑣, 𝐵. 𝑣 = 0𝐵. 𝑣, 𝐴. 𝑣 = 00, 𝐴. 𝑣 = 𝐵. 𝑣0, 𝐴. 𝑣 = 𝐵. 𝑣 = 0

𝐶. 𝑠 = 𝐴. 𝑠, 𝐴 ≥ 𝐵𝐵. 𝑠, 𝐴 < 𝐵

𝑓_𝑎𝑑𝑑 = log 1 + 2𝐵.𝑣−𝐴.𝑣 𝑤ℎ𝑒𝑟𝑒 𝐵. 𝑣 > 𝐴. 𝑣

𝑓_𝑠𝑢𝑏 = log 1 − 2𝐵.𝑣−𝐴.𝑣 𝑤ℎ𝑒𝑟𝑒 𝐵. 𝑣 > 𝐴. 𝑣

Addition/subtractionAddition/subtraction

LNS–Library Validation MethodologyLNS–Library Validation Methodology


X

Y

LNS

Operator

(+,-,,×)

Linear

Operator

(+,-,,×)

LOG

LOG

EXP

Difference

(error)

Reference golden value

Linear domain Linear domainLogarithmic domain

LNS–Library Validation : MAC Case StudyLNS–Library Validation : MAC Case Study


Multiply and Accumulate (MAC) operation

𝑀 =

𝑖=0

𝑛

𝑎 × 𝑖

𝜖 = 𝑀𝑙𝑛𝑠 −𝑀𝑙𝑖𝑛

Error between logarithmic / linear

𝑎 : constant

𝑛 : number of iterations

𝑀𝑙𝑛𝑠 : MAC output (logarithmic)

𝑀𝑙𝑖𝑛 : MAC output (linear)

LNS Library Validation : 2D LNS-DWT ImplementationLNS Library Validation : 2D LNS-DWT Implementation


DWT-based 9/7 CDF filtero JPEG2000/WAAVES

Lifting Schemeo More efficient than the convolution approacho Less memory requirements

Validation results o Absolute error:

• between linear/logarithmic around 7×10−10

1D LNS-DWT

(rows)

1D LNS-DWT

(rows)

Horizontal Transform

1D LNS-DWT

(columns)

1D LNS-DWT

(columns)

Vertical Transform

LOGLOGInput image DWT coefficients

LNS-Q ValidationLNS-Q Validation


DW

T co

effi

cie

nt

valu

e

DWT coefficient location

Small Quantization Error

SummarySummary


• MAC → 7×10−8 (1000 iterations)

• LNS-DWT → 7×10−10

• DWT+LNS-Q

Novel LNS-Library Novel LNS-Library

Image compression compatibility

Virtual zero

Sign flag

Novel logarithmic-based Quantization method (LNS-Q)

o Scaling-based

ValidationValidation

PART IVLogarithmic DWT based Compression Logarithmic DWT based Compression


LNS-DWT/LNS-Q Integration with WAAVESLNS-DWT/LNS-Q Integration with WAAVES


EncoderOriginal

Image LNS-QLNS

DWT

Compression Side

EncoderCompressed

Image

.CODLOG

LimitationsLimitations Limited range of compression ratio .. Why ?

LNS Vs Linear DWT Dynamic RangeLNS Vs Linear DWT Dynamic Range


LNS

Better quality

Linear

Higher compression ratio

LNS Vs Linear DWT Data DistributionLNS Vs Linear DWT Data Distribution


Q: How to combines the advantages of the both domains into a single bit-stream ?

LNS Linear

Hybrid-DWTHybrid-DWT


LL HL

LH HH

LNS Zeros

Zeros Zeros

Zeros Linear

Linear Linear

LNS FLP

FLP FLP

Linear DWT

LL HL

LH HH

LNS DWT Masked LNS DWT

Masked Linear DWT

Merged DWT

LNS/Linear

Stage 1 Stage 2 Stage 3DescriptionDescription

DWT coefficients → 2 parts• LL sub-band → Logarithmic

• The rest sub-bands → Linear

New compression parameter:• NL : number of linear levels

• Trade-off between

o Compression ratio

o Image quality

LNS-DWT Dynamic Range Reduction FilterLNS-DWT Dynamic Range Reduction Filter


IssueIssue

Small values in the linear domain → large negative values in the

logarithmic domain

That affects the encoding efficiency

ObjectiveObjective

To Increase the number of zeros → improve the coding efficiency

HowHow

Threshold (FTH) is used to choose which value are removed

Replace the very large negative values with zeros in LNS-DWT

Part of DWT coefficients before quantization Part of DWT coefficients before quantization

After quantization only After quantization only

After DRRAfter DRR

LNS-WAAVES based on Hybrid-DWT LNS-WAAVES based on Hybrid-DWT


NL

B

FTH

SC

• B : Logarithmic base

• NL : Number of linear DWT level

• FTH : DRR threshold

• q : Quantization step (linear)

• SC : LNS-Q scale factor

q

Input

Image

Hybrid

DWTEncoder

(HENUC)

Compressed

ImageLOG

DRRFilter

Quantization

LNS-Q

Linear-Q

Evaluation Methodology Evaluation Methodology


Experiments outlines:

Log base effect

NL effect

DRR effect

Quantization effect

Experiments outlines:

Log base effect

NL effect

DRR effect

Quantization effect

Image

Image Quality Assessment : PSNR or SSIM ?Image Quality Assessment : PSNR or SSIM ?


𝑷𝑺𝑵𝑹 𝒅𝑩 =𝟐𝟎 𝒍𝒐𝒈𝟏𝟎(𝒎𝒂𝒙𝒊𝒎𝒖𝒎𝒑𝒊𝒙𝒆𝒍 𝒗𝒂𝒍𝒖𝒆)

𝑴𝑺𝑬

𝑺𝑺𝑰𝑴 𝒇,𝒈 =𝟐𝝁𝒇𝝁𝒈 + 𝑪𝟏 + 𝟐𝝈𝒇 𝝈𝒈 + 𝑪𝟐

(𝝁𝒇𝟐𝝁𝒈

𝟐 + 𝑪𝟏)(𝝈𝒇𝟐𝝈𝒈

𝟐 + 𝑪𝟐)

SSIM measures the image quality in terms of:

• Structural

• Luminance

• Contrast

PSNR depends only on the mean square error (MSE):

𝝁𝒇 , 𝝁𝒈 Mean intensity for images f , g

𝑪𝟏 , 𝑪𝟐 Constants

𝝈𝒇 , 𝝈𝒈 Standard deviation for images f , g

Assume an original image and a reconstructed image, f and g respectively

The change-of-base formula

Results : The Log Base EffectResults : The Log Base Effect


Yields a smaller logarithmic value

Less dynamic range

Better compression ratio

Less quality

𝑙𝑜𝑔𝑏 𝑥 =𝑙𝑜𝑔𝑘(𝑥)

𝑙𝑜𝑔𝑘(𝑏)

The higher base of a logarithm (B)

Results : The impact of LNS-Q and NLResults : The impact of LNS-Q and NL


NL = 1 → Max CR = 18 NL = 2 → Max CR = 60 NL = 3 → Max CR = 140

NL: number of linear sub-bands

Results : The Influence of the QuantizationResults : The Influence of the Quantization

29-03-201729-03-2017 3737

SSIM improvement (QUALITY)

Better than JPEG2000 by:

8% to 55% → at SC = 100

5% to 44% → at SC = 10

3% to 22% → at SC = 1

Better than WAAVES by:

7% to 44% → at SC = 100

4% to 38% → at SC = 10

2% to 10% → at SC = 1

LNS-DWT Mohammed IBRAHEEM – LIP6-UMPC-CIRA

Results : The Impact of the DRRResults : The Impact of the DRR


DRR: dynamic range reduction filter

SummarySummary


LNS-WAAVES : novel compression schemeLNS-WAAVES : novel compression scheme

Hybrid-DWTHybrid-DWT

Merging DWT coefficients in a hybrid fashion = linear + logarithmic domains

Based on Hybrid-DWT/LNS-Q1. Log base effect

• B= 2 give the best quality due to less quantization error2. NL effect

• NL = 3 gives the best compression range3. Quality Improvement:

• of 8% up to 34% compared to WAAVES

Part V2D-DWT Hardware Architecture2D-DWT Hardware Architecture


Introduction Introduction


The second research question & Motivation

• Compression SPEED on embedded systems

• Smart EEG requirements

• The need of a high-speed DWT for a video compression (100 fps)

Which DWT Algorithm suitable for hardware (Lifting /convolution) ?

• Lifting is more efficient:

• Less operations

• Less memory requirements (in-place computation)

• Less memory access

DWT Algorithm IssuesDWT Algorithm Issues

29-03-201729-03-2017 PhD Defense: Mohammed IBRAHEEM 4242

Data dependency 1D-DWT for each row, THEN 1D-DWT for each column

Memory access Horizontal transform

• Read the input image• Write the output coefficients

Vertical transform• Read the horizontal coefficients • Write the output vertical coefficients

Input imageInput image

Lo

wL

ow

Hig

hH

igh

LowLow HighHighLowLow HighHigh

Lifting scheme AnalysisLifting scheme Analysis

29-03-201729-03-2017 PhD Defense: Mohammed IBRAHEEM 4343

Split input data vectorEven/Odd

Stage: Predict 1P1 = current even pix + α(pix previous + pix next)

Stage: Update 1U1 = current odd pixel + β (U1 previous + U1 next)

Stage: Predict 2P2 = current P1 + γ (U1 previous + U1 next)

Stage : Update 2U2 = current U1 + δ (P2 previous + P2 next)

Stage: Scaling P2Stage: Scaling U2

The Lifting DWT algorithmIssues

• Each stage depends on the previous one

o Parallelism complexity

• For the 2D transform

o The need to wait the row to processed before

starting processing the columns.

Solution To achieve high parallelism

Efficient memory organization

Partial DWT computation of the image

o Process few rows then,

o Start process the columns

The even/odd data in the columns

can be processed independently

4-Port Memory and External memory interface 4-Port Memory and External memory interface


phase-locked loop

Horizontal / Vertical 1D DWTHorizontal / Vertical 1D DWT


Simple computation units Short critical path (adder +multiplier) 8 pixels in parallel (4 odd + 4 even) Parallel horizontal/ vertical transform

Proposed Unified 2D DWT ArchitectureProposed Unified 2D DWT Architecture


FeaturesFeatures

Line BuffersLine Buffers

[Even/Odd] pixels split on-the-fly

Novel LB scheme two features

• 4-port memories → parallel operation

Data concatenation

• 4 pixels/location

• 4 odd pixels parallel

• 4 even pixels parallel

High throughput

Parallel Horizontal/Vertical transform

Novel custom memories

Scalability

Results : Resources on DE4 FPGA boardResults : Resources on DE4 FPGA board


Altera Stratix IV GX230 resources utilization for 1080p

Results : Architecture ScalabilityResults : Architecture Scalability


a) FPGA prototyping results including DMAs latency

b) F_Exp: Experimental frequency in MHz

c) Maximum core logic frequency in MHz

Results : Comparison with Existing WorksResults : Comparison with Existing Works


Aziz et al.

2012

FPGA

Sameeen et al.

2012

FPGA

Hu et al.

2013

ASIC

Hsia et al.

2013

ASIC

Darji et al.

2014

ASIC

Darji et al.

2014

FPGAThis work

Cycles/pixel 1 1.55 0.5 0.75 0.5 0.5 0.125

Frame/s 53 24 n/a n/a n/a n/a 120

DWT filter 5/3 9/7 & 5/3 9/7 9/7 & 5/3 9/7 9/7 & 5/3 9/7

Sys. Freq 221.44 133.3 50 100 100 100 125

DRR Freq n/a 266 n/a n/a n/a n/a 250

Bit/pixel 8-bit 32-bit 8-bit 16-bit n/a n/a 32-bit

Add/Mul 2/0 n/a 116/188 16/0 16/10 16/10 68/54

Critical Path 2 adders n/a Mul + add 2 Mul+ 4 Add mul Mul + add Mul + add

Scalability No No Yes No No No Yes

Frame size 512×512 1920×1080 512×512 256×256 256×256 1920×1080 1920×1080

SummarySummary


A unified 2D DWT computation architecture

• Horizontal/Vertical transform simultaneously

4-Port Line buffers

• Eliminate the inefficient reading or writing columns of an image from/to DDR

RAM

• Parallel read/write from the external RAM

• Parallel transform

• Memory size optimization by having less temporary buffers (in-place calculation)

Throughput :

• 120 fps 1080p

Scalable architecture

• Support high resolution images up to 4K

Part VIConclusion and Future workConclusion and Future work


An LNS library as ToolAn LNS library as Tool

The virtual zero → efficient encoding

The sign flag → solved the sign ambiguity problem

Novel quantization method LNS-Q

• Scaling operation

• Limited quantization error

Library validation → small Error compared to the FLP ≈ 𝟕 × 𝟏𝟎−𝟕

Hybrid-DWT: Sub-bands → Two parts: logarithmic + linear

Advantages

Enhanced the image quality

better compression ratio

LNS-WAAVESLNS-WAAVES

ConclusionConclusion


LNS-WAAVES has Improvement in the quality:

8% up to 34% better than WAAVES

10% up to 49% better than JPEG2000

ConclusionConclusion


A high throughput of 8 pixels/clock cycle

Processing speed up to 120 fps Full-HD

Novel DWT ArchitectureNovel DWT Architecture

Key FeaturesKey Features

A unified 2D DWT computation

parallel Horizontal/Vertical transform

4-port line buffers → parallel process :

DMA reading/writing

Horizontal/vertical

A 2x reduction in the required DDR RAM bandwidth

Scalable architecture

Future workFuture work


Image compression based logarithmic arithmetic is a promising research area

Exploring the WAAVES HENUC encoder• How to switch the encoding algorithm into the logarithmic domain

• Scan/sort

• To be adapted with the logarithmic DWT coefficients

Building a logarithmic computation unit and integrating it with proposed architecture

• support the hybrid-dwt

Lossless compression mode by including the DWT LeGall 5/3

Logarithmic compression Logarithmic compression

Embedded SystemsEmbedded Systems

List of Publications : 2 International Journals List of Publications : 2 International Journals


L. Lambert, J. Despatin, I. Dhif, I. Mhedhbi, M. Shaaban Ibraheem, A. Syed-Zahid, B. Granado, K. Hachicha, A.

Pinna, P. Garda, F. Kaddouh, M. Terosiet, A. Histace, O. Romain, C. Bellet, F. Durand, J.P. Commes, S. Hochberg, D.

Heudes, P. Lozeron,and N. Kubis. “Telemedecine, electroencephalography and current issues. smart-eeg: An

innovative solution.” European Research in Telemedicine, 4(3):81 – 86, 2015.

Mohammed Shaaban Ibraheem, Khalil Hachicha, Syed Zahid Ahmed, Laurent Lambert, and Patrick Garda. “A

scalable high throughput 2d dwt architecture for a medical application”. Journal of Real-Time Image Processing,

submitted: Jan 2017. (under peer-review )

List of Publications : 4 International ConferencesList of Publications : 4 International Conferences


Mohammed Shaaban Ibraheem, Syed Zahid Ahmed, Khalil Hachicha, Sylvain Hochberg, and Patrick Garda:

“A low ddr bandwidth 100fps 1080p video 2d discrete wavelet transform implementation on fpga”. In

Proceedings of the 2016 ACM/SIGDA International Symposium on Field-Programmable Gate Arrays, FPGA

’16, pages 274–274, New York, NY, USA, 2016. ACM.

M. S. Ibraheem, S. Z. Ahmed, K. Hachicha, S. Hochberg, and P. Garda. “Medical images compression with

clinical diagnostic quality using logarithmic dwt.” In 2016 IEEE-EMBS International Conference on

Biomedical and Health Informatics (BHI), pages 402–405, Feb 2016.

Mohammed IBRAHEEM, Khalil Hachicha, Syed Ahmed, Sylvain Hochberg, and Patrick Garda.

“Logarithmic discrete wavelet transform for medical image compression with diagnostic quality.” In

Proceedings of the 5th EAI International Conference on Wireless Mobile Communication and Healthcare,

MOBIHEALTH’15, pages 272–275, ICST, Brussels, Belgium, Belgium, 2015. ICST (Institute for Computer

Sciences, Social- Informatics and Telecommunications Engineering).

Dhif, M. S. Ibraheem, L. Lambert, K. Hachicha, A. Pinna, S. Hochberg, I. Mhedhbi, and P. Garda. “A novel

approach using waaves coder for the eeg signal compression”. In 2016 IEEE-EMBS International Conference

on Biomedical and Health Informatics (BHI), pages 453–456, Feb 2016.

List of Publications : 5 National WorkshopsList of Publications : 5 National Workshops


M. Shaaban Ibraheem, Khalil Hachicha, Imen Mhedbi, Sylvain Hochberg, Patrick Garda, S. Zahid Ahmed. “Logarithmic-

based dwt for medical images compression”. In Colloque de la Fédération d’Électronique, Thème : Internet des objets pour

les applications biomédicales, Issy-les-Moulineaux, France, 2016.

M. Shaaban Ibraheem, Sylvain Hochberg, Patrick Garda, Syed Zahid Ahmed. “Study of applying logarithmic dwt for

medical images compression”. In 11ème Colloque du GDR SoC-SiP, Nantes, France, 2016.

L. Lambert, S. Z. Ahmed B. Granado K. Hachicha A. Pinna, M. S. Ibraheem I. Dhif and P.Garda. “Smart-eeg, a new

platform for tele-expertise of electroencephalogram.” In 11ème Colloque du GDR SoC-SiP, Nantes, France, 2016.

Dhif, I. Mhedhbi, M. Shaaban Ibraheem, A. Syed-Zahid, B.Granado, K. Hachicha, A. Pinna, P. Garda, F. Kaddouh, M.

Terosiet, A. Histace, O.Romain, C. Bellet, F. Durand, J.P. Commes, S. Hochberg, D. Heudes, P. Lozeron, N.Kubis, L.

Lambert, J. Despatin. “Telemedecine, electroencephalography and current issues smart-eeg: An innovative solution.” In

8ème édition du Congrès SFT ANTEL, Centre Universitaire des Saints Pères, Paris, 2015.

L. Lambert, M. Shaaban Ibraheem, S. Zahid Ahmed, B. Granado, K. Hachicha, A. Pinna, P. Garda,, I. Dhif, “Smart-eeg :

A new platform for tele-expertise of electroencephalogram” In GDR SOC SIP, Paris, 2014.


Thank You !

Technology

Logarithmic Discrete Wavelet Transform for High-Quality Medical Image Compression